JP4459120B2 - Laminated material analysis method - Google Patents

Description

  The present invention relates to a method for analyzing a laminated material, in which a deformation state when bending stress is applied to an analysis object made of a laminated material is analyzed based on mesh model data virtually expressed using a computer.

  2. Description of the Related Art Conventionally, a CAE technique that virtually represents an object using a computer, virtually applies a load to the virtual object, and acquires a deformation amount or the like is widely known. By using such CAE, it is possible to know the strength and the like of the target object at the stage before actually manufacturing the target object, that is, the design stage. As a result, manufacturing costs, manufacturing time, and the like can be reduced.

  When analyzing a target object by such CAE, it is necessary to set the physical property value of the target object in advance. For example, when performing bending analysis of an object, it is necessary to set Young's modulus, plastic deformation rate, and the like in advance. The physical property values used in this analysis are obtained by conducting a material test or the like prior to the analysis.

  Incidentally, some analysis objects are made of a laminated material in which a plurality of materials are laminated. Since this laminated material is made by laminating a plurality of materials having different physical property values, the physical property values of the entire laminated material are often complicated. For example, since a laminated material has anisotropy, it is known that a physical property value such as a Young's modulus changes depending on a deformation type such as tension, bending, and compression.

  Therefore, conventionally, various techniques have been proposed in order to analyze such a laminated material with high accuracy. For example, Patent Document 1 discloses a technique for calculating a strain of a composite when a load is applied, determining whether the calculated strain is a tensile strain or a compressive strain, and performing analysis using a longitudinal elastic modulus corresponding to the strain type. Proposed. Patent Document 2 discloses a technique for setting a Young's modulus for tension and a Young's modulus for compression for a finite element model used for numerical analysis of a composite. According to these techniques, since appropriate physical property values are employed according to the type of deformation, it is possible to analyze the laminated material with high accuracy.

JP 2003-94916 A JP 2003-330975 A

  However, the physical property values of the laminated material may differ depending not only on the type of deformation but also on the direction of deformation. That is, in the case of a laminated material, the Young's modulus differs depending on the bending direction, whether it is a concave bend on the front surface or a concave bend on the back surface, even if the bending deformation is the same. In order to analyze the laminated material more accurately, it is necessary to consider the difference in Young's modulus depending on the bending direction.

  However, none of the prior arts considered the bending direction of the laminated material. Therefore, conventionally, when performing a bending analysis of a laminated material, either one of the Young's moduli on the front side or the back side, or an average value of both is used as the bending Young's modulus. In other words, the same Young's modulus was used when analyzing either the bending to the back side or the bending to the front side. As a result, there is a problem that the accuracy of the analysis result of the laminated material is lowered.

  Therefore, an object of the present invention is to provide a method for analyzing a laminated material that can analyze the laminated material with higher reliability.

The method for analyzing a laminated material according to the present invention is an analysis of a laminated material that analyzes a deformation state when a bending stress is applied to an analysis object made of a laminated material based on mesh model data virtually represented by a computer. The calculation unit of the computer is configured to analyze the analysis object based on the mesh model data of the analysis object stored in the storage unit of the computer and the additional stress condition indicating the condition of the bending stress added to the analysis object. a deformation state at the time of adding the bending stress shown by the additional stress conditions at the object, and the temporary analyzing, using a Young's modulus of the temporary preset, temporary calculation unit of the computer is obtained at the provisional analysis step based on the analysis result data, response to a determination step of determining the bending direction, the calculation unit of the computer, to the determined bending direction determination step Te, a selection step of selecting one of the backside Young's modulus Young's modulus at which the laminate material stored in the storage unit bent in front Young's modulus or the back side is the Young's modulus at the time of bending the front side of the computer The computer has an analysis step for performing a bending analysis of the laminated material using the Young's modulus selected in the selection step.

In a preferred aspect, in the determination step , the calculation unit of the computer calculates the maximum principal stress on the surface of the analysis target portion and the maximum principal stress on the back surface of the analysis target based on the temporary analysis result data, respectively. a main stress calculating step of, comparing the maximum principal stress calculated surface and the back surface of the maximum principal stress, and the execution, it is determined that the bending direction higher side of the maximum principal stress.

When the mesh model is a shell mesh model, in the main stress calculation step , the calculation unit of the computer calculates the maximum main stresses on the front and back surfaces of the shell mesh constituting the analysis target portion. When the mesh model is a solid mesh model, in the principal stress calculation step , the calculation unit of the computer includes a surface target mesh that configures the surface of the analysis target portion and a back target mesh that configures the back surface of the analysis target portion, respectively. The target mesh specifying step to be specified is further executed to calculate the maximum principal stresses on the externally exposed surface of the front surface target mesh and the externally exposed surface of the back surface target mesh, respectively. In the target mesh identification step , the calculation unit of the computer calculates a straight line that passes through the center of gravity of the surface target mesh and is perpendicular to the externally exposed surface of the surface target mesh, and calculates the mesh constituting the back surface of the mesh model. It is desirable to specify the mesh closest to the straight line as the back surface target mesh.

In another preferred aspect, in the temporary analysis step , the calculation unit of the computer analyzes either the front-side Young's modulus or the back-side Young's modulus as a temporary Young's modulus.

  According to the present invention, since the bending direction is automatically determined and the analysis is performed with the Young's modulus corresponding to the bending direction, the reliability of the analysis result can be further improved.

  Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing a functional configuration of an analysis apparatus 10 according to an embodiment of the present invention. The analysis device 10 is physically a computer having a CPU, a memory, a hard disk, and a user interface. The computer CPU functions as an analysis device by reading and executing an analysis program stored in the hard disk.

  The analysis apparatus 10 is functionally configured as shown in FIG. The input / output unit 12 is a user interface that receives an instruction from the user and an input of various data and presents an analysis result to the user. Specifically, the input / output unit 12 includes input means such as a keyboard and a mouse, and output means such as a monitor and a printer. The user inputs various instructions and data via the input means. The input unit stores the input instruction and data in the storage unit 16.

  The communication unit 14 is a communication interface for exchanging data with a computer other than the analysis device or an information communication device. The communication unit 14 receives model data (CAD data) of an analysis object from a CAD device (not shown), and stores the model data in the storage unit 16.

  The mesh model conversion unit 18 converts CAD data input from the CAD device into mesh model data. The mesh model is a model obtained by dividing various shapes into mesh shapes, and is a model that expresses various shapes as a collection of simple shape elements (mesh). This mesh model is roughly classified into a shell mesh model using a two-dimensional mesh and a solid mesh model using a three-dimensional mesh. In this embodiment, a two-dimensional shell model is used to save calculation resources (memory capacity, calculation time, CPU processing capacity, etc.).

The storage unit 16 functions as a storage unit that stores necessary data, and specifically includes a hard disk, a memory, and the like. The storage unit 16 stores analysis conditions necessary for bending analysis of a laminated material described later. The analysis conditions indicate conditions for bending analysis, and include mesh model data, additional stress condition data, physical property value data, wall thickness data, and the like of the analysis object. In this embodiment, this analysis condition is stored as one CAE file. Here, the additional stress condition data is data indicating the condition of the stress applied to the analysis target. Specifically, the data includes the constraint position of the analysis target, the magnitude, range, and position of the applied stress. It is. The physical property value data is data indicating the physical property value of the analysis object. The physical property value is a value indicating a macroscopic mechanical, thermal, electrical, magnetic, or optical property unique to each material, such as Young's modulus, plastic deformation rate, or thermal expansion coefficient of each material. . In this embodiment in which bending analysis is performed, Young's modulus is set as a physical property value. Further, as will be described later, in the case of a laminated material, the Young's modulus differs depending on the bending direction. Therefore, in this embodiment, both the front-side Young's modulus E _ob and the back-side Young's modulus E _re are stored as physical property values. is doing. The wall thickness data is data indicating the wall thickness of the analysis object. That is, in the present embodiment using the two-dimensional shell mesh model, the thickness of the analysis target cannot be grasped from the mesh model. Therefore, the thickness of the object to be analyzed is stored as an analysis condition.

  The analysis execution unit 20 is a calculation unit that executes a bending analysis based on the stored analysis conditions. Similar to the analysis execution unit in the conventional CAE apparatus, the analysis execution unit 20 calculates the stress acting on the mesh for each mesh constituting the mesh model, and calculates the displacement due to the stress based on the Young's modulus. To do. The stress and the amount of displacement acting on each mesh are calculated based on a known physical formula (for example, E = σ / ε, E: Young's modulus, σ: stress, ε: strain, etc.). At this time, if an accurate Young's modulus is not set, an accurate stress value and displacement amount cannot be calculated.

  Therefore, conventionally, the Young's modulus of the object to be analyzed is acquired in advance by experiments or the like, and the value is stored as physical property value data. When executing the bending analysis, the displacement amount and the like are calculated by applying the stored Young's modulus to the physical equation. Here, in the case of an ordinary material, that is, an isotropic material made of a single material, its Young's modulus is constant regardless of the bending direction. Therefore, when performing a bending analysis, the bending analysis may be performed with one Young's modulus obtained by actually performing a bending test or the like. However, in the case of the laminated material to be analyzed in this embodiment, there is a problem that the Young's modulus varies depending on the bending direction. That is, in the case of a laminated material in which a plurality of types of materials are laminated, the Young's modulus differs between when the front side is bent concavely and when the back side is bent concavely. That is, when performing a bending analysis of a laminated material, it is necessary to determine a bending direction for each mesh and calculate a displacement amount and a stress with a Young's modulus corresponding to the bending direction.

  Therefore, the analysis execution unit 20 of the present embodiment includes a temporary calculation unit 22 that performs stress calculation with a temporary Young's modulus, a bending direction determination unit 24 that determines a bending direction based on the temporary calculation result, and a determined bending direction. And a main calculation unit 26 that performs a bending analysis with a Young's modulus corresponding to. This will be described in detail below.

Provisional calculation unit 22, the temporary Young's modulus E _n, to calculate the stress acting on the front and back surfaces of the mesh. Here, the Young's modulus E _n of the tentative, the stress at the calculation of the mesh surface, and the stress at the calculation of the mesh backside, in if the same value may be any value. Therefore, the Young's modulus E _n of the temporary, it is possible to use front Young's modulus E _ob, back Young's modulus E _re, or the like of these average values. In the present embodiment, as the Young's modulus E _n of the provisional uses a front Young's modulus E _ob. 2 and 3 are diagrams showing an example of the provisional calculation result. 2 shows the stress distribution on the surface of the analysis object when stress is applied to the analysis object in the downward direction in the drawing under predetermined analysis conditions, and FIG. 3 shows the stress distribution on the back surface of the analysis object. In FIGS. 2 and 3, the shape of the analysis object before applying stress is indicated by a broken line, and the shape of the analysis object before applying stress is indicated by a solid line. In addition, a portion where a stress greater than a predetermined reference value works is indicated by hatching. As is apparent from FIGS. 2 and 3, it can be seen that the stress distribution differs between the front and back surfaces under the same analysis conditions.

If the stress acting on each mesh is calculated based on the front-side Young's modulus E _ob (temporary Young's modulus E _n ), the provisional calculation unit 22 subsequently calculates the maximum principal stress on each of the front and back surfaces. The principal stress is given as a solution of the following equation:
[Equation 1]
σ ³ − (σ _x + σ _y + σ _z ) σ ² + (σ _x σ _y + σ _y σ _z + σ _z σ _x −τ _xy ² −τ _yz ² −τ _zx ² ) − (σ _x σ _y σ _z −σ _x τ _yz ² −σ _y τ _zx ² −σ _z τ _xy ² + 2τ _xy τ _yz τ _zx ) = 0

Here, σ _x , σ _y , and σ _y are stresses acting in the x, y, and z directions, respectively, and τ _xy , τ _yz , and τ _zx are shear stresses acting in the xy, yz, and zx directions, respectively. Then, σ1, σ2, and σ3 (σ1>σ2> σ3) obtained as a solution of this expression are the maximum principal stress, the intermediate principal stress, and the minimum principal stress, respectively. The temporary calculation unit 22 calculates the maximum principal stress σ1 _ob on the mesh surface and the maximum principal stress σ1 _re on the mesh back surface based on this equation. The calculated maximum principal stresses σ1 _ob and σ1 _re of the front and back surfaces are temporarily stored in a memory as a provisional calculation result.

The bending direction determination unit 24 determines the bending direction of each mesh based on the temporary calculation result stored in the memory. Specifically, the maximum principal stresses σ1 _ob and σ1 _re on the front and back surfaces are compared. As a result of the comparison, when the surface maximum principal stress σ1 _ob is equal to or larger than the back surface maximum principal stress σ1 _re (σ1 _ob ≧ σ1 _re ), it is determined that the bending is a front side bending, that is, a bending in which the front side is concave. On the contrary, when the surface maximum principal stress σ1 _ob is smaller than the back surface maximum principal stress σ1 _re (σ1 _ob <σ1 _re ), it is determined that the bending is the bending toward the back side, that is, the bending where the back side is concave. The bending direction determination unit 24 temporarily stores the determination result in the memory.

The calculation unit 26 performs a bending analysis using the Young's modulus corresponding to the bending direction determined by the bending direction determination unit 24. That is, when it is determined that the bending is to the front side, the stress acting on each mesh is calculated using the front side Young's modulus E _ob . Then, the displacement amount of each mesh is calculated by substituting the calculated stress and Young's modulus E _ob into a known physical formula. On the other hand, when it is determined that the bending is performed on the back side, the stress and the displacement amount acting on each mesh are calculated using the back side Young's modulus _Ere .

  The analysis execution unit 20 repeatedly executes this temporary calculation, bending direction determination, and main calculation for each mesh. When the calculation is completed for all meshes, the analysis is completed. The analysis result is presented to the user via the input / output unit 12.

  Next, the flow of bending analysis of a laminated material by the analysis apparatus 10 of the present embodiment will be described with reference to FIG. FIG. 4 is a flowchart showing a flow of bending analysis of a laminated material. When performing a bending analysis, first, CAD data of an analysis object is converted into mesh model data (S10). Since various conventional techniques can be applied to the conversion to mesh model data, the description thereof is omitted here. The converted mesh model data is stored in the storage unit 16 as one of analysis conditions.

Further, the user inputs the Young's modulus, the applied stress condition, the wall thickness, etc. obtained in the material test (S12). The analysis device 10 stores these input data in the storage unit 16 as one of analysis conditions. At this time, as the Young's modulus, two types of Young's modulus (front-side Young's modulus E _ob ) when the laminated material is bent to the front side and Young's modulus (back-side Young's modulus E _re ) when bent to the back side are input.

If analysis conditions are set, analysis is started for each mesh. Specifically, first, provisional calculation is executed for one mesh (S14, S16). That is, using the front-side Young's modulus E _ob , the maximum surface principal stress σ1 _ob and the maximum back surface principal stress σ1 _re of the mesh are calculated. Subsequently, the bending direction determination unit 24 compares the maximum principal stresses σ1 _ob and σ1 _re on the front and back surfaces to determine the bending direction (S18). As a result of the comparison, if the surface maximum principal stress σ1 _ob is equal to or greater than the back surface maximum principal stress σ1 _re , it is determined that the bending is to the front side (S20). On the contrary, when the surface maximum principal stress σ1 _ob is smaller than the back surface maximum principal stress σ1 _re, it is determined that the bending is to the back side (S22).

If the bending direction can be determined, then this calculation is performed with the Young's modulus corresponding to the bending direction (S24). That is, when it is determined that the bending is to the front side, the stress acting on each mesh and the amount of displacement at that time are calculated with the front side Young's modulus E _ob . On the contrary, when it is determined that the bending is performed on the back side, the stress acting on each mesh and the displacement amount at that time are calculated with the back side Young's modulus _Ere . The obtained calculation result is temporarily stored in the memory in association with the identifier of the mesh.

  When temporary calculation, bending direction determination, and main calculation for one mesh are completed, calculation for another mesh is performed (S28). If calculation for all meshes is completed (S26), the calculation results for all meshes are output as analysis results, and the analysis is completed.

  As is clear from the above description, according to the present embodiment, since stress and displacement are calculated with Young's modulus corresponding to the bending direction, a more reliable bending analysis result can be obtained. Further, since the bending direction is automatically determined based on the provisional calculation result, it is not necessary for the user to determine the bending direction each time. As a result, it is possible to perform bending analysis with higher reliability and more easily.

Next, an example of the analysis result of the bending analysis using the analysis apparatus 10 will be described using a specific example. First, analysis conditions in this specific example will be briefly described. In this specific example, a laminated material 30 having a five-layer structure as shown in FIG. The laminated material 30 is obtained by laminating a nonwoven fabric 30a, glass fibers 30b, a urethane base material 30c, glass fibers 30b, and a film 30d in order from the top. And the Young's modulus of this laminated material 30 is 816.5 when bent to the front side (non-woven fabric side is concave) and 1199.0 when bent to the back side (film side is concave). That is, the back side Young's modulus _{E re} is about 1.5 times the front Young's modulus _{E ob.}

  FIG. 6 is a diagram showing an applied stress condition in this example. In this specific example, the bending deformation state when stress is applied to the rectangular analysis object 32 is analyzed. Both ends of the analysis object are constrained, and a substantially vertical stress is applied to the approximate center of the analysis object. In this specific example, the case where the applied stress is downward (that is, the case where the surface of the analysis target is pressed) and the case where the applied stress is upward (that is, the case where the back surface of the analysis target is pressed) are analyzed.

  FIG. 7 is a graph showing the result of bending analysis based on the above analysis conditions. In FIG. 7, the horizontal axis indicates the amount of displacement, and the vertical axis indicates the load applied to the analysis object. Also, the thin solid line shows the measured value when bent to the front side, the thick solid line shows the measured value when bent to the back side, the thin broken line shows the analysis result when bent to the front side, and the thick broken line shows the result when bent to the back side The analysis results are shown respectively. The displacement amount indicates the displacement amount at point A in FIG. 6, that is, the approximate center point of the laminated material.

  As is apparent from FIG. 7, the actual measurement values differ greatly between the front side bending and the back side bending. That is, it can be seen that the Young's modulus is completely different between the front side and the back side. Therefore, if the Young's modulus corresponding to the bending direction is not used, it can be easily estimated that the accuracy of the analysis result is significantly reduced. However, in this embodiment, as described above, the bending direction is determined, and the bending analysis is performed with the Young's modulus corresponding to the bending direction. As a result, as shown in FIG. 7, the analysis result according to the present embodiment can reproduce the actual measurement value with high accuracy.

  As described above, according to the present embodiment, a more reliable bending analysis of a laminated material can be performed more easily.

  In the present embodiment, the bending analysis is performed using a two-dimensional shell mesh model, but naturally the bending analysis may be performed using a three-dimensional solid mesh model. Also in this case, similarly to the above-described embodiment, the bending direction is determined based on the comparison of the main stresses on the front and back surfaces, and the stress and the displacement amount are calculated with the Young's modulus corresponding to the bending direction. However, in the case of a solid mesh model, the mesh constituting the surface of the analysis target portion is different from the mesh constituting the back surface thereof. That is, as shown in FIG. 8, the mesh constituting the surface of the specific part B of the analysis object is different from the mesh constituting the back surface of the specific part B. Therefore, when analyzing using a solid mesh model, it is necessary to specify the surface target mesh which comprises the surface of an analysis object part, and the back object mesh which comprises the back surface of an analysis object part. A method for specifying the front surface target mesh and the back surface target mesh will be described with reference to FIG. FIG. 9 is a flowchart showing the flow of specifying the target mesh. When specifying the target mesh, first, the mesh constituting the surface of the analysis target portion is first specified as the surface target mesh (S30). Subsequently, a straight line L that passes through the center of gravity of the surface target mesh and is perpendicular to the externally exposed surface of the surface target mesh is calculated (S32). Then, among the plurality of meshes constituting the back surface of the analysis target object, the mesh having the closest center of gravity to the straight line L is specified as the back surface target mesh (S34).

  If the front and back target meshes are specified, the maximum principal stress of each of the front and back target meshes is calculated as in the case of the shell mesh, and the bending direction is determined based on the comparison of the maximum principal stresses. Then, the stress and the displacement amount are calculated with Young's modulus corresponding to the bending direction.

  That is, as is clear from the above description, not only the shell mesh model but also a solid mesh model can be used for highly reliable bending analysis. In addition, the identification method of the front and back surface target mesh demonstrated here is an example, and can take another method suitably. For example, in the above description, the straight line L passes through the center of gravity of the surface target mesh, but does not necessarily pass through the center of gravity.

It is a block diagram which shows the function structure of the analyzer which is embodiment of this invention. It is a figure which shows the stress distribution of the surface of the analysis target object at the time of applying a predetermined stress. It is a figure which shows the stress distribution of the back surface of the analysis target object at the time of applying a predetermined stress. It is a flowchart which shows the flow of the bending analysis in this embodiment. It is a figure which shows an example of the laminated material which is an analysis target object. It is a figure which shows an example of analysis conditions. It is a graph which shows an example of an analysis result. It is a conceptual diagram which shows the mode of target mesh specification in the case of a solid mesh model. It is a flowchart which shows the flow of object mesh specification.

Explanation of symbols

10 analyzer, 12 output unit, 14 communication unit, 16 storage unit, 18 mesh model conversion unit, 20 analyzing unit, 22 temporary calculating unit, 24 direction determining section, 26 present calculation unit, the Young's modulus of _{E n} temporary, E _ob front side Young's modulus, E _re back side Young's modulus, σ1 _ob surface maximum principal stress, σ1 _re back surface maximum principal stress.

Claims (6)

An analysis method of a laminated material that analyzes a deformation state when a bending stress is applied to an analysis object made of a laminated material based on mesh model data virtually expressed using a computer,
Based on the mesh model data of the analysis object stored in the storage unit of the computer and the additional stress condition indicating the condition of the bending stress applied to the analysis object , the calculation unit of the computer adds an additional stress condition to the analysis object. A temporary analysis step for analyzing the deformation state when the bending stress indicated by is applied using a preset temporary Young's modulus;
A determination step for determining a bending direction of the computer based on the temporary analysis result data obtained in the temporary analysis step,
When the calculation unit of the computer is bent to the front side Young's modulus or the back side, which is the Young's modulus when the laminated material stored in the storage unit of the computer is bent to the front side according to the bending direction determined in the determination step A selection step of selecting any one of the backside Young's moduli of
An analysis step in which the calculation unit of the computer performs a bending analysis of the laminated material using the Young's modulus selected in the selection step;
A method for analyzing a laminated material, comprising: A method for analyzing a laminated material according to claim 1,
In the determination step , the calculation unit of the computer
Based on the provisional analysis result data, a principal stress calculation step for calculating the maximum principal stress on the surface of the analysis target portion and the maximum principal stress on the back surface of the analysis object,
Comparing the calculated maximum principal stress on the front surface with the maximum principal stress on the back surface;
Is performed, and the surface side with the highest principal stress is determined as the bending direction. A method for analyzing a laminated material according to claim 2,
When the mesh model is a shell mesh model, in the principal stress calculation step , the calculation unit of the computer
Analysis method of the product layer material you and calculates the front and back surfaces of the maximum principal stress in the shell mesh constituting an analysis target part, respectively. A method for analyzing a laminated material according to claim 2,
When the mesh model is a solid mesh model, in the principal stress calculation step , the calculation unit of the computer
Further executing a target mesh specifying step for specifying a front surface target mesh that configures the surface of the analysis target portion and a back surface target mesh that configures the back surface of the analysis target portion,
A method for analyzing a laminated material, wherein the maximum principal stresses of the externally exposed surface of the front surface target mesh and the externally exposed surface of the back surface target mesh are respectively calculated. A method for analyzing a laminated material according to claim 4,
In the target mesh identification step , the computer calculation unit includes:
Calculate a straight line that passes through the center of gravity of the surface target mesh and is perpendicular to the externally exposed surface of the surface target mesh,
A method for analyzing a laminated material, wherein a mesh closest to a calculated straight line is specified as a back surface target mesh among meshes constituting a back surface of a mesh model. A method for analyzing a laminated material according to any one of claims 1 to 5,
In the temporary analysis step , the calculation unit of the computer analyzes either the front-side Young's modulus or the back-side Young's modulus as a temporary Young's modulus.

Images