JP2017211887A - Finite element analysis method, finite element analysis device, analysis service system, and record medium storing finite element analysis program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a finite element analysis method, a finite element analysis device, and an analysis service system, which are easy to use both beginners and experienced even if a material of an analysis object is a composite material, and to provide a record medium storing finite element analysis program.SOLUTION: A composite of finite elements includes: parent finite elements in which finite element divides an analysis area into a mesh; and a single element or plural child finite elements each of which has arbitrary plural nodes of parent finite elements as angular nodes. A computer has a function to calculate the ratio of physical property values and/or a prediction error between the child elements and the parent elements in a data input step, and if unacceptable errors are predictable, a warning is output, and the analysis is suspended as desired. Based on the input data, the computer calculates physical values of the parent element and child elements composing the complex element and dimension of the child elements using a pattern specification method based on local element number of compound element, and/or an element specification method to search based on connectivity.SELECTED DRAWING: Figure 1

Description

The present invention records an analysis method, an analysis apparatus, an analysis service system, and a finite element method analysis program for performing analysis by a finite element method, which is easy for beginners and veterans to use even if the material to be analyzed is a composite material. The provision of media.

<Energy saving and environmental load reduction>
As measures to prevent global warming, reduction of energy consumption and reduction of global warming gas emissions are being promoted by reducing the weight of transportation equipment, etc., and double-phase metal materials and frp (fiber reinforced plastic, fiber) The use of reinforced composite materials is promising.

In particular, frp has the feature that the volume content of the high-strength material of the second phase, its arrangement (orientation), form, and size can be artificially controlled by devising the manufacturing process, so it is tailored to the use of the final product. By optimizing the manufacturing process at the same time as material development, it is no longer a dream to develop a new material with superior functions and properties compared to the case where conventional metals, ceramics, and resins are used alone.

<Fiber reinforced composite material>
For example, in the case of frp, a short fiber reinforced composite material in which fine fibers of glass or carbon fiber are cut to a length of several mm or less as a second-phase high-strength material and kneaded and blended with a base material such as a resin is an injection molding process. Has been used for relatively early time. Since this material has a relatively random orientation of the fibers of the molded body, characteristics close to isotropic properties can be obtained. Therefore, the technology in the case of a resin alone can be easily used in designing and manufacturing, and has been used easily.

On the other hand, in recent years, long fiber reinforced composite materials in which high-strength and fine continuous fibers such as carbon fibers are bundled and laminated as yarns, woven fabrics, and knitted fabrics, and impregnated and solidified with resin or the like have been put into practical use. Although this material shows high strength in tensile and compression in the longitudinal direction of the fiber, it is difficult to optimize the design because the strength is extremely lowered when the load direction deviates from the longitudinal direction. That is, it is an anisotropic material related to strength, and it is important to orient the fibers by predicting the direction of high load in the product usage environment.

Conventionally, a simulation test close to the actual machine has been carried out, from among many conditional factors such as the combination of fiber and resin dimensions and shape, fiber manufacturing process, intermediate material form and product assembly process, etc. Optimization has been carried out mainly through experiments. It takes a lot of time, labor, and cost to maximize the high value added by the functions and characteristics of the product, so it is efficient to omit the experimental conditions as much as possible and quickly obtain near-optimal conditions. Development methods are important.

Non-Patent Document 1 is a document related to frp, and describes prediction formulas for stress and strain in an in-plane tensile / compression test of an anisotropic frp sheet to which material mechanics is applied. According to this, not only can the mechanical characteristics of the prepreg as an intermediate material be intuitively grasped but also quantitatively predicted, it is convenient as a mechanical test method.

However, actual composite materials have various manufacturing methods and many parameters, so individual correspondence is difficult in the above formula, and it is not practical. Therefore, numerical analysis using a computer has been actively tried in recent years.

<Aircraft structural materials>
In general, prepregs are laminated and bonded by alternately changing the fiber direction of multiple sheets to ensure the strength of the product, so when an impact load that strikes the product surface vertically is applied, the resin layer near the bonding surface It had the property of being easily broken and separated to cause defects. This is because the laminated structure is a structure in which there is no high-strength yarn that reinforces the tensile stress in the thickness direction acting near the joint surface of the prepreg, and this part selectively acts as the weakest link. . It is a so-called Benkei shin, and for this reason, application to primary structural materials such as aircraft that are easily linked to loss of human life has not been realized until relatively recently.

Non-Patent Document 2 is a document on cfrp (carbon fiber reinforced plastic), and the history and technical overview of cfrp development and the main breakthrough points are briefly described in text and illustrations. .

Patent Document 1 and Patent Document 2 relate to a product patent for a resin material that prevents the resin layer breakage in the vicinity of the related adhesive surface and a method patent for a manufacturing process thereof.

Usually, a prepreg made of a combination of high-strength carbon fiber and epoxy resin obtained by graphitizing high-stretched pan-based fibers at a high temperature (maximum temperature of 3000 degrees) is applied to a structural material that requires high strength, but is cured. Epoxy resins are hard and brittle at room temperature because the glass transition temperature Tg is as high as about 200 degrees. Therefore, a special epoxy resin having both strength and toughness has been developed by finely dispersing elastomer particles having a diameter of sub-μm, whose glass transition temperature Tg is considerably lower than room temperature, in the epoxy resin.

In addition, when polymerizing a low molecular weight epoxy resin with a benzene ring as a polymer by heating, a glass transition point can be obtained by appropriately blending appropriate functional groups, hydrogen groups, and halogen groups in the bond. In addition to reducing the temperature Tg, flame retardancy is imparted.

Furthermore, a resin film having both strength and toughness is formed by locally gathering powder resin particles having a low glass transition temperature Tg near the fiber-resin interface. As a result, the strength and toughness of the fiber in the width direction and the thickness direction are improved, so that the fracture strength of the resin in the vicinity of the adhesive interface is improved, and it is adapted to the primary structural material of aircraft.

Patent Document 3 is a method patent relating to an improvement of an rtm (resin transfer molding) molding method used when molding a frp structure, and in particular, a fiber volume content (hereinafter referred to as f and fr) of the frp molded body to be molded. It is related with the rtm shaping | molding method which can improve the improvement and can obtain the molded object which was excellent in intensity | strength and lightweight property.

The feature of this method is that a high-strength fiber precursor is molded in advance in a mold, and a resin is injected into the precursor and integrated by impregnation and solidification to form a frp structure. Therefore, compared with the method of laminating prepregs, there is a feature that the degree of freedom of the shape of the product is high and the productivity is excellent by automation, and reduction of the total cost is expected.

<Vibration, heat transfer, electricity, magnetism, humidity resistance, temperature resistance>
In general, resin has considerably different environmental resistances of vibration, heat, electricity, magnetism, temperature and humidity compared to metal materials. Therefore, when changing from metal materials to cfrp, these characteristics are added to product values as high product value. The design to make use of is important. For example, in the case of an aircraft structural member, comfort is improved by reducing unpleasant vibration and noise due to the vibration damping effect of cfrp. Further, humidification, which has been limited for metals that are weak in humidity, can be applied due to the moisture resistance of cfrp, and further, the compression of the ear tympanic membrane is reduced by improving the pressurization in the machine by improving the strength of cfrp, further improving comfort.

On the other hand, an aluminum alloy is a good conductor of heat and electricity, so even if it is locally heated, the heat does not stay in one place and it is easy to maintain an appropriate temperature. In addition, lightning is shielded, so there is less danger in the event of a lightning strike. Therefore, when changing the material to cfrp, it is necessary to improve the characteristic that the resin is a defective conductor of heat and electricity. The component of carbon fiber of cfrp is a high-quality conductor because it is graphite, and by adopting cfrp, a portion of 50% or more by volume is replaced with a network structure of high-quality conductors, so conductive fine powder can be added to the resin. Improved to the level necessary for practical use.

<Material cost>
According to Non-Patent Document 2, cfrp for aircraft needs ultra high temperature heat treatment of 2000 degrees to 3000 degrees for unidirectionally oriented graphitization. Therefore, the fiber is expensive and the electric energy consumption per unit volume is as high as a battery. Therefore, for the purpose of energy saving and environmental load reduction, it will be difficult to achieve the purpose unless the initial production energy debt can be recovered early. In the case of aircraft, it is reasonable that the amount of fuel consumed is extremely large and the collection period is short.

<Automobile>
Since automobiles consume relatively less fuel than aircraft, the recovery period is longer. Therefore, the purpose of LCA is difficult to achieve unless it is used for a long period of time such as recycling. If the initial cost is not reduced by lowering the grade of the material, etc., there is a risk that application to a popular car will be limited.

However, since automobiles are overwhelmingly produced in comparison with aircraft, a slight improvement may lead to a great improvement. For this reason, automakers and cfrp material makers have jointly started developing eco-cars.

The current situation seems to be a trial-and-error stage for a luxury car of a major automaker in the world, but it may take a lot of time to accumulate a lot of experimental data and to use it for a popular car. In particular, automobiles have strict safety regulations, and are highly dependent on national and regional laws and cultures, such as recycling and cost reduction. In addition to strength, vibration, heat transfer, electricity, magnetism, There are many design goals for safety and comfort, such as humidity resistance and temperature resistance.

<Other applications>
Non-Patent Document 2 describes a typical application example of cfrp as a high-load-value product that has established a market by causing booms such as sports equipment in early development, especially fishing rods, tennis rackets, golf clubs, and recent bicycle body frames. I give you. In addition, niche markets were indispensable for large telescopes, rockets and satellites, and future promising markets were predicted for eco-car materials such as hydrogen tanks and fuel cells.

In the future, industrial applications are expected to expand rapidly and the market will continue to expand. Accordingly, frp, which can cope with a balance of various required product characteristics by selecting materials, selecting a molding method, and optimizing process conditions, diversifies the manufacturing process according to the type of product to be applied. Development of industrial applications means that demand for optimal design is increasing between material manufacturers and parts and product assembly manufacturers, and the market expands due to the availability of systems that can be used by ordinary engineers at low cost in a short period of time. Is one of the key tech. If it takes half a century from conception to practical use like an aircraft, commoditization of popular automobiles is hopeless, and market expansion will decline.

<Necessity of an experimental alternative method for optimal design>
As mentioned above, artificial materials such as composite materials are attracting attention as eco-materials, but for practical use, individual application development is necessary to realize the added value required for specific applied products. become. However, in the past, even in the field of promising products with high application effects, steady research and development over a long period of nearly half a century was necessary, and many companies failed to develop. In future product development, various physical characteristics such as vibration, heat transfer, electricity, magnetism, humidity resistance, and temperature resistance were comprehensively considered in order to efficiently optimize many factors. Optimal design and the development of efficient methods are important.

Especially in the case of composite materials with remarkable physical property anisotropy, materials developers and machine designers collaborate with engineers in various fields in the manufacturing process to mold the fibers and resin of the materials into product shapes. Opportunities for technological development increase, and it is highly possible that boundary technologies in different fields will lead to breakthroughs. Therefore, it is important that the optimization method can be easily used even by beginners.

<Material mechanics>
In Non-Patent Document 12, when the volume fraction of the reinforcing material (high-strength material) of the composite material is specified, the execution parameter of the physical property as the composite material is determined from the physical properties of the base material matrix and the reinforcing material using the composite law. A method for predicting upper and lower limits has been disclosed. In general, since composite materials are optimized and arranged in the direction in which the largest load acts, the upper limit value of the effective parameter is important. This corresponds to loading in the fiber direction with respect to the sheet on which the prepreg is laminated, and it is understood that this is an important parameter in the design.
However, in an actual design, it is necessary to cope with a load in an arbitrary direction. Therefore, the following computer simulation is performed.

<Alternative to experiment by simulation>
Patent Document 4 is a technique related to a finite element method (hereinafter sometimes abbreviated as FEM), which is a typical general-purpose simulation technique. According to this, the FEM is positioned as follows.

One of the typical discretization methods for numerically solving the initial value and boundary value problems of a partial differential equation expressing a physical phenomenon is FEM. In FEM, a problem is solved by solving a linear equation by generating a mesh in an object or space of an analysis model, dividing it into finite elements, and assuming a simple variable distribution such as a linear expression as the variable distribution in the finite element. To return to. An approximate solution of this linear equation can be obtained by matrix calculation, and a complicated variable distribution of the analytical model can be numerically simulated.

A simulation system using FEM includes an input unit for inputting data such as the shape, mesh, material characteristics, boundary conditions, etc. of an analysis model, an analysis unit for performing analysis by FEM based on data input to the input unit, and an analysis An output unit that visualizes and outputs the analysis result of the unit in a format according to the purpose. Most of the calculation cost in the simulation system is spent on the matrix calculation for solving the linear equation, and the calculation cost of the matrix calculation increases exponentially as the scale of the analysis model increases. For this reason, various techniques for speeding up the matrix calculation have been developed. For example, a technique for improving the convergence of an asymmetric matrix solution method using an iterative method that sequentially calculates vectors approaching the solution and a sparse matrix solution method using an iterative method has been developed.

Patent Document 5 is directed to an FEM for efficiently analyzing large strain and nonlinear deformation behavior in a plastic working process as an interface for finite element analysis. In this case, unlike the patent document 4, since the direct solution of the symmetric matrix is applied, the matrix variables to be stored are significantly increased compared to the iterative method. Therefore, there is a problem that the technique disclosed in Patent Document 4 cannot be used. Therefore, in order to reduce the number of variables, the numbering of nodes is devised when generating meshes with finite elements, and a special interface has been developed because normal preprocessing cannot be applied.

<FEM for fracture prediction of frp>
Patent Document 6 is by a sports manufacturer and a plurality of universities, and discloses various material strength tests of a plate material in which about 8 layers of a base resin prepreg having carbon fiber as a strength material are laminated, and simulation technology by the finite element method. It was. Finite structure that can be processed in a practical analysis time considering the dimensional shape and position of the peeling defect while considering the physical properties, dimensional shape and fiber orientation of each material, and the monolithic structure consisting of fiber, resin and adhesive The element mesh modeling was devised, and a method of evaluating with an error of several percent was disclosed.

That is, the purpose of Patent Document 6 is to provide a quasi-three-dimensional model that can accurately simulate the three-dimensional deformation behavior in a relatively short time under a limited CPU performance. It is intended to provide a method for using and analyzing composite laminates.

In other words, the fiber and resin present in the composite laminate are independently grasped, the fiber part is a shell element that takes into account the strength anisotropy due to the fiber orientation angle, and the resin part is modeled by a beam element. A quasi-three-dimensional model is created by combining the elements to constrain the shell elements. Using this quasi-three-dimensional model, tensile analysis, bending analysis, natural vibration analysis, tensile damage analysis or residual strength analysis of composite laminates are performed.

Patent Document 7 is from a material manufacturer such as a prepreg, and the analysis model of the composite material laminate using the quasi-three-dimensional model is improved to improve the prediction accuracy of the analysis. Therefore, the analysis techniques disclosed in Patent Document 6 and Patent Document 7 are put into practical use as a standard FEM analysis method for those skilled in the art of manufacturing frp products. However, since the vicinity of the laminated interface of the prepreg, which is likely to break, is modeled by a beam element, microscopic information on the break starting point important for material development cannot be obtained.

As disclosed in Patent Documents 1 and 2, in order to overcome the weaknesses of the laminated prepreg, it is important to develop a rational resin alloy technology based on microscopic fracture mechanics. To that end, it is important to develop an analytical method that predicts the concentration of stress and strain microscopically.

<FEM for identifying physical properties of frp>
Patent Document 8 is from an electric communication company, and an unknown material constant estimation system useful for improving analysis accuracy such as structural analysis of a tire as a filler composite material by a multi-scale model disclosed by a tire manufacturer of Patent Document 9 is disclosed. It was done. Composite materials such as radial tires have various rubber and hard fillers depending on the observation position under microscopic observation, but function with the average hardness of rubber and filler when observing the tire visually. Multi-scale model is a coupled or uncoupled simulation of macroscopic analysis of finite element meshes of macroscopic products with average material properties and microscopic analysis of finite element meshes of typical unit structures made of rubber and filler. To do. Patent Document 8 is necessary for microscopic analysis, but generally predicts unknown material constants efficiently.

That is, a load condition providing unit that provides a load condition of a material test performed on a composite material including the first material and the second material, and a test of the composite material is controlled based on the load condition, and the test result is obtained. Provides a test control unit for outputting, a first temporary material constant temporarily set as a first material constant representing an unknown physical property of the first material, and a second material constant representing a known physical property of the second material A material constant providing unit that performs stress analysis on a model of the composite material based on the load condition, the first temporary material constant, and the second material constant, and outputs an analysis result, and a test result And an error determination unit that determines whether or not an error between the analysis result and the analysis result is within a preset allowable range. The error determination unit determines the first temporary material constant as the first material constant when the error is within an allowable range.

<FEM based on relationship between macroscopic characteristics and microscopic characteristics of frp>
Non-Patent Document 3 and FIG. 15 show a unit structure of microscopic analysis (including two fibers) by multi-scale analysis using commercially available FEM software in which a large deformation mechanism of a prepreg laminate made of carbon fiber and thermoplastic resin was investigated. ) Three-dimensional finite element mesh, 8 node hexahedral elements (25 × 25 × 20 = 12,500 elements), and the solver was a dynamic explicit method. Multi-scale analysis is a method that creates a relationship between the macroscopic behavior and microscopic behavior of a material as an analytical model based on the respective dimensions. Is a general term.

In the case of frp, the macroscopic characteristics show remarkable anisotropy, but the microscopic characteristics of the diameter of the high-strength material yarn can be modeled by a combination of isotropic resin and yarn, so it is rudimentary isotropic. Can be processed by FEM analysis. In particular, in Non-Patent Document 3, the homogenization method was applied focusing on the fact that the grid structure of frp yarns can be approximated by a rectangular parallelepiped periodic structure, so that the coupled analysis of both models could be performed with commercially available software.

In general, multi-scale analysis requires a large amount of calculation, which increases the calculation time and cost, and the practical use of the latest high-performance computers and the application of the homogenization method stand out and attract attention. I came. In the above-mentioned aircraft applications, there is a strong potential need to predict the behavior of separation defects on fibers with a diameter of about several μm or the same joint interface. The technology is useful.

<Composite FEM analysis by polymerization mesh method>
Non-Patent Document 4 relates to an FEM analysis using a global mesh and a local mesh in the case where a dissimilar material having different defects or characteristics exists in a part of the material. Since a notch can be modeled with a local mesh as a notch when a hole is made in a prepreg and a strength test is performed as a notch material, the pre-processing is simple. However, it is necessary to create a solver.

<FEM analysis of composite mesh and its composite>
Patent Document 10 and FIG. 13 relate to provision of a method for creating a finite element model that can perform a finite element method analysis in consideration of a twisting torque generated by twisting a cord. That is, in FIG. 13, the cord A includes a solid element 1 that forms the substance of the cord A, an axial truss element 2 a that adjusts the longitudinal extension of the cord A with respect to the tension acting on the cord A, and A spiral truss element 2 inclined in the circumferential direction of the cord A with respect to the longitudinal direction, and in the circumferential direction of the cord A at a node 3 on the outer surface of the cord A against a tension acting on the cord A The model is divided into the spiral truss element 2b that generates the component force.

The composite is a belt made of an elastomer that forms a cord and a shape for transmitting a load. The entire belt is mesh-divided with pentahedral solid elements as an elastomer, and the code is mesh-divided with three-dimensional truss elements. Since the FEM analysis is performed by superimposing both meshes as an integral mesh, the pre-processing is simplified as in the superposition mesh method.

However, in the disclosed drawings, since the beam elements are joined to the nodes of different pentahedral solid elements, the solver process is complicated because the beam elements protrude from the structure of the non-zero array variable of the stiffness matrix of the elastomer. Moreover, since the two mesh divisions of the elastomer and the cord are performed, there is a problem that the work of pre-processing increases.

Patent Document 11 and FIG. 14 show an anisotropic strength characteristic of a reinforcing cord as shown in (B) for a tire model having a cylindrical reinforcing cord at the center of a plurality of rubber plate members as shown in (A). It replaced with the membrane element which has, and was put between the solid elements of the rubber plate without a code | cord | chord, and it was set as the approximation model. The membrane element is an element that transmits only in-plane force, that is, only tension, compression, and shear in the direction along the plane. In this example, a quadrilateral membrane element is illustrated.

In the composite meshes of Patent Document 10 and Patent Document 11, since the base material and the mesh of the reinforcing material are separately generated and managed, management is required to ensure consistency between the two. In response to automation, costs and time are required for management of pre-processing, particularly programs.

International Publication Number WO2009-119467 International Publication Number WO2012-102201 Japanese Patent No. 4104413 Japanese Patent No. 497957 JP 2006-164219 A JP-A-6-305105 JP 2008-108242 A International Publication Number WO2011-108468 Japanese Patent No. 4093994 JP 2007-34728 A JP 2003-094916 A JP2015-032295A

Miyao Hiroo, Goto Graduates: Introduction to Reinforced Plastics (2007), Nikkan Kogyo Shimbun. Toru Hiramatsu: Carbon fiber book (2012), Nikkan Kogyo Shimbun. Ryuta Kamiya, Tetsuro Otsuka: Proceedings of the 66th Joint Conference on Plasticity Processing (2015), 57. Katsuyuki Suzuki and three others: Journal of Applied Mechanics Vol.7 (2004), pp.383-389. Tadashi Horibe: Easy Fundamentals of Finite Element Method (2008), Morikita Publishing. Daichi Tateno, Takeshi Yoneyama and 4 others: Proceedings of the 66th Joint Conference on Plasticity Processing (2015), 53. Hiroshi Ashiya, Tetsuro Oie, Jun Yanagimoto: Proceedings of the 66th Joint Conference on Plasticity Processing (2015), 55. Hiroya Ashiya, Jun Yanagimoto: 2014 Spring Meeting of Plastic Processing (2014), 207-208. Ferreira. A. J. M: Matlab codes for finite element analysis. Portugal, Springer publication.

The problem to be solved is that the divisional and project development systems are generalized due to the high level of expertise required in each field when developing characteristics such as cfrp products and adding high value. In particular, it is difficult for beginners to understand the most basic common product strength prediction technology. In other words, it has been difficult to rationally combine the strong macroscopic anisotropy of composite materials with the microscopic fracture behavior of the strength limit in the primary analysis of traditional material mechanics that has been used in the past. Alternative finite element analysis such as multi-scale analysis by computer has been proposed. However, there has been a fatal problem that multi-scale analysis cannot be easily understood or used not only by beginners but also by skilled artisans.

On the other hand, compared to the early days when products for development were niche high-priced products such as some sporting goods, these products are now being extended to low-priced popular products called commodities. It is important to establish a comprehensive optimization system from the viewpoint of product life cycle assessment (PLA) such as materials, design, manufacturing, utilization and recycling. In particular, in today's global competitive era, price competitiveness is emphasized, and the market will not expand unless products with the targeted specifications can be developed and supplied in a short time at a low cost and in a stable manner. Therefore, it is important to evaluate and judge whether or not it is possible to design at the product planning stage. For that purpose, it is reasonable to use theory and computer simulation without relying only on experiments, especially so-called multi-science such as material strength, heat, fluid, electricity / magnetism, vibration, physics, chemistry, etc. Establishing a comprehensive optimization system based on this is an important issue. However, the multi-science analysis has a fatal problem that it cannot be easily understood by not only the beginners but also the skilled person.

In recent years, the use of commercial FEM analysis software made in foreign countries has become common, and it has been recognized as a useful tool by R & D institutions in industry, academia and government. And since the response | compatibility to said multiscale analysis and multiscience analysis is also performed, the application example to a composite material has increased. However, in general, there is no finite element registered that can independently handle a base material and a high-strength material of different materials. Therefore, as disclosed in Patent Document 10, Patent Document 11, and Patent Document 12, the material of the base material is not registered. The element to which the element is provided and the element to which the material of the high-strength material is provided are separately generated, and a mesh that combines both in the middle of the analysis is applied.

Therefore, analysis of composite materials tends to be large-scale analysis and difficult analysis compared to analysis of a single material. For example, in multi-scale analysis, various methods are excessively prone and users use which one. After all, modeling may be outsourced to a commercial FEM analysis software vendor. Therefore, the problem in this case is to define dedicated elements for composite materials in the product software to simplify the calculation process and avoid large-scale analysis. However, such composite finite elements are not found in commercial product software.

In addition, in order to establish an analysis method using composite finite elements as an alternative to primary analysis such as material mechanics, a place such as a factory or office like a calculator is not used for analysis processing in a conventional computer room. It is important that it can be used easily without being limited by time. As a countermeasure, it is an important issue to develop a system capable of performing an analysis process using a tool such as a smartphone and a communication device.

The present invention has been made in view of such problems, and is easy to use even for beginners. A finite element method analysis method, a finite element method analysis device, an analysis service system, and a recording medium on which a finite element method analysis program is recorded. The purpose is to provide.

In order to solve the above-mentioned problems, the present invention regards a composite material as a sandwich model of a yarn or fiber bundle and a resin imitating a network structure of a high-strength material, and allows some inconsistencies such as material mechanics. On the other hand, the main feature is that automatic mesh generation of high-strength material and base material is achieved with a newly developed special composite FE element by combining both materials.

That is, the first invention is a finite element method analysis method in which a computer performs analysis by a finite element method on an analysis model,
Computer can define analysis model shape, select finite element type, mesh division condition, element property values and dimensions, boundary condition, solver condition, result output condition and analysis by user operation or input file reading A data input process for inputting analysis data relating to conditions;
A mesh generation step in which the computer divides the analysis region into finite elements based on the input data;
A computer generates a matrix of each element based on the generated mesh, and incorporates the matrix into the matrix of the entire analysis region;
A boundary condition setting step in which a computer generates a solver overall matrix by setting boundary conditions for the overall matrix according to the input data;
A solving process in which a computer derives unknowns and derived data by the solver for the solver overall matrix;
An output process in which a computer outputs an analysis result obtained by the solving process;
Have
The finite element is a composite finite element composed of a parent finite element that meshes an analysis region and a single or plural child finite elements whose corner nodes are any of a plurality of nodes of the parent finite element;
The computer has a function of obtaining a ratio of physical property values of child elements to a parent element and / or a prediction error in the data input process, outputting a warning when an unacceptable error is predicted, and interrupting the analysis if desired. And
Based on a pattern designating method and / or connectivity based on the local element number of the composite element and the physical property values of the parent element and the child element and the dimensions of the child element constituting the composite element based on the input data It is characterized in that it is implemented by an element designation method by search.

The second invention is a finite element method analysis apparatus in which a computer performs analysis by a finite element method on an analysis model,
Computer can define analysis model shape, select finite element type, mesh division condition, element property values and dimensions, boundary condition, solver condition, result output condition and analysis by user operation or input file reading Data input means for inputting analysis data on conditions;
A computer, mesh generating means for dividing the analysis region into finite elements by the input data;
A computer generates a matrix of each element based on the generated mesh, and incorporates the matrix into the matrix of the entire analysis region;
A boundary condition setting means for generating a solver overall matrix by setting a boundary condition for the overall matrix according to the input data;
A solving means for a computer to derive unknowns and derived data by the solver for the solver overall matrix;
An output means for outputting an analysis result obtained by the solution finding means;
Have
The finite element is a composite finite element composed of a parent finite element that meshes an analysis region and a single or plural child finite elements whose corner nodes are any of a plurality of nodes of the parent finite element;
The computer has a function of obtaining a ratio of physical property values of child elements to a parent element and / or a prediction error by the data input means, outputting a warning when an unacceptable error is predicted, and interrupting the analysis if desired. And
Based on a pattern designating method and / or connectivity based on the local element number of the composite element and the physical property values of the parent element and the child element and the dimensions of the child element constituting the composite element based on the input data It is characterized in that it is implemented by an element designation method by search.

The third invention is a finite element method analysis method comprising a macroscale model, a mesoscale model, and a microscale model,
A macro-analysis step of obtaining a macro-scale result by a computer modeling the meso-scale model with the composite finite element and performing an analysis of the macro-scale model using the finite element method analysis method according to claim 1;
A micromesh generation process in which a computer defines an arbitrary composite finite element as an analysis region and meshes a desired microstructure with a desired number of finite elements;
A micro boundary condition setting step of interpolating the result of the macro scale of the child element to a finite element node of the micro mesh corresponding to the child element of the composite finite element and setting as a boundary condition;
A micro-solving process in which a computer derives unknowns and derived data by a solver;
The computer comprises a micro output process for outputting an analysis result of the micro solution process.

Furthermore, the fourth invention is an analysis service system in which a computer registers, manages and distributes a data file of claim 1 to a server via the Internet.
The data input process, the mesh generation process, the whole matrix generation process, the boundary condition setting process, the solution finding process, and the output process of the finite element analysis method according to claim 1 Recording means for recording as a finite element data file on a computer-readable recording medium;
A registration processing means for the computer to input the finite element data file from the recording medium, attach it to an email with an identification name, and send and register to a server via the Internet;
A management means for a computer to search for an e-mail registered in the server via the Internet and manage the finite element data file attached to the registered e-mail;
The registration in which a computer reads a delivery plan file in which a destination mail address and / or the finite element data file and / or an identification name of the registered e-mail is recorded, and the finite element data file is attached by the management means And a transmission means for transmitting the e-mail to the corresponding e-mail address of the delivery plan file,
4. The finite element analysis device based on the finite element analysis method according to claim 1 and / or the finite element analysis file attached to the e-mail sent by the destination user, or the finite element analysis device according to claim 2. An analysis means that inputs to the finite element method analysis apparatus and performs analysis by the finite element analysis apparatus,
It is characterized by the following.

The fifth invention is characterized in that the composite finite element is generated and analyzed by diverting a finite element of general-purpose analysis software to the parent finite element and / or the child element.

Furthermore, a sixth invention is a computer-readable recording medium on which the finite element method analysis program according to claim 1 is recorded.

In the finite element analysis of the composite material that is the subject of the present invention, attention is paid to the fact that the specific strength characteristics are excellent, and therefore mechanical analysis relating to strength is mainly employed. Therefore, in the following description, the description will be made on the mechanical analysis. However, in recent years, since it is possible to perform a general engineering system analysis by the Galerkin method, these are naturally objects of the present invention. Specifically, there are many such as heat transfer, vibration, electrical conduction.

First, the first invention will be described with reference to the explanatory diagram relating to the process of finite element analysis in FIG.

Step (1) is a data input step. In this step, the mesh of the finite element shown in FIGS. 8a and 8b is generated. In general, since the strength of the base material matrix is small in frp, it is rational to use a beam element (beam element) in consideration of bending rigidity as a reinforcing material in order to stabilize the calculation. In addition, by adopting a grid-like mesh division as shown in FIGS. 8a and 8b, if a typical composite element configuration is defined by one element, this configuration exists in each grid-like grid. It is advantageous to copy to individual finite elements to facilitate automatic meshing.

Also, commercially available FEM software requires analysis model shape definition, finite element type selection, mesh partitioning conditions, element physical properties and dimensions, boundary conditions, solver conditions, output conditions for results, Analysis data related to analysis conditions can be entered.

These data can be entered in a text format in a predetermined format to form an input file. If the analysis model is complicated, the model shape can be drawn by using commercially available CAD software to obtain CAD data, which can be finally added to the input file as finite element data by conversion software or the like. At this time, the boundary condition data may be designated by CAD software, but this can be finally added to the input file.

In the composite material, it is necessary to input at least a plurality of physical property values of the base material resin and the high-strength material yarn, and this can also be read as an input file. At that time, the ratio of each physical property of the high-strength yarn and the base resin can be obtained and used for prediction of an error to be described later.

Step (2) branches to step (3) when the physical property ratio or prediction error is predicted as an unacceptable error.

In step (3), a warning is output to sound, light, vibration, a monitor connected to the computer, a printer, or the like to notify the user that the input data is not appropriate. Upon receiving this warning, the user can stop the analysis halfway by manual operation and recalculate by correcting the data. Further, the analysis can be forcibly interrupted after the computer generates a warning if desired.

Step (4) is a mesh generation step. Based on the mesh data of the base material input in the input file, a two-dimensional mesh is generated based on the two-dimensional problem, and a three-dimensional mesh is generated based on the selected finite element. Here, an overall node number and an element number are generated, and for the node, each node coordinate is obtained, and for an element, the overall node number (connectivity) of the node belonging to each element is obtained. In some cases, CAD software or the like can add the node coordinates and the entire node number of the element to the input file. In this case, the validity is verified.

Next, a high-strength material is processed, but it can be generated from only the node of the base material element from the definition of the composite element. Therefore, since the node coordinates and local node numbers of all the high-strength materials related to the element are known in advance, no special processing is required.

What is necessary is just to set the physical property value of the element of a base material and a high strength material, the thickness of a base material element, and the diameter or representative dimension of a high strength material element.

Step (5) is whole matrix generation. The computer generates a matrix of each element based on the generated mesh data, and generates an entire matrix by incorporating it into the matrix of the entire analysis region. Here, the matrix is a matrix necessary for finite element analysis, which is called a stiffness matrix in elastic analysis or the like, and is optimized in the vicinity of the diagonal term by optimizing the entire node number as disclosed in Patent Document 5. It becomes a sparse matrix with dense non-zero elements.

If the node numbers are not optimized, the node numbers can be renumbered based on the optimization algorithm. For example, an algorithm based on a tree structure search is often used.

Step (6) is a boundary condition setting step. The boundary condition is processed for the degree of freedom of the corresponding node of the right side vector related to the whole matrix and the node force when the displacement of the node is known by addition or the load acting on the node is known. The processing method includes a known variable elimination method and a penalty method, and can be selected as appropriate. If the boundary condition is not set, the entire matrix becomes singular and cannot be processed. Therefore, in order to distinguish from this, the processed whole matrix is distinguished as a solver whole matrix. A boundary condition is set for the entire matrix by the input data to generate a solver entire matrix.

Step (7) is a solution finding step. This is a process for obtaining an unknown vector from the entire solver matrix and the right-hand vector, which is also detailed in Patent Document 5. In the past, solving the simultaneous equations using direct or iterative solvers has been the mainstream, but in recent years, dynamic explicit methods have often been used that approximate the equations of motion and solve them approximately using time differences. became.

In general, unknowns correspond to the degrees of freedom of each node such as displacement and speed, so derived data such as stress and strain related to the element is derived.

Step (8) is an output step. Various analysis results derived in the solution process are output as numerical data files in a predetermined format. In addition, since it is difficult to understand intuitively with a large amount of numerical data, it can be converted into data for graphic display and output as desired. Furthermore, it can be output in a known format such as XML for reuse.

The composite finite element disclosed in the preliminary study includes a parent finite element of a base material in which the finite element meshes the analysis region, and a single or a plurality of high-strength materials having a plurality of nodes of the parent finite element as corner nodes. Consists of child finite elements of thread elements. This is due to the material mechanical idea and allows the base material and the high-strength material yarn to share the same space.

Commercially available software is mainly provided with a function that positively eliminates, as a contradiction, that elements allow the same space as a contact function. Therefore, it is clear that an analysis error due to such a contradiction is unavoidable. Therefore, the user needs to perform analysis with this in mind. Material mechanics can intuitively derive a correct answer without a computer while allowing such contradiction. Since the analysis error is verified in advance by the ancestor, the validity of the practically used one is recognized if it is within the recommended allowable range.

On the other hand, in the case of the composite element, since such error verification is generally not performed, the user must verify it individually. It can be verified directly by obtaining the correct solution of the same problem by ordinary analysis in commercial software and comparing it with the solution by the complex element.

In addition, it is possible to confirm the occurrence of an error by setting a problem that can be easily obtained by an elementary analysis such as material mechanics and analyzing the problem with the composite element. The inventor set up the problem of pulling the unidirectional prepreg with a uniform displacement in the axial direction of the high-strength material yarn, and solved this by primary analysis. The load acting on the end of the yarn was as follows: I found that it was displayed.

Since the volume content f of the continuous long fiber cfrp yarn is considerably high and exceeds 50%, the base material exceeds the volume of the yarn due to the neglect of the above-mentioned mutual interference, which may be a cause of error. A straight fiber having a longitudinal elastic modulus Es and E and a cfrp material having a uniform cross section S in a unidirectional orientation and a base material are uniformly elastically pulled in the fiber direction with a strain e. Assuming that the correct load by the primary analysis is F1 and the load by the composite element is F2, the prediction error error is predicted by the equation shown in equation (1). Note that * indicates multiplication.

Since the volume content f of the continuous long fiber cfrp yarn is considerably high and exceeds 50%, the base material exceeds the volume of the yarn due to the neglect of the above-mentioned mutual interference, which may be a cause of error. However, as disclosed in claims 1 and 2, the approximate model error can be managed by using a prediction error formula.

Using the physical property values disclosed in Non-Patent Document 1 and Non-Patent Document 2, trial calculation was attempted as follows.
Pan IM is Es = 290Gpa, epoxy resin (EP) is 3.1Gpa,
(f, e) is (0.5, 0.0106), (0.8, 0.0107), (0.907, 0.0107)
It was found that the load error was overestimated by about 1% at maximum, so it was acceptable.

It is clear that the prediction error e is a function of Es, Em and f. Further, in the case of the above cfrp where Em / Es is about 0.01, the error can be roughly predicted by obtaining Em / Es. If the error is significant, it is convenient to perform a warning or forced stop to prevent unnecessary calculation processing.

Therefore, in the data input process, the computer calculates the ratio of the physical property values of the child element and parent element and / or prediction error, and outputs a warning if an unacceptable error is predicted, and interrupts the analysis if desired. Can be used.

In addition to dynamics, in general finite element analysis, the prediction error is small when the ratio of the conduction parameter (property value) between the child element and the parent element is small. Is possible. Therefore, there are cases where this method can be used by confirming whether it can be predicted by comparing with a known problem analytically.

Laminated prepregs are made by forming a sheet by impregnating and solidifying a resin with a high-strength yarn arranged in a lattice like a furoshiki, so the smallest square (mesh) surrounded by the warp and weft is flat and finite. As elements, as many finite elements as there are furoshiki meshes are arranged. For example, if the number of warp and weft yarns is 1000, 1 million meshes, that is, 1 million composite elements are required.

On the other hand, if the furoshiki warp and weft are arranged in a grid pattern, the mesh shape is square, and any mesh cannot be distinguished. Therefore, if one of them is designed on behalf of the whole, the entire structure of the furoshiki can be determined uniquely, which is much more labor-saving than the individual structural design and has a good outlook.

Similarly, even in the case of a prepreg, the computer uses the pattern designation method based on the local element number of the composite element and the physical property value of the parent element and the child element constituting the composite element based on the input data and the dimension of the child element. Or it can implement by the element designation | designated system by the search based on connectivity.

Furthermore, even in the case of a laminated prepreg, the prepreg of each layer is divided into composite elements in the same manner as a two-dimensional mesh, and is made three-dimensional by extruding it in the thickness direction. Then, the laminated prepreg can be easily modeled by laminating the three-dimensional mesh of each layer in the thickness direction.

Next, the second invention will be described with reference to FIG.
By comparing FIG. 1 and FIG. 2, the contents of each means can be easily understood, so detailed description will be omitted.

Next, a third invention will be described with reference to FIG.
In frp, when a material is observed from a distance, it is difficult to distinguish from a metal material in a plate shape. This state is analyzed by a normal method as a macro scale model. However, when the material is observed by hand, a structure in which a high-strength fiber fabric is solidified with a resin can be confirmed, and the structural characteristics of the frp material become clear. This state is described by a mesoscale model. In the case of frp, when attention is paid to one stitch of the fabric, it is often arranged periodically in a plane. This is called a unit cell or unit cell, and this mechanical property is examined to apply this property to the whole. In particular, the finite element homogenization method can be used in commercially available programs because it can describe complex unit cells. In this case, the unit cell also serves as a microscale model.

On the other hand, analysis is performed with a macro-scale model, focusing on the element where strain and stress are concentrated, and using this element area as a new analysis area, detailed modeling is performed using the macro-scale analysis results as boundary conditions. . This is called zooming and an approximate solution is obtained relatively easily. A multi-scale finite element method analysis method for performing such macro-scale analysis and micro-scale analysis will be described.

In the macro analysis step of FIG. 3, macro scale analysis is performed by the method disclosed in claim 1 to make known the displacements of all the nodes and to examine the elements on which the strain and stress of the base material are concentrated. In cfrp, the rigidity of the base material is as small as one-hundredth of that of the high-strength material, so it deforms according to the deformation of the high-strength material. Destroy. If the base material breaks and the high-strength material is exposed, the high-strength material buckles and does not load in the case of compressive displacement, leading to ultimate destruction.

Next, in the micro mesh generation step, a new detailed finite element mesh is generated by using an element in which stress and strain are concentrated as an analysis region by a zooming technique. In this case, the macro-scale analysis did not take into account defects such as the base metal and plastic deformation, but mainly carried out the elastic analysis of the network structure of the high-strength material. This is because not only the rigidity of the base material is small but also the volume fraction (volume content) is as small as about 20 to 30%, so that defects and plastic deformation of the base material are hardly affected. On the other hand, in the microscale analysis, since the concentration of stress and strain of the base material can be observed in detail in consideration of defects and material changes, it is possible to predict the occurrence of fracture. If the fracture condition is reached even a little, there is a risk that the fiber will be stripped from the high-strength material in the worst case, so it is good to generate a mesh with defects by applying fracture mechanics.

4 shows a two-dimensional problem, and FIG. 5 shows a three-dimensional problem. The left side shows a composite finite element, and the right side shows a detailed micro-scale mesh by zooming. Artificial cracks have been introduced into the micro-scale mesh. For example, when the fracture toughness of the base material (such as the threshold value of the stress intensity factor) is reached by obtaining the stress intensity factor, Conceivable.

Also, in the micro boundary condition setting process, since the sub-element of the composite finite element in the analysis region, that is, the macro displacement of the high-strength material is known, the macro-scale result of the sub-element is interpolated to the finite element node of the micro mesh. And set it as a boundary condition. In the case of dynamic analysis, it is preferable to match the center line of the child element with the center line of the high strength material of the micromesh. It should be noted that when the high-strength material surrounds the periphery of the base material element in a frame shape, the center line of the micro-mesh high-strength material corresponds to the peripheral boundary of the analysis region.

Next, in the micro solution step, the stiffness matrix after application of the boundary condition is solved by the solver, and unknowns and derived data are derived. Since the unknowns are nodal displacements and velocities, they are converted into strains and stresses to generate derived data.

Further, in the micro output process, the analysis result of the micro solution process is output to a file or a display. This is the end of a simple problem, but when plastic deformation occurs in the base metal, the evolution of plastic strain must be traced over time by repeated calculations. In this case, as shown by the broken line in FIG. Strictly speaking, the plastic deformation of the base material affects the macro deformation, but its degree can be ignored, so that the simple zooming analysis of FIG. 3 can be used approximately, which is convenient.

Next, a fourth invention will be described with reference to FIGS.

Means (1) is a recording means for writing data processed in each step of the finite element analysis method shown in FIG. 1 mainly as text data as a finite element data file. For example, a commercially available analysis software can generate a restart file so that it can be resumed from the middle of calculation.

(2) The registration processing means inputs a finite element data file, attaches it to an electronic mail with an identification name, and transmits and registers it to a mail server via the Internet. In this way, since the finite element data is stored in the server, the data can be protected from security, power failure, and the like. Also, cloud computing is preferable because data security is increased. The identification names are unified in a method suitable for later management such as date and time, data contents, and users.

(3) The management means searches the registered e-mail on the mail server via the Internet and manages the finite element data file attached to the registered e-mail. Here, management is processing such as deleting unnecessary data and backing up important data. Indexes are also important for speeding up searches. In general, since the capacity that can be stored is limited, priority is given in this range for management.

(4) The transmission means reads the distribution plan file in which the destination mail address and / or the finite element data file and / or the identification name of the registration e-mail is recorded, and the electronic means of registration to which the finite element data file is attached by the management means. In addition to searching for mail, the electronic mail is sent to the corresponding destination mail address in the distribution plan file. In this case, the destination is the mail address registered in the Internet server.

(5) The analysis means inputs the finite element data file attached to the e-mail sent by the user of the transmission destination to the finite element analysis apparatus according to claim 5, and the finite element analysis apparatus performs the analysis. In order to set the finite element analysis apparatus, the user obtains the finite element method analysis method program file according to the first aspect of the invention by downloading or the like and installs it on a personal computer or the like.

In the composite finite element, the mechanical characteristics of frp can be expressed by a single element. The number of nodes per composite finite element is the same as that of the finite element of the base metal, so when high strength materials are approximated by truss elements, both are the same unknown, and when they are approximated by beams, the degree of freedom in bending Is added. However, comparing the entire unknown with a homogenization method that divides more than 10,000 elements into a three-dimensional mesh, it looks like garbage, so it is less burdensome to distribute by email.

Next, a fifth invention will be described. In recent years, using a general-purpose finite element analysis system that has spread worldwide. Performing various simulations has become common. This is thought to be because not only user experience and knowledge but also input data and results for analysis were accumulated in term products with many users, and the reliability was improved as a benchmark test. In other words, it may be possible to use a logic or model that can be easily used with commercially available software.

Since the composite finite element is composed of a parent element and a child element, if these parent and child elements can be generated, the composite finite element can be processed. In general, most of the finite elements of general-purpose analysis software can be selected as a library. For example, in the case of FIG. 4, a composite finite element can be generated and analyzed by diverting a parent element as a quadrangular two-dimensional element and a child element as a one-dimensional truss element or beam element. Therefore, it is possible to easily analyze composite materials by using a finite element program for education as well as for universities and companies.

Next, the sixth invention will be described. The Finite Element Analysis Pro Prolam cannot be used without a computer such as a personal computer. Therefore, it can be stored and distributed in a recording medium as an electronic file that can be read by a computer.

The finite element method analysis method of the first invention is conceived of a composite finite element that simultaneously processes the base material and the high strength material by unifying each element of the base material and the high strength material yarn into one element. Since it has been devised so that it can be used with commercially available FEM analysis software, there is an advantage that it is possible to analyze various composite materials that have been difficult to understand.

The finite element method analysis apparatus of the second invention is conceived of a composite finite element that simultaneously processes the base material and the high-strength material by unifying each element of the base material and the high-strength material yarn into one element. Since it has been devised so that it can be used with commercially available FEM analysis software, there is an advantage that it is possible to analyze various composite materials that have been difficult to understand.

The finite element method analysis method of the third invention is based on the reasonable assumption that the deformation of the base material follows the deformation of the high-strength material. Microscale analysis when boundary conditions are defined can be analyzed even when plastic deformation or fracture occurs by a simple zooming method. In the homogenization method, if a nonlinear phenomenon occurs on a microscale, the amount of calculation is greatly increased compared to an elastic analysis, which is inconvenient, so the model of the present invention is convenient.

Since the analysis service system of the fourth invention can register, manage, and distribute various data used in the finite element analysis by the composite finite element to the Internet mail server, the user needs from a smartphone or a personal computer connected to the Internet. There is an advantage that data can be received and analysis by the composite finite element method can be executed. Therefore, it can be used for educational purposes and consulting purposes, which helps to spread analysis technology.

Since the finite element method analysis method of the fifth invention can be analyzed using existing programs such as commercial software and educational software, development cost and maintenance are almost unnecessary, and it is reasonable.

The recording medium on which the finite element method analysis program of the sixth invention is recorded has the advantage that it can be used easily because the program and data can be distributed to the user using the analysis service system of the third invention.

FIG. 1 is an explanatory diagram showing a method for carrying out the finite element method analysis method. FIG. 2 is an explanatory view showing an implementation method of the finite element method analysis apparatus. FIG. 3 is an explanatory view showing a method for carrying out the finite element method analysis method. FIG. 4 is an explanatory diagram showing a method for carrying out the finite element method analysis method. FIG. 5 is an explanatory diagram showing a method for carrying out the finite element method analysis method. FIG. 6 is an explanatory diagram showing an implementation method of the analysis service system. FIG. 7 is an explanatory diagram showing an implementation method of the analysis service system. FIG. 8a is an explanatory diagram showing a method of executing a finite element mesh generated by a finite element method analysis method, wherein an arrow indicates a tension direction, a thick line indicates a child element, a square indicates a parent element, and (1) indicates a tension direction. When the axial directions of the child elements are 0 ° and 90 °, (2) is the case of ± 45 °. FIG. 8b is an explanatory view showing a method of executing a finite element mesh generated by the finite element method analysis method, wherein an arrow indicates a tension direction, a bold line indicates a child element, a square indicates a parent element, and (3) indicates a tension direction. When the axial directions of the child elements are 0 ° and 90 °, (4) is the case of ± 45 °. FIG. 9a is an explanatory diagram showing an implementation result of applying the technology of the present development to the problem disclosed in FIG. 8a. FIG. 9b is an explanatory diagram showing an implementation result of applying the technology of the present development to the problem disclosed in FIG. 8a. The scale interval on the vertical axis in FIG. 9a was changed. FIG. 10a is an explanatory diagram showing an implementation result of applying the technology of the present development to the problem disclosed in FIG. 8b. FIG. 10b is an explanatory diagram showing an implementation result of applying the technology of the present development to the problem disclosed in FIG. 8b. The scale interval on the vertical axis in FIG. 10a was changed. FIG. 11 shows a cfrp tensile test material in which three unidirectional prepregs are laminated. When the upper part is laminated with the fiber direction aligned, the lower part shows the case where only the center is laminated in the perpendicular direction. The center stage is a quadrilateral tensile test material, the arrow indicates the direction of the tensile load, and the number is the load condition number for the listed material. FIG. 12 shows a comparison between the experimental results and the dimensionless loads of the analysis results for the cfrp tensile test under the conditions of FIG. FIG. 13 is an explanatory diagram showing a known prior art implementation method. The cord A includes a solid element that forms the substance of the cord A, a shaft truss element 2a that adjusts the amount of elongation in the longitudinal direction of the cord A with respect to the tension acting on the cord A, and a cord that extends in the longitudinal direction of the cord A. A spiral truss element 2 inclined in the circumferential direction of A, the spiral generating a circumferential force of the cord A at a node 3 on the outer surface of the cord A with respect to a tension acting on the cord A The model is divided into the truss element 2b. 14A is a cross-sectional perspective view of a ply that is a composite, and FIG. 14B is an exploded perspective view of the finite element model. FIG. 15 is an explanatory view showing a known prior art implementation method. It is a micro model of multi-scale finite element analysis, and is composed of approximately 12,500 finite elements by estimation.

A composite finite element was devised to counter the problem at its most upstream source, and this was used as a finite element analysis method that can be used with commercially available FEM software from the viewpoint of industrial applicability. For the strength design of cfrp, a truss element or beam element of high-strength material yarn is generated as a child finite element in a line connecting all two nodes included in the single parent finite element of the base resin, A high-strength material is automatically arranged according to a designated shape pattern or designated area with respect to the physical property values of each element of the composite element. In addition, the child element which does not set a high-strength material yarn makes a physical property value zero, or excludes it from a process in a whole matrix production | generation process.

Hereinafter, the analysis results of FIGS. 9a and 9b will be mainly described with reference to the examples of FIGS. 8a and 8b.

<Mechanical properties of long fiber materials by individual pulling of yarn>
Both sides of the rectangular flat plate-shaped composite material in which fibers are oriented in the longitudinal direction and the width direction are fixed, and the laminated yarn ends are individually pulled in the yarn direction at the other ends. When the base material is extremely softened, the yarn is rigidly displaced in the pulling direction, and elements on both sides of the yarn are intensively sheared in the plane. This explains the rigid body displacement of the specific yarn and the mechanism of the kinking of the adjacent weft observed in the press experiment disclosed in Non-Patent Document 9. In addition, when a uniform stress and zero resultant stress are applied to the edge in a tensile test of the base material sheet alone, the stress generated at a position more than the same distance as the edge width is not affected by the disturbance stress. Uniform stress. On the other hand, in the case of a long fiber composite material, it is predicted that the St. Bunnan principle is difficult to apply due to the effect of the rigid displacement of the yarn, and this is empirically compatible.

This suggests that the two-dimensional composite finite element on the left in FIG. 4 and the three-dimensional composite finite element on the left in FIG. 5 function as a material dynamic model. Material mechanics has hardly changed during the last century, so the most recent composite materials cannot be described. On the other hand, since a site connecting two arbitrary nodes in a single parent element is known for a composite finite element, it can be classified in a pattern as to which site a high-strength material is arranged. Also, since unknowns and loads are defined by the finite element method, this is also easy to grasp in a pattern. In the first place, adopting composite elements ignoring errors due to spatial overlap is material dynamic modeling. Therefore, in the extreme case where the rigidity of the base material is one hundredth of that of the high-strength material as in cfrp, a high-precision approximation is predicted in terms of material mechanics.

<Pre-processing by pattern selection>
Taking a plain weave cloth as an example, (1) in FIG. 8a shows a tensile pattern of a fiber method, and (2) in FIG. 8a shows an FE mesh with a tensile pattern in the direction of ± 45 degrees. In the former, the yarn before loading is in the same straight line as the tension state and high load, whereas in the latter, it allows the rotation of the rigid body of the yarn and the displacement of the base material in the pulling direction and the contraction displacement in the perpendicular direction. This is consistent with the experimental results disclosed in Non-Patent Document 10. In addition, kink generation and Sambunan principle verification can also be analyzed with the meshes of FIGS. 8a and 8b.

Assuming that the high-strength material is replaced with a cylindrical beam and the diameter of the beam is assumed to be constant, if you specify the placement pattern of the high-strength material and its volume fraction, all geometrical quantities can be calculated from simple volume formulas. Conditions are known. This is convenient because, for example, the relationship between the volume fraction and the diameter is described for each arrangement pattern. In particular, in the case of a structured grid-like mesh, it can be formulated.

<Prediction of deformation shape of high-strength material and base material by network structure model>
As mentioned above, it is mainly high-strength materials that dominate the deformation field of the actual material, and assuming that the base material follows this, a macroscopic model imitating the actual material and a part of it are extracted with high accuracy. This assumption holds for the detailed model. Therefore, if attention is paid to the improvement of the deformation prediction accuracy of the high-strength material in each of the actual, macroscopic, and detailed models, the multiscale analysis can be performed by focusing on the network of the high-strength material. That is, the detailed model of the actual material is a unit element of the macroscopic model, and information exchange and deformation control of both models are performed so that the center point positions of both ends of the beam element of the macroscopic model and both ends of the high-strength material of the detailed model are the same. I do. In the detailed analysis using the proposed network structure model, the base material deforms mechanically and rationally following the deformation of the high-strength material, and the deformation error of the base material falls within that of the high-strength material. There is expected.

<Coupled analysis based on various physical properties of composite materials>
Since the molding load and the deformation characteristics of the material depend on the material temperature, coupled analysis of mechanical analysis and thermal stress analysis is expected, and the present invention contributes to a reduction in the amount of calculation processing. In addition, as a good conductor of heat, electricity, and magnetism required for structural members of aircraft, coupled analysis is promising by changing various physical properties of the parent element and the child element.

This is because a composite finite element can be automatically generated for a general application of a structure in which prepregs are stacked as in the second embodiment, and in the commercial software, only the type of differential equation that is the target of the finite element is selected. Multi-science other than mechanics is possible. For example, an aircraft is required to have lightning resistance, but in the case of cfrp, the graphite fiber is a high-quality conductor, so it can be adapted to the standard with a slight resin improvement. Estimating the improvement effect with a composite finite element contributes to work efficiency. Similarly, since graphite fiber has good thermal conductivity, heat does not accumulate in part, and it is preferable to use it for composite finite elements for optimization of heat transfer design.

FIG. 7 is an explanatory diagram of one embodiment of the system of the present invention, and shows the apparatus configuration of the analysis service system. The servers 62, 63, and 64 have a typical Internet service computer configuration, which realizes a function in a mail server (application server) and can also consider security settings. The server may be based on cloud computing. Reference numeral 65 denotes a LAN installed in the office, and each server is connected using this LAN. Reference numeral 66 denotes the Internet or a LAN connected to the Internet, and only 62 Internet servers are connected for security reasons. In addition, a plurality of client computers 61 operated by the user 60 are connected to the Internet 66, and 61 and 62 can exchange information instantaneously even on the opposite side of the earth, and the user can analyze at a desired place and time. Convenient because the service is available.

FIG. 11 is an explanatory view showing a composite tensile test piece in which three cfrp prepregs disclosed in Non-Patent Document 11 are laminated. When the upper stage is oriented in one direction, the lower stage is oriented at a right angle in the center, In (1) to (5), the tensile load direction is the direction indicated by the arrow.

In FIG. 12, the horizontal axis represents each test number, and the vertical axis represents the gradient of the stress-strain diagram made dimensionless with the value of condition 1. This is a result of automatically calculating the condition of each number from the fiber volume content and the boundary condition by designating a pattern using only one composite element. Assuming that it is linear, the analysis result is reasonable, but in the experiment, the load up to the breaking load is applied, so the influence of the resin breakage may have caused nonlinearity.

From this result, it is very convenient to use the composite element of the invention for the composite material of the ordinary laminated structure. By adopting the composite finite element model in the textbook of material mechanics, technical high school, technical college and elementary school It is suitable for material design and exercises of the latest aircraft, windmill wings and kites, golf shafts, mountain bikes, etc. in companies.

Note that the analysis of FIG. 12 was performed by using the plane stress and plane beam program of Non-Patent Document 12 as a subroutine, so that the analysis was simple and easy to see in a short time. Also, the three-dimensional composite element of FIG. 5 was created, and the same result as FIG. 12 was obtained as a result of the two-dimensional composite element. All programs are designed to automate pre-processing by inputting patterns and volume fractions of high-strength materials (fibers), so they can be fully used with technical knowledge of technical high schools.

As the pre-processing, in the case of the two-dimensional composite element shown in FIG. 4, a triangular element can be selected as a child element. In this case, if the physical properties of the base material parent element, particularly the conduction parameter, is set to be small, and that of the child element is set to be large, anisotropy can be easily manipulated because various transmission amounts are concentrated on the child element. Further, in the case of the three-dimensional composite element of FIG. 5, since child elements such as a triangular element, a quadrangular element, and a tetrahedral element can be selected, the types of anisotropic operations are significantly increased.

In the description so far, it seems that the parent element and the child element are isotropic. However, the claims are not limited to this, and an anisotropic element can naturally be adopted. In this case, the anisotropic setting can be complicated and diversified by variously changing the child elements as described above.

Furthermore, although a simple zooming method was explained as a multiscale analysis, a homogenization method can be easily used by periodically arranging composite finite elements. This is because a composite finite element functions as a single element, and thus it is easy to apply this to a technique that can be normally made of a finite element.

Incorrectly, the elastic constant of the base resin was set to the same level as that of the fiber, but in this case, Es / E = 1 at the data input stage warned that the approximation accuracy of the model was bad, so unnecessary analysis was not performed. I'm sorry.

A command that directly assigns input parameters to variables was inserted into the main m-file, and immediately after execution, the storage variables were output as a text file with save file_name. Therefore, the main m-file and the text file of the result were stored as e-maile attachments in a cloud service mail server so that the subject could be understood by themselves. Since m-file can be processed by a smartphone application, simple analysis was possible by calling an email and executing the attached file at the place where wifi is connected.

Since an acquaintance wanted to try the analysis, we introduced a dedicated app that works with m-file and was able to transfer the stored emails. In addition, an organization that had commercial software inquired about how to analyze it. In the same way as above, we introduced a dedicated app that works with m-file, and forwarded the stored mail for trial. Now that the program flow is clear, the same problem can be reproduced as a benchmark test by devising the input data of commercial software.

When the volume content of the high-strength material was small and the truss element was applied to the child element, it was a reasonable deformation, so if the volume content was significantly increased, an abnormal deformation that was physically unreasonable occurred . Therefore, when a change was made to the beam element, a reasonable solution was obtained. For this reason, truss structures such as quadrangular frames are less likely to be subjected to shear deformation than those of triangular frames, so they tend to be unstable and have the disadvantage of increased free copper for bending. It is safe if you do. In particular, it is no exaggeration to say that a beam element is indispensable for a frp material having a volume content of a high-strength material of 50% or more.

Since the fiber reinforced composite material frp exhibits strong anisotropy, it was difficult to obtain a reliable result in the strength evaluation based on the material mechanics. However, according to the present invention, a commercially available FEM analysis software using a composite finite element suitable for the composite material is used. Because it is easy to use for beginners, it is possible to analyze the strength of products for designers and material developers.

u-nofiber-a Tensile displacement in tension in the fiber direction as shown in Fig. 8a when there is no reinforcement
v-nofiber-a Tensile direction and vertical displacement in fiber direction tension as shown in Fig. 8a without reinforcement
u-woven-a Tensile displacement in tension in the fiber direction as shown in Fig. 8a (1)
v-woven-a Tensile direction and vertical displacement in the fiber direction tension shown in Fig. 8a (1)
u-woven2-a Displacement in the tensile direction in ± 45 ° tension in the fiber direction as shown in Fig. 8a (2)
v-woven2-a Tensile direction and vertical displacement in ± 45 ° tension in fiber direction as shown in Fig. 8a (2)
u-rovingx-a Displacement in the tensile direction in the fiber direction tension of unidirectionally arranged fibers under the boundary condition of Fig. 8a
v-rovingx-a Tensile direction and vertical displacement in fiber direction tension of unidirectionally arranged fibers under the boundary condition of Fig. 8a
u-rovingy-a Fiber direction of unidirectionally arranged fiber in the boundary condition of Fig. 8a and tensile direction displacement in vertical tension
v-rovingy-a Tensile direction and vertical displacement in the fiber direction and vertical tension of unidirectionally arranged fibers in the boundary condition of Fig. 8a
nofiber-c Tensile displacement in tension in the fiber direction as shown in Fig. 8b without reinforcement
woven-c Tensile direction displacement in fiber direction tension as shown in Fig. 8b (3)
woven2-c Tensile direction displacement in fiber direction tension as shown in Fig. 8b (4)
rovingx-c Tensile direction displacement in fiber direction tension of unidirectionally arranged fiber under boundary condition of Fig. 8b
rovingy-c Fiber direction of unidirectionally distributed fiber in the boundary condition of Fig. 8b and tensile direction displacement in main direct tension A code 2a Axial truss element 2b Spiral truss element 3 Node on outer surface of code A 60 User 61 Client computer Or smart phone 62 Internet server (62, 63, 64 may be mail server function, cloud computing or rental server)
63 Application server 64 Database server 65 Local area network 66 Internet

Claims (6)

A finite element method analysis method in which a computer analyzes an analysis model by a finite element method,
Computer can define analysis model shape, select finite element type, mesh division condition, element property values and dimensions, boundary condition, solver condition, result output condition and analysis by user operation or input file reading A data input process for inputting analysis data relating to conditions;
A mesh generation step in which the computer divides the analysis region into finite elements based on the input data;
A computer generates a matrix of each element based on the generated mesh, and incorporates the matrix into the matrix of the entire analysis region;
A boundary condition setting step in which a computer generates a solver overall matrix by setting boundary conditions for the overall matrix according to the input data;
A solving process in which a computer derives unknowns and derived data by the solver for the solver overall matrix;
An output process in which a computer outputs an analysis result obtained by the solving process;
Have
The finite element is a composite finite element composed of a parent finite element that meshes an analysis region and a single or plural child finite elements whose corner nodes are any of a plurality of nodes of the parent finite element;
The computer has a function of obtaining a ratio of physical property values of child elements to a parent element and / or a prediction error in the data input process, outputting a warning when an unacceptable error is predicted, and interrupting the analysis if desired. And
Based on a pattern designating method and / or connectivity based on the local element number of the composite element and the physical property values of the parent element and the child element and the dimensions of the child element constituting the composite element based on the input data A finite element method analysis method characterized in that it is carried out by an element designation method by search. The computer is a finite element method analysis device that performs analysis by a finite element method on an analysis model,
Computer can define analysis model shape, select finite element type, mesh division condition, element property values and dimensions, boundary condition, solver condition, result output condition and analysis by user operation or input file reading Data input means for inputting analysis data on conditions;
A computer, mesh generating means for dividing the analysis region into finite elements by the input data;
A computer generates a matrix of each element based on the generated mesh, and incorporates the matrix into the matrix of the entire analysis region;
A boundary condition setting means for generating a solver overall matrix by setting a boundary condition for the overall matrix according to the input data;
A solving means for a computer to derive unknowns and derived data by the solver for the solver overall matrix;
An output means for outputting an analysis result obtained by the solution finding means;
Have
The finite element is a composite finite element composed of a parent finite element that meshes an analysis region and a single or plural child finite elements whose corner nodes are any of a plurality of nodes of the parent finite element;
The computer has a function of obtaining a ratio of physical property values of child elements to a parent element and / or a prediction error by the data input means, outputting a warning when an unacceptable error is predicted, and interrupting the analysis if desired. And
Based on a pattern designating method and / or connectivity based on the local element number of the composite element and the physical property values of the parent element and the child element and the dimensions of the child element constituting the composite element based on the input data A finite element method analyzer characterized in that it is implemented by an element designation method by search. A finite element method analysis method comprising a macroscale model, a mesoscale model, and a microscale model,
A macro-analysis step of obtaining a macro-scale result by a computer modeling the meso-scale model with the composite finite element and performing an analysis of the macro-scale model using the finite element method analysis method according to claim 1;
A micromesh generation process in which a computer defines an arbitrary composite finite element as an analysis region and meshes a desired microstructure with a desired number of finite elements;
A micro boundary condition setting step of interpolating the result of the macro scale of the child element to a finite element node of the micro mesh corresponding to the child element of the composite finite element and setting as a boundary condition;
A micro-solving process in which a computer derives unknowns and derived data by a solver;
A finite element method analysis method, characterized in that the computer comprises a micro output step for outputting an analysis result of the micro solution step. An analysis service system in which a computer registers, manages, and distributes data files of claim 1 to a server via the Internet,
The data input process, the mesh generation process, the whole matrix generation process, the boundary condition setting process, the solution finding process, and the output process of the finite element analysis method according to claim 1 Recording means for recording as a finite element data file on a computer-readable recording medium;
A registration processing means for the computer to input the finite element data file from the recording medium, attach it to an email with an identification name, and send and register to a server via the Internet;
A management means for a computer to search for an e-mail registered in the server via the Internet and manage the finite element data file attached to the registered e-mail;
The registration in which a computer reads a delivery plan file in which a destination mail address and / or the finite element data file and / or an identification name of the registered e-mail is recorded, and the finite element data file is attached by the management means And a transmission means for transmitting the e-mail to the corresponding e-mail address of the delivery plan file,
4. The finite element analysis device based on the finite element analysis method according to claim 1 and / or the finite element analysis file attached to the e-mail sent by the destination user, or the finite element analysis device according to claim 2. An analysis means that inputs to the finite element method analysis apparatus and performs analysis by the finite element analysis apparatus,
An analysis service system characterized by comprising The composite finite element is generated and analyzed by diverting a finite element of general-purpose analysis software to the parent finite element and / or the child element. Finite element analysis method. A computer-readable recording medium on which the finite element method analysis program according to claim 1 is recorded.