JP2014137747A - Structure analyzer, structure analysis method, and structure analysis program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a structure analyzer capable of accurately analyzing even a structure switched from an elastic state to a plastic state.SOLUTION: A structure analyzer 1 includes: material state computation means 3 which computes an acceleration of each particle of model data 2 and computes incremental strain after time increment, from the acceleration; material state determination means 4 which determines which of an elastic state and a plastic state the particle after time increment is in, in accordance with a stored state of each particle and the incremental strain; breakdown determination means 5 which, if the particle is in the elastic state, computes elastic stress of the particle to determine whether the particle is broken down or not; stress correction computation means 6 which, if it is broken down, computes corrected stress of the particle and corrects and stores the state of the particle; and termination determination processing means 7 which outputs the stored state of each particle to the outside.

Description

  The present invention relates to a structure analysis apparatus, a structure analysis method, and a structure analysis program, and more particularly to a structure analysis apparatus that enables accurate analysis even when a structure transitions from an elastic state to a plastic state.

  A finite element method is known as one of the techniques for simulating the behavior of a structure during the process of deformation of the structure, for example, metal cutting or pressing. As an example, Non-Patent Document 1 describes a technique for performing an elasto-plastic analysis by applying a finite element method to cutting of a metal plate.

  The metal is deformed as the cutting process proceeds, and transitions from an elastic state to a plastic state in which permanent deformation remains. At that time, the stress increment is calculated from the relational expression of elastic stress increment-strain increment, and this is added to the stress before the time increment to calculate the current stress. In the elastoplastic theory, it is considered that the stress satisfies the equation of the yield surface, but the stress calculated from the relational expression of elastic stress increment-strain increment does not satisfy the equation. Therefore, it is necessary to correct distortion and stress according to the state transition.

  On the other hand, as a method for simulating the behavior of such a structure, there is a particle method as one of the methods that have been actively researched and attracted attention in recent years. Among them, methods such as SPH (Smoothed Particle Hydrodynemics) and MPS (Moving Particle Simulation) are widely used.

  In the particle method, a structure is modeled by a plurality of particles of the same size, so it is easier and quicker for structures with complex shapes than the finite element method, in which a model must be created for each element. There is an advantage that a model can be created. In addition, when the structure is greatly deformed, the element is crushed by the finite element method, so it is necessary to repeat element creation for analysis, but the particle method has an advantage that it is not necessary.

  As technical literature related to this, there are the following. Among them, Patent Document 1 describes an analysis method of simulating metal pressing by a shell element model. Patent Document 2 describes a method of simulating deformation due to contact between the first and second structures using a particle model. Patent Document 3 describes a technique in which the ingot shape of aluminum is predicted by solidification temperature analysis and elastoplastic stress analysis.

  Patent Document 4 describes a technique of suppressing excessive vibration of a stress calculation result by a dynamic explicit finite element method. Patent Document 5 describes a nonlinear calculation analysis method in which element stress = 0 when a porous member reaches a fracture stress. Patent Document 6 describes a material analysis method in which an elastic stress state is calculated from an elastic stress tensor.

  Patent Document 7 describes a finite element analysis method in which the superposition mesh method can be applied to an object having a nonlinear solid problem. Patent Document 8 describes an ultrasonic diagnostic apparatus that analyzes blood flow inside a blood vessel of a human body. Patent Document 9 describes a structure analysis apparatus in which a structure is divided into a plurality of elements and analyzed by a finite element method.

JP 2004-042098 A JP 2008-152423 A Japanese Patent Application Laid-Open No. 11-057947 JP 2001-201408 A JP 2005-308595 A JP 2006-313094 A JP 2009-086807 A JP 2010-125203 A JP 2010-230644 A

Manabe et al., “Analysis of Cutting Mechanism by Implicit Elastic-Plastic Finite Element Method: Formulation and Chip Curl Analysis by Radial Return Method”, Journal of Precision Engineering, vol. 62, no. 8, 1996

  Even in structural analysis that needs to take into account the elasto-plastic properties of structures, such as metal cutting, if the particle method can be applied, high-precision simulations can be performed in a short time by taking advantage of the above advantages. It is thought that this is the case, and in fact, such attempts have been made in some areas.

  However, in the particle method according to the existing technology, the transition from the elastic state to the plastic state of the structure is not considered. When this transition is performed along with the deformation of the structure, it is necessary to correct the strain and stress as in the finite element method described in Non-Patent Document 1 described above. Without this correction, the analysis accuracy will be greatly reduced.

  Techniques for solving this point and enabling structural analysis by applying the particle method to a structure in which a transition from an elastic state to a plastic state is performed are described in Patent Documents 1 to 9 and Non-Patent Document 1 described above. Is not listed.

  An object of the present invention is to provide a structure analysis apparatus, a structure analysis method, and a structure analysis program that enable accurate analysis by applying a particle method to a structure that transitions from an elastic state to a plastic state. is there.

  In order to achieve the above object, a structural analysis apparatus according to the present invention models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structural analysis by particle method on the model data. A structural analysis apparatus that calculates acceleration for each particle of model data, calculates a strain increment after a time increment from the acceleration, and stored state and strain of each particle The material state determining means for determining whether the particle after the time increment has passed is in an elastic state or a plastic state from the increment, and when the state of the particle is in an elastic state, the elastic stress of the particle is calculated. Yield determination means for determining whether or not the particles yielded, stress correction calculation means for correcting and calculating the stress of the particles when the particles yield, and the state of each stored particle To the outside And having a termination determination processing means for force.

  In order to achieve the above object, a structural analysis method according to the present invention models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structural analysis by a particle method for the model data. The material state calculating means calculates the acceleration for each particle of the model data, and the material state calculating means calculates the strain increment after the lapse of time from this acceleration. The material state determination means adds the strain increment to the particle state, the material state determination means determines whether the particle after the time increment has elapsed is in an elastic state or a plastic state, and the particle state is in an elastic state. In some cases, the yield determination means calculates the elastic stress of the particle, and from this elastic stress, the yield determination means determines whether or not the particle yields, and when the particle yields, the stress correction calculation means Stress Positive calculated by correction storage state of the particles, termination determination processing means the state of each particle stored, characterized in that the output to the outside.

  In order to achieve the above object, the structural analysis program according to the present invention models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structural analysis by the particle method for the model data. In the structural analysis apparatus for performing the above, the processor included in the structural analysis apparatus calculates the acceleration for each particle of the model data, calculates the strain increment after the time increment from the acceleration, each stored Procedure for adding strain increment to particle state, procedure for determining whether the particle is in an elastic state or a plastic state after elapse of time increment, and elastic stress of the particle when the particle state is in an elastic state A procedure to calculate whether or not the particle has yielded from this elastic stress, and a method to correct and store the state of the particle by correcting and calculating the stress of the particle when the particle yields , And the stored end determining processing means the state of each particle was characterized by executing the instructions outputted to the outside.

  As described above, the present invention is configured to determine whether or not the particle has yielded, and to correct the stress of the particle when yielding, so that the transition from the elastic state to the plastic state due to yielding is performed. Analysis including it becomes possible. As a result, a structural analysis device, a structural analysis method, and a structural analysis program with excellent features that the particle method can be applied to a structure that transitions from an elastic state to a plastic state and an accurate analysis is possible. Can be provided.

It is explanatory drawing shown about the structure of the structural analysis apparatus which concerns on the basic form of this invention. It is explanatory drawing shown about the structure of the structural analysis apparatus which concerns on embodiment of this invention. It is a flowchart shown about operation | movement of the structural analysis apparatus shown in FIG. It is a continuation of FIG. It is a flowchart shown about the detail of the process by the yield determination means and stress correction calculation means shown as steps S112-113 of FIG. It is explanatory drawing shown about the particle | grain model used as the object of the calculation performed with the structural analysis apparatus shown to FIGS. In the particle model shown in FIG. 6, the relationship between the equivalent plastic strain and the equivalent stress for the particle located at the center of the contact surface of the rectangular parallelepiped that collides with the plate is simulated by the structural analysis device shown in FIGS. It is a graph shown about.

(Basic form)
Hereinafter, the basic configuration of the present invention will be described with reference to FIG.
First, the basic contents of the basic form will be described, and then more specific contents will be described.
A structural analysis apparatus 1 according to a basic form models a structure with a plurality of particles, stores model data 2 including the state of each particle in advance, and performs structural analysis by a particle method on the model data From the material state calculation means 3 for calculating the acceleration for each particle of the model data and calculating the strain increment after the time increment from the acceleration, and the stored state of each particle and the strain increment, the time The material state determining means 4 for determining whether the particle after the incremental progress is in an elastic state or a plastic state, and whether the particle is in an elastic state, is the elastic stress of the particle calculated or yielded? Yield determining means 5 for judging whether or not, stress correction calculating means 6 for correcting and storing the state of the particle when the particle yields, and storing the state of each stored particle End output to And a constant processing means 7.

With the above configuration, the structural analysis apparatus 1 can perform accurate analysis even when the structure transitions from an elastic state to a plastic state.
Hereinafter, this will be described in more detail.

  FIG. 1 is an explanatory diagram showing the configuration of a structural analysis apparatus 1 according to the basic form of the present invention. In the structural analysis apparatus 1, model data 2 including a state of each particle obtained by modeling a structure with a plurality of particles is stored in advance. The material state calculation means 3, the material state determination means 4, the yield determination means 5, the stress correction calculation means 6, and the end determination processing means 7 sequentially calculate the state of each particle stored in the model data 2. And output the result to the outside.

  The material state calculation means 3 calculates an acceleration for each particle, and calculates a strain increment after a lapse of time from this acceleration. The material state determination means 4 determines whether the particle after the time increment has elapsed is in an elastic state or a plastic state from the stored state of each particle and the strain increment. When the state of the particle is an elastic state, the yield determination means 5 calculates the elastic stress of the particle and determines whether or not the yield has occurred.

  And when a particle yields, the stress correction calculation means 6 corrects and calculates the stress of the particle and stores the state of the particle. The end determination processing means 7 outputs the state of each particle finally stored to the outside.

  By providing this configuration, it is possible to output the state of the particles reflecting the stress when transitioning from the elastic state to the plastic state and obtain a more accurate analysis result. In addition, the specific calculation content of each said process is described in detail by embodiment after this.

(Embodiment)
Subsequently, the configuration of the embodiment of the present invention will be described with reference to FIG.
First, the basic content of the present embodiment will be described, and then more specific content will be described.
The structural analysis apparatus 10 according to the present embodiment models a structure with a plurality of particles, stores in advance model data 27 including the state of each particle, and performs structural analysis on the model data by a particle method. Device. This structural analysis apparatus 10 calculates an acceleration for each particle of the model data, calculates a strain increment after a time increment from the acceleration, and a state and strain increment of each stored particle. From the above, the material state determining means 22 for determining whether the particle after the lapse of time is in an elastic state or a plastic state, and when the state of the particle is in an elastic state, the elastic stress of the particle is calculated. Yield determination means 23 for determining whether or not the particles yielded, stress correction calculation means 24 for correcting and storing the state of the particles by correcting the stress of the particles when the particles yield, and each stored particle And end determination processing means 25 for outputting the state of the above to the outside.

  Further, the end determination processing means 25 determines whether or not the processing has been completed for all the target particles and time, and the state of each particle stored when it is determined that the processing has been completed. Output to the outside. The yield determination means 23 has a function of determining whether or not the particle yields by calculating the trial equivalent stress of the particle, and the stress correction calculation means 24 performs the trial equivalent stress when the particle yields. Based on the above, it has a function of correcting and calculating the stress of the particle.

  Further, the material state calculation means 21 searches the neighboring particles for each particle to determine whether or not there is a contact between different materials, and when there is a contact, the acceleration calculated from the discretized equation of motion is calculated for the particle. It has a function to add to the acceleration. The yield determining means 23 has a function of determining whether or not the yield is obtained by calculating the elastoplastic stress of the particle when the state of the particle is a plastic state.

With the above configuration, the structural analysis apparatus 1 can perform an accurate analysis by applying the particle method even when the structure transitions from an elastic state to a plastic state.
Hereinafter, this will be described in more detail.

  FIG. 2 is an explanatory diagram showing the configuration of the structural analysis apparatus 10 according to the embodiment of the present invention. The structural analysis device 10 has a configuration as a general computer device. That is, a processor 11 which is a main body for executing a computer program, a main storage means 12 (RAM: Random Access Memory) for temporarily storing data being processed, and a fixed storage means for temporarily storing programs and data 13. The fixed storage unit 13 is typically a hard disk drive or a flash memory.

  The structural analysis apparatus 10 further includes an input unit 14 that inputs data to be processed from the outside, and an output unit 15 that outputs a processing result to the outside. Typically, the input unit 14 is a keyboard, a mouse, and the like, and the output unit 15 is a display, a printer, or the like, but other devices connected via a network function as the input unit 14 and the output unit 15. Of course it is possible.

  The processor 11 functions as a material state calculation unit 21, a material state determination unit 22, a yield determination unit 23, a stress correction calculation unit 24, and an end determination processing unit 25, which will be described later, by operating the plastic deformation analysis program. Further, material state identification information 26 described later is temporarily stored in the main storage unit 12, and model data 27 used for analysis is stored in the fixed storage unit 13 in advance. More specifically, the model data 27 includes respective numerical values such as a particle number, a particle coordinate, a particle velocity, a particle acceleration, a particle material number, a material property value, and the like. The model data 27 reflects the processed material state identification information 26.

(Basic concept of analysis)
In the present embodiment, analysis using SPH (Smoothed Particle Hydrodynamics) is performed among the particle methods. As is well known, SPH models a structure with a plurality of particles, and among them, the physical quantity of the particle of interest is approximately expressed using a weight function. The basic concept will be described below.

  A cubic spline function can be used as the weight function. x is the position of the center of the particle of interest, x 'is the position of the center of the neighboring particle of the particle of interest, h is the diameter of the particle, D is the spatial dimension, and z is defined as

  The weight function W (z) can be defined as the following Expression 2.

  The physical quantity f (x) of the particle of interest can be expressed approximately using the weighting function W as in the following Equation 3.

Further, when J is the number of the neighboring particle, x ^J is the position of the center of the particle J, m ^J is the mass of the particle J, and ρ ^J is the density of the particle J, the physical quantity f (x) of the particle of interest is It can be expressed by discretization as shown in Equation 4.

  Further, the gradient and divergence of f (x) can be expressed as the following equations 5 and 6, respectively.

(flowchart)
3 to 4 are flowcharts showing the operation of the structural analysis apparatus 10 shown in FIG. 3 to 4 show one sheet divided into two sheets for the sake of space. First, the material state calculation means 21 reads the model data 27, and necessary information is temporarily stored in the main storage means 12 (step S101). This includes material state identification information 26 described later.

  Next, the material state calculation means 21 searches the model data 27 for particles located inside a sphere having a radius centering on the particle I, which is the i-th particle, and sets the particle number of the particle I and the inside of the sphere. The particle numbers of the particles other than the positioned particles I are associated and temporarily stored in the main storage unit 12 (step S102).

  Subsequently, the material state calculation unit 21 calculates the acceleration of the particle I, and temporarily stores the particle number of the particle I in association with the acceleration in the main storage unit 12 (step S103). And the material state calculation means 21 determines the presence or absence of the contact between different materials (step S104). More specifically, if the distance between the center of the particle I and the center of the particle J of the different material is equal to or less than the diameter of the particle, it is determined that the two particles are in contact. If contacted, the process proceeds to step S105, and if not contacted, the process proceeds to step S106.

When it is determined in step S104 that there is contact between different materials, the material state calculation means 21 uses the equation of Equation 8 obtained by discretizing the equation of motion shown in Equation 7 below to calculate the acceleration of the particle I. This is obtained and added to the acceleration of the particle I obtained in step S103. The material state calculation unit 21 temporarily stores the particle number of the particle I in association with the acceleration in the main storage unit 12 (step S105). Here, a _i ^I is the acceleration component of the particle I, and σ _ij ^{I, n} is the stress component of the particle I when the time increment has advanced n times. When this process ends, the process proceeds to step S106.

Subsequently, the material state calculation means 21 performs a particle velocity calculation process (step S106). Assuming that the particle velocity at the time when the time increment has advanced n times is v _i ^{I, n} , the acceleration at the current time at which the time increment has advanced Δt is v _i ^{I, n + 1} is the current value obtained in steps S103 and S105. Using the velocity a _i ^{I, n + 1} of the particle I in time, the following equation 9 is obtained. Here, not only the speed and acceleration but also other variables are expressed in the same manner as v and a. The material state calculation means 21 also temporarily stores the calculated speed in the main storage means 12 in association with the particle number of the particle I and the speed.

  The material state calculation means 21 calculates a velocity gradient between this particle and neighboring particles from the velocity of the particle I calculated in step S106 (step S107). This velocity gradient is obtained as shown in the following equation (10).

Then, the material state calculation means 21 calculates the strain rate of the particle I from the velocity gradient of the particle I calculated in step S107 (step S108). The strain rate of the particle I is obtained as shown in the following formula 11. Further, by multiplying this by the time increment Δt, the current time strain increment Δε _ij ^{I, n + 1} shown in Equation 12 can be obtained. The processing by the material state calculation means 21 is up to here.

  Subsequent to the above processing, the material state determination unit 22 reads the material state identification information 26 stored in the main storage unit 12 (step S109). The material state identification information 26 is stored in the main storage means 12 in the above-described step S101 and steps S114 and S117 described later, and is a binary value indicating whether the material is in an elastic state or a plastic state. It contains data.

  Then, the material state determination unit 22 determines whether the read material state identification information 26 is an elastic state or a plastic state (step S110). If “elastic state”, the process proceeds to step S111, and if “plastic state”, the process proceeds to step S115.

If it is determined in step S110 that the state is “elastic state”, the yield determination means 23 first calculates the elastic stress of the particles (step S111). In this calculation, the particle I strain increment vector {Δε _ij ^{I, n + 1} } calculated in step S108 is multiplied by the elastic matrix [D _e ], and the particle I stress increment vector {Δσ shown in Equation 13 below. _ij ^{I, n + 1} } is calculated. Further, the stress increment Δσ _ij ^{I, n + 1} is added to the stress σ _ij ^{I, n} before the time increment Δt to calculate the current time stress σ _ij ^{I, n + 1} as shown in _Equation 14.

Here, the elastic matrix [D _e ] is expressed as the following Expression 15. E is the Young's modulus of the particle I, and ν is the Poisson's ratio of the particle I.

  The yield determination means 23 determines the yield of the particles (step S112), and subsequently the stress correction calculation means 24 corrects the stress of the particles (step S113). FIG. 5 is a flowchart showing details of processing by the yield determination means 23 and the stress correction calculation means 24 shown as steps S112 to S113 in FIG. Hereinafter, these processes will be described with reference to FIG.

The yield determination means 23 first calculates the hydrostatic pressure strain increment of the particles (step S201). The hydrostatic strain increment Δε _m ^{I, n + 1} is calculated as shown in the following equation 16 using the strain increment Δε _ij ^{I, n + 1} of the particle I calculated in the above-described step S108.

Subsequently yield determination unit 23, the distortion increment [Delta] [epsilon] _ij ^I of the current time calculated at step S108 described ^above, from ^{n + 1,} the current time of the hydrostatic strain increment [Delta] [epsilon] _m ^I calculated in step ^S201, by subtracting the ^{n + 1} The deviation distortion increment Δe _ij ^{I, n + 1} of the current time expressed by the following equation 17 is calculated (step S202).

Subsequently, the yield determination means 23 uses the hydrostatic pressure stress Δσ _m ^{I, n} before the time increment Δt of the particles, using the current time stress calculated in the above-described step S111, as shown in the following Expression 18. Calculate (step S203).

続いて降伏判定手段２３は、粒子の時間増分Δｔ前の偏差応力ｓ_ｉｊ ^Ｉ，ｎを、応力σ_ｉｊ ^Ｉ，ｎからステップＳ２０３で算出された静水圧応力Δσ_ｍ ^Ｉ，ｎを減算して、以下の数１９で示されるように算出する（ステップＳ２０４）。

Subsequently, the yield determining means 23 subtracts the deviation stress s _ij ^{I, n} before the time increment Δt of the particle from the hydrostatic pressure stress Δσ _m ^{I, n} calculated in step S203 from the stress σ _ij ^{I, n} . Calculation is performed as shown in the following equation 19 (step S204).

Subsequently, the yield determination means 23 obtains the trial deviation stress increment 2GΔe _ij obtained by multiplying the deviation stress increment s _ij ^{I, n} before the particle time increment Δt by the deviation strain increment calculated in step S202 by the transverse elastic modulus G. ^{I, n + 1} is added to calculate the trial deviation stress (s _ij ^{I, n + 1} ) ^T of the current time expressed by the following equation 20 (step S205).

  Then, the yield determination means 23 calculates a trial equivalent stress expressed by the following formula 21 from the trial deviation stress calculated in step S205 (step S206).

  Based on the calculation results so far, the yield determination means 23 determines whether or not the trial equivalent stress of the particle I for the current time calculated in step S206 is greater than or equal to the yield stress Y, that is, whether the particle I has yielded. It is determined whether or not (step S207). If this trial equivalent stress is less than the yield stress Y, it can be determined that the particles I are in an “elastic state” because they have not yielded. In this case, the stress correction (step S113 in FIG. 3) shown in the following steps S208 to 213 is omitted, and the process proceeds to step S114 in FIG.

  When the trial equivalent stress is equal to or greater than the yield stress Y (Yes in step S207), in this case, it is determined that the particle I yields and is in the “elastic state”. The equivalent plastic strain increment of the particle I indicated by is calculated (step S208). Here, H is a function of the following Expression 23 indicating the relationship between the equivalent plastic strain and the equivalent stress.

  Here, when the function H in Expression 23 is a non-linear function, an iterative method of a non-linear equation, for example, a Newton method can be used to obtain the equivalent plastic strain increment. When H is a linear function, the equivalent plastic strain increment can be easily obtained.

  Then, the stress correction calculation unit 24 calculates the equivalent stress σ of the particle I expressed by the following formula 24 using the equivalent plastic strain increment obtained in step S208 (step S209). Here, when it is registered that the plasticity of the material assumed in the model data 27 is isotropic hardening, the equivalent stress of the yielded particle I is used as the yield stress to be used after the time increment Δt. The particle number is temporarily stored in the main storage means 12.

Subsequently, the stress correction calculation means 24 calculates the current time deviation stress s _ij ^{I, n + 1} of the particle I expressed by the following equation 25 using the equivalent stress σ obtained in step S209 (step 209). S210).

Furthermore, the stress correction calculation means 24 uses the hydrostatic pressure strain increment Δε _m ^{I, n + 1} obtained in step S201, and the hydrostatic pressure stress increment Δσ _m ^{I, n + 1 of the} particle I represented by the following equation (26) at the current time. Is calculated (step S211). Here, K is a bulk modulus.

Subsequently, the stress correction calculation means 24 uses the hydrostatic stress increment Δσ _m ^{I, n + 1} obtained in step S211 to use the hydrostatic stress σ _m ^{I, n + 1 at} the current time of the particle I expressed by the following equation (27). Is calculated (step S212).

そして応力修正計算手段２４は、粒子Ｉの現時間の偏差応力に静水圧応力を加算して、以下の数２８で示される粒子Ｉの応力を算出する（ステップＳ２１２）。

Then, the stress correction calculation unit 24 adds the hydrostatic stress to the deviation stress of the particle I at the current time, and calculates the stress of the particle I expressed by the following formula 28 (step S212).

  Returning to FIG. 3, the stress correction calculation means 24 updates the material state identification information 26 (step S114). According to the result of the processing shown in S112 to 113 (FIG. 5), the “plastic state” is stored if the particle I yields, and the “elastic state” is stored in correspondence with the particle number if it does not yield.

On the other hand, when it is determined in the above-described step S110 that it is “plastic state”, the yield determination means 23 calculates the elastoplastic stress of the particles I (step S115). More specifically, the stress increment of the particle I is obtained by multiplying the elastoplastic matrix [D _ep ] by the current strain increment vector {Δε _ij ^{I, n + 1} } obtained in step S108 by the following equation 29. Vector {Δσ _ij ^{I, n + 1} } is calculated. Further, similarly to step S111 (the above-described equation 14), the obtained stress increment Δσ _ij ^{I, n + 1} is added to the stress σ _ij ^{I, n} before the time increment Δt, and the current stress σ _ij ^{I, n + 1} is obtained. calculate.

Here, the elastic-plastic matrix [D _ep ] is defined by the following _Equation 30. [D _p ] is a target matrix, G is a transverse elastic modulus, σ is equivalent stress, H ′ is a differential value of the function H expressed by Equation 23, s _ii is a deviation stress component, and τ _ij is a shear stress component.

  And the yield determination means 23 performs the yield determination of particle | grains (step S116). It is determined whether or not the equivalent stress σ of the current time obtained in step S115 is greater than or equal to the yield stress Y, that is, whether or not the particles I have yielded. If this equivalent stress is less than the yield stress Y, the particle I has not yielded, so it can be determined to be “elastic state”. Further, when the plasticity of the material assumed in the model data 27 is registered as isotropic hardening, the equivalent stress of the yielded particle I is used as the yield stress after the time increment Δt. It is temporarily stored in the main storage means 12 in association with the particle number.

  Further, similarly to the above-described step S114, the yield determination means 23 associates the “plastic state” with the particle number if the particle I yields and the “elastic state” with the particle number if it does not yield the material state identification information 26. Update and save (step S117).

  The material state identification information 26 updated by the above processing is reflected and stored in the model data 27 on the fixed storage means 13 by the end determination processing means 25, and is drawn and output on the output means 15 (step). S118).

  Then, the end determination processing means 25 determines whether or not the processing has been completed for all the particles to be processed (step S119), and if not completed, proceeds to the next particle (step S120) and step S102. Return to and repeat the process. If the processing has been completed for all the particles, it is determined whether or not the processing has been completed for all the times (step S121). If not, the time increment is added to the next time. Proceed (step S122) and return to step S102 to repeat the process.

  When the processing is completed for all particles and time to be processed, the processing ends.

(Example of calculation)
An example of calculation performed on the actual particle model by the operation described above will be shown below.

  FIG. 6 is an explanatory diagram illustrating a particle model 300 that is a target of calculation performed by the structural analysis apparatus 10 illustrated in FIGS. The particle model 300 includes a rectangular parallelepiped 301 and a plate 302, and is modeled with a particle size (diameter) of 0.25 mm.

  The rectangular parallelepiped 301 is made of aluminum, and the material properties thereof are Young's modulus 7100 kgf / mm 2 (69.6 Gpa), Poisson's ratio 0.33, density 2.752E-10 kgf · sec / mm 4 (2.7 g / cm 3), and plastic configuration. It is an elasto-plastic body in which the law (relationship between equivalent plastic strain and equivalent stress) satisfies the following Ludwick law.

  The plate 302 is made of stainless steel, and the material properties thereof are a rigid body having a Young's modulus of 21000 kgf / mm 2 (205.8 Gpa), a Poisson's ratio of 0.33, and a density of 7.954E-10 kgf · sec / mm 4 (7.8 g / cm 3). It is.

  Under the above conditions, the analysis was performed such that the rectangular parallelepiped 301 with an initial velocity of 4500 mm / sec and a gravitational acceleration applied dropped 0.135 mm (assuming a 1 m free fall of the rectangular parallelepiped) and collided with the plate 302 constrained in all directions.

  FIG. 7 shows the particle model 300 shown in FIG. 6, and the structure shown in FIGS. 2 to 4 shows the relationship between the equivalent plastic strain and the equivalent stress for the particles located at the center of the contact surface of the rectangular parallelepiped 301 that collides with the plate 302. It is the graph 400 shown about the result simulated with the analysis apparatus. The graph 400 includes three curves: a theoretical value 401 of the plastic constitutive law, an analysis result 402 by the particle method of the present embodiment in which stress correction is performed, and an analysis result 403 by the conventional particle method in which stress correction is not performed. .

  As can be seen from FIG. 7, in the analysis result 403 by the conventional particle method, the equivalent stress corresponding to each equivalent plastic strain is clearly smaller than the theoretical value 401 of the plastic constitutive law, and the maximum compared to the theoretical value. The error is about 42%.

  On the other hand, in the analysis result 402 by the particle method of the present embodiment, the theoretical value of the plastic constitutive law and the equivalent stress corresponding to each equivalent plastic strain are relatively well matched, and the maximum error compared to the theoretical value is About 0.9%. Therefore, according to this embodiment, it has been confirmed that the error can be reduced by about 40% as compared with the existing particle method.

(Overall operation of the embodiment)
Next, the overall operation of the above embodiment will be described.
In the structure analysis method according to the present embodiment, a structure is modeled by a plurality of particles, model data including the state of each particle is stored in advance, and a structure analysis apparatus 10 that performs structure analysis by the particle method on the model data. Then, the material state calculation means calculates the acceleration for each particle of the model data (FIG. 3, step S103), and the material state calculation means calculates the strain increment after the time increment from this acceleration (FIG. 3). Steps S104 to 108), the material state determination unit adds the strain increment to the stored state of each particle, and the material state determination unit determines whether the particle after the time increment has elapsed is in an elastic state or a plastic state. Judgment is made (FIG. 3, step S110), and when the state of the particle is an elastic state, the yield determination means calculates the elastic stress of the particle (FIG. 3, step S111), and the particle is calculated from the elastic stress. The yield determination means determines whether or not the yield has occurred (step S112 in FIG. 3), and when the particle yields, the stress correction calculation means corrects the stress of the particle and corrects and stores the state of the particle ( In FIG. 3, step S113), the end determination processing means outputs the stored state of each particle to the outside (FIG. 3, step S118).

Here, each of the above-described operation steps may be programmed to be executable by a computer, and may be executed by the processor 11 included in the structural analysis apparatus 10 that directly executes each of the steps. The program may be recorded on a non-temporary recording medium, such as a DVD, a CD, or a flash memory. In this case, the program is read from the recording medium by a computer and executed.
By this operation, this embodiment has the following effects.

  According to this embodiment, even for structural analysis that needs to take into account the elastoplastic properties of the structure, while correcting the strain and stress accompanying the transition from the elastic state to the plastic state of the structure, Structural analysis can be performed by applying the method. This makes it possible to perform a highly accurate simulation in a short time. The actual results are as shown in FIGS.

  The present invention has been described with reference to the specific embodiments shown in the drawings. However, the present invention is not limited to the embodiments shown in the drawings, and any known hitherto provided that the effects of the present invention are achieved. Even if it is a structure, it is employable.

  Regarding the embodiment described above, the main points of the new technical contents are summarized as follows. In addition, although part or all of the said embodiment is summarized as follows as a novel technique, this invention is not necessarily limited to this.

(Supplementary Note 1) A structure analysis apparatus that models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structure analysis on the model data by a particle method,
A material state calculation means for calculating an acceleration for each particle of the model data and calculating a strain increment after a time increment from the acceleration;
A material state determining means for determining, from the stored state of each particle and the strain increment, whether the particle after the time increment has elapsed is an elastic state or a plastic state;
Yield determination means for determining whether or not the yield was calculated by calculating the elastic stress of the particle when the state of the particle is an elastic state;
Stress correction calculation means for correcting and storing the state of the particle by correcting and calculating the stress of the particle when the particle yields;
A structural analysis apparatus comprising: an end determination processing means for outputting the stored state of each particle to the outside.

(Supplementary Note 2) The termination determination processing means
It is determined whether or not the processing has been completed for all the particles and time to be processed, and when the processing is determined to be completed, the stored state of each particle is output to the outside. The structural analysis apparatus according to appendix 1.

(Additional remark 3) While the said yield determination means has the function to judge whether the particle | grain yielded by calculating the trial equivalent stress of the said particle | grain,
The structural analysis apparatus according to appendix 1, wherein the stress correction calculation unit has a function of correcting and calculating the stress of the particle based on the trial equivalent stress when the particle yields.

(Additional remark 4) The said material state calculation means searches the vicinity particle | grain with respect to each said particle | grain, determines the presence or absence of the contact between different materials, and the acceleration calculated from the motion equation discretized when there exists contact The structural analysis apparatus according to appendix 1, characterized by having a function of adding to the acceleration of the particles.

(Additional remark 5) The said yield determination means has a function which judges whether it yielded by calculating the elastic-plastic stress of the particle | grain when the state of the said particle | grain is a plastic state, 1. The structural analysis apparatus according to 1.

(Supplementary Note 6) In a structural analysis apparatus that models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structural analysis by a particle method on the model data,
The material state calculating means calculates acceleration for each particle of the model data,
The material state calculation means calculates the strain increment after the time increment from this acceleration,
The material state determination means adds the strain increment to the stored state of each particle,
The material state determining means determines whether the particle after the time increment has elapsed is in an elastic state or a plastic state,
When the state of the particle is an elastic state, the yield determination means calculates the elastic stress of the particle,
The yield determination means determines whether or not the particles yield from this elastic stress,
When the particle yields, the stress correction calculation means corrects the stress of the particle and corrects and stores the state of the particle,
A structure analysis method, wherein the end determination processing means outputs the stored state of each particle to the outside.

(Additional remark 7) The process which outputs the state of the said completion | finish determination process means each said particle | grain to the outside,
It is determined whether or not the processing has been completed for all the particles and time to be processed, and when the processing is determined to be completed, the stored state of each particle is output to the outside. The structural analysis method according to appendix 6.

(Supplementary Note 8) The process of determining whether or not the particle yields is to determine whether or not the particle yielded by calculating the trial equivalent stress of the particle,
The structural analysis method according to appendix 6, wherein the process of correcting and calculating the stress of the particle is to correct and calculate the stress of the particle based on the trial equivalent stress when the particle yields .

(Additional remark 9) The process which calculates acceleration with respect to each said particle | grain searches the vicinity particle | grain for each said particle | grain, determines the presence or absence of the contact between different materials, and the motion discretized when there exists a contact The structural analysis method according to appendix 6, including a process of adding the acceleration calculated from the equation to the acceleration of the particle.

(Additional remark 10) When the process which judges whether the said particle | grain yielded is a state of the said particle | grain, it is judged whether the elastoplastic stress of the particle | grain was calculated and yielded. The structural analysis method according to appendix 6, characterized in that it exists.

(Supplementary Note 11) In a structural analysis apparatus that models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structural analysis on the model data by a particle method,
In the processor included in the structural analysis device,
A procedure for calculating acceleration for each particle of the model data;
A procedure for calculating the strain increment after the time increment from this acceleration,
Adding the strain increment to the stored state of each particle;
A procedure for determining whether the particles after the time increment have been in an elastic state or a plastic state;
A procedure for calculating the elastic stress of the particle when the particle is in an elastic state;
A procedure to determine if the particle yielded from this elastic stress,
A procedure for correcting and storing the state of the particle by correcting and calculating the stress of the particle when the particle yields,
And a structure analysis program for causing the end determination processing means to output the stored state of each particle to the outside.

  The present invention can be widely applied to applications for analyzing the deformation of structures. However, the deformation accompanying a transition from an elastic state to a plastic state of a structure, such as simulation of metal cutting and pressing. Suitable for analysis.

DESCRIPTION OF SYMBOLS 1,10 Structure analyzer 2,27 Model data 3,21 Material state calculation means 4,22 Material state determination means 5,23 Yield determination means 6,24 Stress correction calculation means 7,25 End determination processing means 11 Processor 12 Main memory Means 13 Fixed storage means 14 Input means 15 Output means 26 Material state identification information 300 Particle model 301 Cuboid 302 Plate 400 Graph 401 Theoretical value 402, 403 Analysis result

Claims (7)

A structure analysis apparatus that models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structural analysis by a particle method on the model data,
A material state calculation means for calculating an acceleration for each particle of the model data and calculating a strain increment after a time increment from the acceleration;
A material state determining means for determining, from the stored state of each particle and the strain increment, whether the particle after the time increment has elapsed is an elastic state or a plastic state;
Yield determination means for determining whether or not the yield was calculated by calculating the elastic stress of the particle when the state of the particle is an elastic state;
Stress correction calculation means for correcting and storing the state of the particle by correcting and calculating the stress of the particle when the particle yields;
A structural analysis apparatus comprising: an end determination processing means for outputting the stored state of each particle to the outside. The termination determination processing means is
It is determined whether or not the processing has been completed for all the particles and time to be processed, and when the processing is determined to be completed, the stored state of each particle is output to the outside. The structure analysis apparatus according to claim 1. The yield determination means has a function of determining whether or not the particle has yielded by calculating a trial equivalent stress of the particle,
The structural analysis apparatus according to claim 1, wherein the stress correction calculation unit has a function of correcting and calculating the stress of the particle based on the trial equivalent stress when the particle yields.   The material state calculation means searches neighboring particles for each particle to determine the presence or absence of contact between different materials, and when there is contact, the acceleration calculated from the discretized equation of motion is calculated for the particle. The structural analysis device according to claim 1, wherein the structural analysis device has a function of adding to acceleration.   2. The yield determination unit according to claim 1, wherein when the state of the particle is a plastic state, the yield determination unit has a function of determining whether or not the particle has yielded by calculating an elastoplastic stress of the particle. Structural analysis device. In a structural analysis apparatus that models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structural analysis by a particle method on the model data,
The material state calculating means calculates acceleration for each particle of the model data,
The material state calculation means calculates the strain increment after the time increment from this acceleration,
The material state determination means adds the strain increment to the stored state of each particle,
The material state determining means determines whether the particle after the time increment has elapsed is in an elastic state or a plastic state,
When the state of the particle is an elastic state, the yield determination means calculates the elastic stress of the particle,
The yield determination means determines whether or not the particles yield from this elastic stress,
When the particle yields, the stress correction calculation means corrects the stress of the particle and corrects and stores the state of the particle,
A structure analysis method, wherein the end determination processing means outputs the stored state of each particle to the outside. In a structural analysis apparatus that models a structure with a plurality of particles, stores model data including the state of each particle in advance, and performs structural analysis by a particle method on the model data,
In the processor included in the structural analysis device,
A procedure for calculating acceleration for each particle of the model data;
A procedure for calculating the strain increment after the time increment from this acceleration,
Adding the strain increment to the stored state of each particle;
A procedure for determining whether the particles after the time increment have been in an elastic state or a plastic state;
A procedure for calculating the elastic stress of the particle when the particle is in an elastic state;
A procedure to determine if the particle yielded from this elastic stress,
A procedure for correcting and storing the state of the particle by correcting and calculating the stress of the particle when the particle yields,
And a structure analysis program for causing the end determination processing means to output the stored state of each particle to the outside.

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