Structural analysis method, program, recording medium, and structural analysis apparatus for anisotropic materials

Abstract

This technology enables the numerical analysis of the effect that anisotropic materials have on the overall rigidity of a structure when the material is anisotropic. [Solution] A structural analysis method for an anisotropic material according to one aspect of the present invention comprises the steps of: assigning calculation points to structural data (S11); assigning material properties including anisotropy to structural data (S12); assigning load points, support points, and arbitrary points to the calculation points (S13); and determining an index (A) based on the ratio of a first work required for the displacement of the load point when the material axis vector at the arbitrary point is set according to the anisotropy of the material properties, and a second work required for the displacement of the load point when the direction of the material axis vector is rotated to coincide with the displacement direction of the load point. * The steps involve calculating the index (A) while changing an arbitrary point. * ) is calculated, and the index (A) in the structural data is calculated. * The system comprises the steps of calculating the distribution of (S14-S16) and

Description

[Technical Field]

[0001] The present invention is useful for structural analysis methods, programs, recording media, and structural analysis apparatus for anisotropic materials. [Background technology]

[0002] In this invention, "isotropy" means that the physical properties of a material do not differ essentially depending on the direction, and "isotropic material" means a material having the above-mentioned "isotropy". In this invention, "anisotropy" means that the physical properties of a material differ essentially depending on the direction, and "anisotropic material" means a material having the above-mentioned "anisotropy".

[0003] When designing structures, structural optimization methods that minimize stress using stress as an indicator, or maximize stiffness using stiffness as an indicator, are widely used. General optimization calculations are useful in that they derive the optimal solution within given constraints. However, the reasons why the structure is optimal, and the process by which that structure is derived, are often unclear.

[0004] One way to solve this problem is U * A method has been proposed to analyze the quality of a structure from the perspective of load transmission by introducing a load transmission index called (Ustar). For example, Japanese Patent Publication No. 2019-133600 (Patent Document 1) describes the index U * This invention discloses an apparatus and method for performing optimization calculations of a structure by representing the clarity of the force transmission paths of the structure and performing calculations to improve the clarity of said force transmission paths. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2019-133600 [Overview of the project] [Problems that the invention aims to solve]

[0006] The analytical methods described in the above-mentioned literature assume that the structure is made of isotropic material. On the other hand, in the case of anisotropic material, such as composite material containing reinforcing materials like fibers, physical properties such as stiffness differ depending on the direction. Until now, no method has been considered for evaluating the effect that the anisotropy of anisotropic material has on the overall stiffness of a structure when the structure is made of anisotropic material.

[0007] The object of the present invention is to enable the analysis of the effect that anisotropic materials have on the overall rigidity of a structure, when such materials are used in the structure, through numerical calculations. [Means for solving the problem]

[0008] (1) A structural analysis method according to one aspect of the present invention is a structural analysis method performed by a computer, comprising the steps of: assigning calculation points to structural data; assigning material properties including anisotropy to structural data; assigning load points, support points, and arbitrary points to the calculation points; calculating a first index based on the ratio of a first work required for the displacement of a load point when the material axis vector at the arbitrary point is set according to the anisotropy of the material properties, and a second work required for the displacement of a load point when the direction of the material axis vector is rotated to coincide with the displacement direction of the load point; and calculating the distribution of the first index in structural data by calculating the first index while changing the arbitrary point.

[0009] With this configuration, the first index can represent the change in the contribution of an anisotropic material to the overall stiffness of a structure at any point in the structure to which the material axis vector is assigned, depending on the direction of the material axis vector. By calculating the first index while changing the arbitrary point using a computer, the distribution of the first index in the structure data can be calculated. Therefore, when a structure is made of anisotropic material, the effect that the anisotropic material has on the overall stiffness of the structure can be analyzed by numerical calculation.

[0010] In general, in anisotropic materials, physical properties such as stiffness differ fundamentally depending on the direction. In the above configuration, the "material axis vector" may be a vector that shows the direction dependence of the physical properties. For example, in the case of fiber-reinforced composite materials, the orientation vector representing the orientation of the reinforcing fibers can be adopted as the "material axis vector".

[0011] (2) A structural analysis method according to one aspect of the present invention further comprises the step of calculating the distribution of load transfer indices in structural data by changing the arbitrary point, while setting the material axis vectors according to anisotropy, and calculating a load transfer index based on the ratio of the work required for the displacement of the load point when an arbitrary point is constrained to the work required for the displacement of the load point when the arbitrary point is not constrained.

[0012] This configuration allows for the calculation of the distribution of load transfer indices in structural data. Generally, the load transfer path within a structure can be considered to lie along a ridge where the stiffness changes gradually from the load point to the support point. By drawing a line with a gentle slope of the load transfer index distribution from the load point to the support point, the load transfer path within the structure can be analyzed.

[0013] (3) A structural analysis method according to one aspect of the present invention further comprises the step of calculating the distribution of the second index in structural data by calculating a second index which is the product of a first index and a load transfer index for any point.

[0014] With this configuration, the second index can represent the magnitude of the change in the overall stiffness of a structure by changing the direction of the material axis vector at any point in the structure data, when the structure is made of anisotropic material. By calculating the second index while changing arbitrary points using a computer, the distribution of the second index in the structure data can be calculated. Therefore, it is possible to select locations within the structure where changing the direction of the material axis vector is effective in increasing the overall stiffness of the structure.

[0015] (4) A program relating to one aspect of the present invention is a program that causes a computer to execute the structural analysis method of an anisotropic material described in any of (1) to (3) above.

[0016] (5) A recording medium according to one aspect of the present invention is a computer-readable recording medium on which the program described in (4) above is recorded.

[0017] (6) A structural analysis apparatus according to one aspect of the present invention comprises: a data acquisition unit that accepts structural data and material properties including anisotropy; an index calculation unit that assigns calculation points to the structural data, assigns load points, support points, and arbitrary points to the calculation points, assigns material properties to the structural data, and calculates an index relating to the stiffness of the structural data; and an output unit that outputs the results calculated by the index calculation unit. The index calculation unit is configured to calculate a first index based on the ratio of a first work required for the displacement of a load point when the material axis vector at an arbitrary point assigned to the structural data is set according to the anisotropy of the material properties, and a second work required for the displacement of a load point when the direction of the material axis vector is rotated to coincide with the displacement direction of the load point, while changing the arbitrary point, and to calculate the distribution of the first index in the structural data.

[0018] With this configuration, the first index can represent the change in the contribution of an anisotropic material to the overall stiffness of a structure at any point in the structure to which the material axis vector is assigned, depending on the direction of the material axis vector. The index calculation unit calculates the first index while changing the arbitrary point, thereby calculating the distribution of the first index in the structure data. Therefore, when a structure is made of anisotropic material, the effect that the anisotropic material has on the overall stiffness of the structure can be analyzed by numerical calculation.

[0019] (7) In a structural analysis apparatus according to one aspect of the present invention, the index calculation unit is further configured to calculate a load transfer index based on the ratio of the work required for the displacement of the load point when an arbitrary point placed in the structural data is constrained, and the work required for the displacement of the load point when an arbitrary point of the anisotropic material is not constrained, while changing the arbitrary point, with the material axis vector set according to anisotropy, and to calculate the distribution of the load transfer index in the structural data.

[0020] This configuration allows for the calculation of the distribution of load transfer indices in structural data. Generally, the load transfer path within a structure can be considered to lie along a ridge where the stiffness changes gradually from the load point to the support point. By drawing a line with a gentle slope of the load transfer index distribution from the load point to the support point, the load transfer path within the structure can be analyzed.

[0021] (8) In a structural analysis apparatus according to one aspect of the present invention, the index calculation unit is further configured to calculate the distribution of the second index in the structural data by calculating a second index which is the product of the first index and the load transfer index for any arbitrary point.

[0022] With this configuration, the second index can represent the magnitude of the change in the overall stiffness of a structure by changing the direction of the material axis vector at any point in the structure data, when the structure is made of anisotropic material. The index calculation unit calculates the second index while changing the arbitrary point, thereby calculating the distribution of the second index in the structure data. Therefore, it is possible to select locations in the structure where changing the direction of the material axis vector is effective in increasing the overall stiffness of the structure. [Effects of the Invention]

[0023] According to the present invention, when a structure is made of an anisotropic material, the effect that the anisotropic material has on the overall rigidity of the structure can be analyzed by numerical calculation. [Brief explanation of the drawing]

[0024] [Figure 1] This is a first schematic diagram showing the state in which a load is applied to a structure that is the target of the analysis method according to an embodiment of the present invention. [Figure 2] This is a second schematic diagram showing the state in which a load is applied to a structure that is the target of the analysis method according to an embodiment of the present invention. [Figure 3] This figure shows the change in index A*. [Figure 4] This is a functional block diagram showing an example configuration of a structural analysis device according to an embodiment of the present invention. [Figure 5] Figure 4 is a block diagram showing an example of the hardware configuration of the analysis device. [Figure 6] This flowchart shows the process for calculating the distribution of index A* in anisotropic structure data using a structural analysis method according to an embodiment of the present invention. [Figure 7] This flowchart shows the process for calculating the distribution of index U* in anisotropic structure data using a structural analysis method according to an embodiment of the present invention. [Figure 8] This flowchart shows the process for calculating the distribution of index F* in anisotropic structure data using a structural analysis method according to an embodiment of the present invention. [Figure 9] This is a diagram showing the first model of the structure to be analyzed. [Figure 10] This figure shows a second model of the structure being analyzed. [Figure 11] This figure shows the distribution of the index U* in the structure under analysis, calculated using the first model. [Figure 12] This figure shows the distribution of index A* in the structure under analysis, calculated using the first model. [Figure 13] This figure shows the distribution of index F* in the structure under analysis, calculated using the first model. [Figure 14] This figure shows the changes to the model shown in Figure 9. [Figure 15] This figure shows the distribution of the index U* in the model shown in Figure 14. [Figure 16] This figure shows the distribution of index A* in the model shown in Figure 14. [Figure 17] This figure shows the distribution of the index U* in the second model shown in Figure 10. [Figure 18] This figure shows the distribution of index A* in the second model. [Figure 19] This figure shows the distribution of the index F* in the second model shown in Figure 10. [Figure 20] This figure shows the changes to the model shown in Figure 10. [Figure 21] This figure shows the distribution of the index U* in the model shown in Figure 19. [Figure 22] This figure shows the distribution of index A* in the model shown in Figure 19. [Modes for carrying out the invention]

[0025] Embodiments of the present invention will be described in detail with reference to the drawings. Note that identical or corresponding parts in the drawings are denoted by the same reference numerals, and their descriptions will not be repeated.

[0026] [overview] The structural analysis method for anisotropic materials according to an embodiment of the present invention evaluates the load transmission path considering the anisotropy of the material and the degree of influence of anisotropy on the overall stiffness of the structure. For this purpose, the embodiment of the present invention introduces a new index A * (Astar: A-star) and F * A structural analysis method using (Fstar) is proposed. Index A * and index F * These correspond to the "first indicator" and the "second indicator" in the present invention, respectively.

[0027] [Indicator A * [Definition] FIG. 1 is a first schematic diagram showing a state in which a load is input to a structure that is an object of an analysis method according to an embodiment of the present invention. In FIG. 1, the entire structure 1 is represented by points A, B, C, and three-dimensional springs connecting two of these three points. When an isotropic material is assigned to the structure, the three-dimensional spring exhibits isotropy (isotropic spring), and when an anisotropic material is assigned to the structure, the three-dimensional spring exhibits anisotropy (anisotropic spring). Point A is a load point, point B is a support point, and point C is an arbitrary point.

[0028] In an embodiment of the present invention, an anisotropic material is employed as the material assigned to the structure 1 to be analyzed. An anisotropic material has direction dependence regarding physical properties. As an example, when the material of the structure 1 is a composite material mainly including a base material and a reinforcing material, anisotropy occurs in the physical properties of the structure 1 due to the orientation distribution of the reinforcing material. When the composite material is a fiber-reinforced resin, the orientation direction of the fiber as the reinforcing material affects the anisotropy of the physical properties of the structure 1.

[0029] The physical properties of the structure 1 at point C have direction dependence. The vector n is a vector indicating the direction of the material axis 2 of the structure 1 at point C. The direction of the material axis 2 at point C may be involved in the direction dependence of the physical properties at point C. For example, when the structure 1 is a fiber-reinforced resin, the direction of the material axis vector can be set to the orientation direction of the fiber as the reinforcing material.

[0030] The loads at points A, B, and C are represented as P A , P B , P C and the displacements at points A, B, and C are represented as d A , d B , d C . The relationship between the load P A , P B , P C and the displacement d A , d B , d C is represented by Equation (1).

[0031]

Equation

[0032] In equation (1), K represents the internal stiffness of structure 1. Internal stiffness can be considered as the strength of a spring connecting any two of points A, B, and C.

[0033] Since point B is a support point, the displacement d B = 0. On the other hand, point C is not constrained. From equation (1), the load P A This can be expressed by the following equation (2).

[0034]

number

[0035] Work done on the displacement of point A (load P) A Let U represent the work done by the vectors. The work U is expressed by equation (3) below, using the relationship shown in equation (2). In equation (3), the symbol "·" represents the dot product of the vectors.

[0036]

number

[0037] Figure 2 is a second schematic diagram showing the state in which a load is applied to a structure that is the target of the analysis method according to an embodiment of the present invention. It is assumed that the direction of the material axis 2 is equal to the load direction at point C. That is, as shown in Figure 2, the material axis vector is rotated by an angle Δθ from the original state shown in Figure 1 to coincide with the displacement direction of the load (load direction) at point A. In this case, the internal stiffness of structure 1 is represented as K(Δθ).

[0038] The load at points A, B, and C is P'. A ,P' B ,P' C This is expressed as follows, and the displacement at points A, B, and C is d. A ,d' B ,d' CThis is expressed as follows. Similar to equation (1), the load P' A ,P' B ,P' C and displacement d A ,d' B ,d' C The relationship between them is expressed by equation (4).

[0039]

number

[0040] Since point B is a support point, the displacement d' B = 0. As in the state shown in Figure 1, point C is not constrained. Using equation (4), the load P' A This is expressed by the following equation (5). Note that K AA (Δθ)=K AA That is the case.

[0041]

number

[0042] In the state of structure 1 shown in Figure 2, the work required for the displacement of point A (load P') A Let U' represent the work done by the process. Using the relationship shown in equation (5), the work U' can be expressed by the following equation (6).

[0043]

number

[0044] By rotating the material axis vector, the work required to displace point A changes by (U'-U). From equations (3) and (6), (U'-U) is expressed by the following equation (7).

[0045]

number

[0046] By dividing (U'-U), expressed in equation (7), by U, the change in work required for the displacement of point A is made dimensionless. Equation (7) is transformed into equation (8) below.

[0047]

number

[0048] Index A * It is defined by the following equation (9) using (U' / U-1) above.

[0049]

number

[0050] As shown in equation (9), index A * This corresponds to a first index based on the ratio (U' / U) of the first work U required for the displacement of a load point (point A) when the material axis vector at an arbitrary point (point C) of structure 1 to which an anisotropic material is assigned is set according to the orientation of the reinforcing material contained in the anisotropic material, and the second work U' required for the displacement of the load point when the material axis vector is rotated to coincide with the displacement direction of the load point.

[0051] [Indicator A * [Meaning] Figure 3 shows indicator A * This figure shows the change in the index A. The hyperbolic tangent function (tanh function) takes values ​​from -1 to 1, so index A * The range of values ​​is -1 * < 1. If (U' / U-1) > 0, then index A * The range of values ​​is 0 * If <1 and (U' / U-1) < 0, then index A * The range of values ​​is -1 * It becomes < 0.

[0052] ​​​When (U’ / U - 1)>0 (i.e., when U’>U), it means that by aligning the direction of the material axis vector at any point of the structure with the direction of the displacement at the load point, the work required for the displacement of the load point increases. In other words, when the value of the index A * at any point is within the range of 0 < A * < 1, it means that at that arbitrary point, when the orientation of the material involved in anisotropy coincides with the direction of the displacement at the load point, the contribution to the overall stiffness of the structure 1 at that point increases.

[0053] When U’ < U, it means that by aligning the direction of the material axis vector at any point of the structure with the direction of the displacement at the load point, the work required for the displacement of the load point decreases. In other words, when the value of the index A * is within the range of -1 < A * < 0, it means that at that arbitrary point, when the orientation of the reinforcing material contained in the anisotropic material coincides with the direction of the displacement at the load point, the contribution to the overall stiffness of the structure 1 at that point decreases.

[0054] Thus, the index A * can represent the change in the contribution to the overall stiffness of the structure 1 according to the direction of the material axis vector (the orientation of the reinforcing material contained in the anisotropic material) at any point of the structure to which the anisotropic material is assigned.

[0055] [Definition of index F * As an index that can represent the load transfer path inside the structure, U * has been proposed. The index U * , which is a load transfer index, indicates the strength of the connection with the load point for any point inside the structure.

[0056] ​Returning to Figure 1, let U be the work required to displace point A when point C of structure 1, to which the anisotropic material is assigned, is not constrained, and let U' be the work required to displace point A when point C of structure 1, to which the anisotropic material is assigned, is constrained. Note that the direction of the material axis vector at point C is set according to the orientation of the reinforcing material contained in the anisotropic material, and no processing such as rotation of the direction of the material axis vector is performed.

[0057] Index U * This is an index based on the ratio of work U' to work U (U' / U), and U * It is defined as =1-U / U'. Using the relationship between load and displacement at points A, B, and C (see equation (1)), the index U * This can be expressed as shown in equation (10) below.

[0058]

number

[0059] Index U * It takes a value between 0 and 1. When point C, which is close to the support point, is constrained, U and U' become approximately equal, and the index U * The value will be close to the minimum value of 0. On the other hand, if point C, which is close to the load point, is constrained, U' will be a sufficiently large value with respect to U, and the index U * The value will be close to the maximum value of 1. Therefore, by drawing a line with a gentle slope of the load transfer index distribution from the load point to the support point, the load transfer path in structure 1 to which anisotropic material is assigned can be analyzed, and the points that contribute significantly to the overall stiffness of structure 1 can be identified from the obtained load transfer path.

[0060] Index U * For comparison, index A * Work U, internal stiffness K, displacement d A It is expressed using the following. From equations (8) and (9), the index A * It can be expressed according to the following equation (11).

[0061]

number

[0062] Equation (10) represents the strength of the bond between point A and point C due to an isotropic spring. In other words, the index U * This can be considered an index representing the magnitude of the spring constant of the isotropic spring connecting point A and point C. On the other hand, equation (11) represents the directional dependence of the coupling strength of the anisotropic spring connecting point A and point C. That is, index A * This represents the change in the spring constant, which indicates how much the spring constant changes in response to the rotation of the anisotropy direction of the anisotropic spring.

[0063] In the embodiment of the present invention, the index U * and indicator A * The combined index F * The following is proposed: The index F * The indicator U * and indicator A * It is the product of the two.

[0064]

number

[0065] Index F * The sign is index A * This coincides with the sign of the index F. Therefore, the index F * The sign indicates whether the contribution to the overall stiffness of structure 1 increases or decreases when the orientation of the reinforcing material contained in the anisotropic material is aligned with the direction of displacement at the load point at any point in structure 1. Index F * The absolute value of indicates the degree of change in the contribution to the overall stiffness of structure 1 when the orientation of the reinforcing material contained in the anisotropic material is aligned with the direction of displacement at the load point at any given point.

[0066] [Configuration of the analysis device] Figure 4 is a functional block diagram showing an example of the configuration of a structural analysis apparatus according to an embodiment of the present invention. The analysis apparatus 10 shown in Figure 4 is an apparatus for performing a structural analysis method according to an embodiment of the present invention, and is realized by executing a program using hardware that conforms to a general-purpose computing architecture. For example, the analysis apparatus 10 having the configuration shown in Figure 4 is realized by a computer executing analysis software that implements the finite element method.

[0067] As shown in Figure 4, the analysis device 10 comprises a control unit 11, a data acquisition unit 12, a storage unit 14, an index calculation unit 16, and an output unit 18.

[0068] The control unit 11 controls the overall operation of the analysis device 10. The data acquisition unit 12 acquires data related to the structure to be analyzed (hereinafter referred to as "structure data"). Structural data can be acquired in the form of, for example, CAD data created by 3D CAD (Computer Aided Design). The data acquisition unit 12 functions as an input unit that accepts data related to anisotropic materials (hereinafter referred to as "anisotropic material data").

[0069] The storage unit 14 stores data acquired by the data acquisition unit 12, various parameters necessary for calculating indicators, and indicators calculated by the indicator calculation unit 16.

[0070] The index calculation unit 16 generates calculation points in the structural data acquired by the data acquisition unit 12, and assigns load points, support points, and arbitrary points to the generated calculation points. Note that when applying methods such as the finite element method, the above "calculation points" can be replaced with "nodes." Based on the anisotropic material data acquired by the data acquisition unit 12, the structural data, and the load points, support points, and arbitrary points set in the structural data, the index calculation unit 16 calculates index A * ,F * ,U * Calculate.

[0071] The index calculation unit 16 calculates an index A as a first index regarding the rigidity of the structure data (hereinafter referred to as "anisotropic structure data") to which anisotropic material data is assigned. * The index calculation unit 16 calculates the index A while changing an arbitrary point C. * By calculating the index A in the anisotropic structure data, * the distribution of the index A is calculated. Similarly, the index calculation unit 16 calculates an index F as a second index regarding the rigidity of the anisotropic structure data. * For this purpose, the index calculation unit 16 calculates an index U which is a load transfer index of the anisotropic structure data. *

[0072] The index calculation unit 16 calculates the index U while changing an arbitrary point C. * By calculating the index U in the anisotropic structure data, * the distribution of the index U is calculated. The work U used for the calculation of the index U is the same as the work U used for the calculation of the index A. * The index calculation unit 16 calculates an index F as a second index which is the product of the index A * and the index U. * * *

[0073] The index A and the index U are calculated for all points C necessary for the analysis of the anisotropic structure data. Therefore, by calculating the index F for each of a plurality of points, * the index calculation unit 16 calculates the distribution of the index F in the anisotropic structure data. * Here, "all points necessary for the analysis of the anisotropic structure data" means all the nodes selected as necessary for the purpose of analysis among the nodes when applying a method such as the finite element method. * *

[0074] The output unit 18 outputs the index A * , F * , U * calculated by the index calculation unit 16. The output unit 18 outputs the index A * , F* ,U * It can output the index A stored in the memory unit 14. * ,F * ,U * It can output indicator A. Furthermore, under the control of the control unit 11, the output unit 18 outputs indicator A. * ,F * , U * It is also possible to selectively output one or more of these.

[0075] The control unit 11 uses the post-processing function of the finite element analysis software to determine index A in the anisotropic structure data. * Distribution map of indicator U * Distribution map of and index F * The output unit 18 outputs data for drawing at least one of the distribution maps on a display (not shown).

[0076] Next, the configuration of the index calculation unit 16 will be described in detail. The index calculation unit 16 consists of a finite element method calculation unit 21, a stiffness matrix calculation unit 22, a position change unit 23, a work / displacement calculation unit 24, and A * Calculation unit 25 and U * Calculation unit 26 and F * It includes a calculation unit 27.

[0077] The finite element method calculation unit 21 calculates the deformation of the structure under analysis, which is an elastic body, using the finite element method. The stiffness matrix calculation unit 22 uses the finite element method calculation unit 21 to calculate the stiffness matrix K using the inspection load method. AC ,K AC (Δθ) is determined. The position changing unit 23 changes the position of point C so that it sequentially traverses all points C necessary for the analysis of the structure.

[0078] The work / displacement calculation unit 24 calculates the deformation of the structure when a displacement is applied to point A while point B is fixed, using the finite element method, and calculates the work U and the displacement amount (d) of all points. A d C ,d' CThe work U is calculated as follows: work U is the work required for the displacement of point A when point C is not constrained and the material axis vector at point C is set according to the orientation of the reinforcing material contained in the anisotropic material.

[0079] A * The calculation unit 25 calculates the work U and the components K of the stiffness matrix. AC ,K AC (Δθ), displacement d A d C ,d' C From equations (8) and (9), the index A * Calculate the value of U. * The calculation unit 26 calculates the work U at point C and the components K of the stiffness matrix. AC and displacement d A d C Therefore, according to equation (10), the load transfer index U * Calculate the value of F. * The calculation unit 27 is A * Index A calculated by the calculation unit 25 * and U * Load transfer index U calculated by calculation unit 26 * Multiplying by this, the index F * Calculate.

[0080] The configuration shown in Figure 4 is an example of an analysis apparatus according to an embodiment of the present invention. Therefore, the analysis apparatus 10 may include additional components.

[0081] Figure 5 is a block diagram showing an example of the hardware configuration of the analysis device shown in Figure 4. The hardware shown in Figure 5 executes the software to configure the analysis device 10 as shown in Figure 4.

[0082] The analysis device 10 comprises a processor 31, a primary storage device 32, a secondary storage device 33, an external device interface 34, an input interface 35, an output interface 36, a communication interface 37, and a bus 38. The processor 31, the primary storage device 32, and other elements exchange data, signals, etc., through the bus 38.

[0083] The processor 31 processes programs and data stored in the primary storage device 32. The primary storage device 32 stores programs executed by the processor 31 and data that are referenced. In some cases, DRAM (Dynamic Random Access Memory) may be used as the primary storage device 32. The processor 31 implements the control unit 11 and the index calculation unit 16 shown in Figure 4.

[0084] The secondary storage device 33 stores programs and data non-volatilely. In some cases, non-volatile memory such as an HDD (Hard Disk Drive) or SSD (Solid State Drive) may be used as the secondary storage device 33. Therefore, the secondary storage device 33 corresponds to a computer-readable recording medium that stores programs executed by the computer. The secondary storage device 33 realizes the storage unit 14 shown in Figure 4.

[0085] The external device interface 34 is used when connecting external devices to the analysis device 10, etc. The external device interface 34 is, for example, a USB (Universal Serial Bus) interface.

[0086] The input interface 35 is used to connect input devices such as a keyboard 41 and a mouse 42. The input interface 35 accepts user operations and user input through these input devices.

[0087] The data acquisition unit 12 shown in Figure 4 is realized by either or both of the input interface 35 and the external device interface 34.

[0088] The output interface 36 is used to connect an output device, such as a display 43. The output interface 36 implements the output unit 18 shown in Figure 4.

[0089] The communication interface 37 is used for the analysis device 10 to communicate with external devices. For example, the communication interface 37 is used for communication of the analysis device 10 over a network. Communication with external devices may be via wireless or wired communication.

[0090] Optionally, the analysis device 10 may have an optical drive. The optical drive reads programs stored on a recording medium that permanently stores computer-readable programs (for example, an optical recording medium such as a DVD (Digital Versatile Disc)). The programs read from the recording medium may be installed on a secondary storage device 33 or the like. In addition, various programs executed by the analysis device 10 may be downloaded from a server device on a network and installed on the analysis device 10.

[0091] [Structural analysis method] The structural analysis method according to the embodiment of the invention is index A * ,U * ,F * This includes calculating the distribution of [the value]. Figure 6 shows the index A in anisotropic structure data according to the structural analysis method of the embodiment of the present invention. * This is a flowchart showing the process for calculating the distribution.

[0092] In step S11, the index calculation unit 16 assigns calculation points to the structural data. In step S12, the index calculation unit 16 assigns material properties, including anisotropy, to the structural data. In step S13, the index calculation unit 16 assigns load points, support points, and arbitrary points to the calculation points assigned to the anisotropic structural data in step S11.

[0093] In step S14, the index calculation unit 16 (see Figure 4) calculates the displacement (d) of points A and C when the material axis vector at point C is set according to the orientation of the reinforcing material contained in the anisotropic material. A d CThe work U required for the displacement of point A is calculated using the finite element method with the overall stiffness matrix. Furthermore, in step S14, the index calculation unit 16 calculates the displacement (d') of points A and C when the direction of the material axis vector at point C is rotated to coincide with the direction of the displacement at point A. A ,d' C This is calculated using the finite element method with the global stiffness matrix.

[0094] In step S15, the index calculation unit 16 calculates the component K of the stiffness matrix using the inspection load method. AC ,K AC (Δθ) is calculated. In step S16, the index calculation unit 16 calculates the work U and the component K of the stiffness matrix. AC ,K AC (Δθ) and displacement (d A d C ),(d' A ,d' C ) and, according to equations (8) and (9), index A * We will calculate this. Note that the inspection load method is publicly known, so a detailed explanation will not be repeated here.

[0095] In step S17, the index calculation unit 16 calculates index A for all points C necessary for the analysis of the structure. * Determine whether or not the calculation was performed. Indicator A * If there are still points to calculate (NO in step S14), the process proceeds to step S18. In step S18, the index calculation unit 16 updates point C. The process returns to step S14.

[0096] On the other hand, for all points C, index A * If calculated (YES in step S17), the index calculation unit 16 calculates index A * The calculation is completed. Change point C while performing index A * By repeating the calculation, the index A in anisotropic structure data is obtained. * The distribution is calculated.

[0097] Figure 7 shows the index U in anisotropic structure data obtained by the structural analysis method according to an embodiment of the present invention.* This is a flowchart showing the process for calculating the distribution.

[0098] In step S21, the index calculation unit 16 calculates the displacement (d) of points A and C when the material axis vector at point C is set according to the orientation of the reinforcing material contained in the anisotropic material. A d C The work U required for the displacement of point A is calculated using the finite element method with the overall stiffness matrix. In step S22, the index calculation unit 16 calculates the component K of the stiffness matrix using the inspection load method. AC Calculate.

[0099] In step S23, the index calculation unit 16 calculates the work U and the component K of the stiffness matrix. AC and displacement (d A d C ) From this, according to equation (10), the index U * Calculate.

[0100] In step S24, the index calculation unit 16 calculates the index U for all points C necessary for the analysis of the structure. * Determine whether or not the calculation was performed. Index U * If there are still points to calculate (NO in step S24), the process proceeds to step S25. In step S25, the index calculation unit 16 updates point C. The process returns to step S21. Meanwhile, index U is calculated for all points C necessary for the analysis of the structure. * If the calculation is performed (YES in step S24), the index calculation unit 16 calculates the index U * The calculation is completed. Change point C while performing index U * By repeating the calculation, the index U in anisotropic structure data is obtained. * The distribution is calculated.

[0101] Note that index A shown in Figure 6 * By this calculation, the displacement (d A d C ), work U and components K of the stiffness matrix ACIf this is required, the processing in steps S21 and S22 can be omitted. For example, the storage unit 14 stores the displacement (d A d C ), work U and components K of the stiffness matrix AC If the data is stored, in step S23, the index calculation unit 16 retrieves from the storage unit 14 the work U for each of the multiple points C and the components K of the stiffness matrix. AC and displacement (d A d C ) read out and, according to equation (10), index U * Calculate.

[0102] Furthermore, the index calculation unit 16 calculates the index U in the anisotropic structure data from the load point toward the support point. * The load transfer path in the structure may be determined by drawing a line where the slope of the distribution is gentle.

[0103] Figure 8 shows the index F in anisotropic structure data obtained by the structural analysis method according to an embodiment of the present invention. * This is a flowchart showing the process for calculating the distribution.

[0104] In step S31, the index calculation unit 16 calculates index A at point C. * and index U * The product of these gives the index F * The index calculation unit 16 calculates the index F for all points C necessary for the analysis of the structure. * Determine whether or not the index F has been calculated. * If there are still points for which the index U needs to be calculated (NO in step S32), the process proceeds to step S33. In step S33, the index calculation unit 16 updates point C. The process returns to step S31. Meanwhile, the index U is calculated for all points C necessary for the analysis of the structure. * If the calculation is performed (YES in step S32), the index calculation unit 16 calculates the index F * The calculation is completed. Change point C while adjusting index F * By repeating the calculation, the index F in anisotropic structure data is obtained. *The distribution is calculated.

[0105] [Example of structural analysis] Figure 9 shows the first model of the structure to be analyzed. A fiber-reinforced resin plate was adopted as the structure to be analyzed. The analysis model shown in Figure 9 is a square structure, and arrow 2A represents the fiber orientation (material axis vector at an arbitrary point). In the first model, the fiber orientation is aligned in the Y-axis direction (90° to the X-axis). The structure to be analyzed is a two-dimensional square region of 10 × 10 elements, and the existence of thickness in the Z-axis direction in Figure 9 is not considered.

[0106] The left end is completely displacement-constrained, and the center of the right end is the load point. The load point is displaced to the right (+X direction). In other words, a tensile load is applied to the structure. At this time, the stiffness in the X direction of each element is k = 1.96 × 10⁻⁶. 3 Let the stiffness be [N / m], and the stiffness in the Y direction be k = 6.56 × 10⁻⁶. 3 The elastic modulus is given as [N / m]. Furthermore, the elastic modulus in the X direction for each element is set to 5.03 [GPa], and the elastic modulus in the Y direction is set to 116.14 [GPa].

[0107] Figure 10 shows a second model of the structure under analysis. Similar to the first model, a fiber-reinforced resin plate was used as the structure under analysis. The analysis model shown in Figure 10 is a square structure, and arrow 2B represents the fiber orientation (corresponding to the material axis vector at an arbitrary point). In the second model, the fiber orientation is aligned in the direction of 0° with respect to the X-axis direction. The structure under analysis in Figure 10 is a two-dimensional square region of 10 × 10 elements, and the existence of thickness in the Z-axis direction in Figure 10 is not considered.

[0108] The leftmost element is fully displacement-constrained, and the lower right vertex is designated as the load point. The load point is then displaced downwards (in the -Y direction). In other words, a shear load is applied to the structure. At this time, the stiffness in the X direction of each element is k = 6.56 × 10⁻⁶. 2 Let the stiffness be [N / m], and the stiffness in the Y direction be k = 2.91 × 10⁻⁶. 2The elastic modulus is given as [N / m]. Furthermore, the elastic modulus in the X direction for each element is set to 116.14 [GPa], and the elastic modulus in the Y direction is set to 5.03 [GPa].

[0109] Figure 11 shows the index U for the structure under analysis, calculated using the first model. * This figure shows the distribution of [the index U]. * The broken lines shown in the distribution diagram represent the load transfer paths obtained by drawing lines with gentle slopes in the distribution of load transfer indices.

[0110] Figure 12 shows the index A of the structure under analysis, calculated using the first model. * This figure shows the distribution of index A shown in Figure 12. * The distribution map shows where the contribution to the stiffness of the structure under analysis increases or decreases by changing the orientation of the fibers in the fiber-reinforced resin. Region 101, enclosed by a dashed line, is the region near the load point. In region 101, index A * The value indicates a positive value. Indicator A directly below the load point. * The value is the largest.

[0111] Figure 13 shows the index F of the structure under analysis, calculated using the first model. * This is a figure showing the distribution of the index F shown in Figure 13. * The distribution map shows the distribution of the change in the amount of contribution (signed) to the stiffness of the structure under analysis due to the change in fiber orientation. Note that region 101A, enclosed by a dashed line in Figure 13, is the region near the load point and includes region 101 shown in Figure 12. Indicator F in region 101A * It is a positive value. And the index F in the region near the load point. * The value is large.

[0112] Figure 14 shows the modification of the model shown in Figure 9. The region 101B enclosed by the dashed line is the region near the load point and corresponds to region 101A shown in Figure 13. Arrow 2C indicates the fiber orientation in region 101B. Arrow 2A indicates the fiber orientation in the model shown in Figure 9. As can be seen from the comparison between arrows 2A and 2C, the fiber orientation in region 101B is rotated by 90° relative to the original orientation. In this case, the stiffness in the X direction of each element in region 101B is k = 6.56 × 10⁻⁶. 3 Let the stiffness be [N / m], and the stiffness in the Y direction be k = 1.96 × 10⁻⁶. 3 It is expressed as [N / m].

[0113] Figure 15 shows the index U in the model shown in Figure 14. * This figure shows the distribution of . Figure 16 shows index A in the model shown in Figure 14. * This figure shows the distribution of [the index]. In Figure 15, the index U * The broken line shown in the distribution diagram represents the load transfer path obtained by drawing a line with a gentle slope in the distribution of the load transfer index. By aligning the fiber orientation in region 101B shown in Figure 14 with the displacement direction of the load point, the load transfer path changes to a path along the fiber direction from the load point. As shown in Figure 16, index A * This changes in the positive direction in the region 101C (shown by the dashed line) on the fully displacement-constrained side of the structure. In other words, by aligning the fiber orientation in the region near the load point with the displacement direction of the load point, it can be seen that the area where fiber orientation should be considered has shifted to the fully displacement-constrained region.

[0114] Figure 17 shows the index U in the second model shown in Figure 10. * This is a figure showing the distribution of the index U. * The broken line shown in the distribution diagram represents the load transfer path obtained by drawing a line with a gentle slope in the distribution of the load transfer index. Figure 18 shows index A in the second model. * This figure shows the distribution of [the variable]. The region 102 enclosed by the dashed line is the region near the load point. Indicator A in region 102 * The value of is positive, and index A in other domains* It is greater than the value of [the specified value].

[0115] Figure 19 shows the index F in the second model shown in Figure 10. * This figure shows the distribution of [the variable]. The region 102A enclosed by the dashed line is the region near the load point. As shown in Figure 19, the index F in region 102A * The value of is positive, and the index F in other domains is positive. * It is larger than that.

[0116] Figure 20 shows the modification of the model shown in Figure 10. The region 102B enclosed by the dashed line is the region near the load point and corresponds to region 102A shown in Figure 19. Arrow 2D indicates the fiber orientation in region 102B. Arrow 2B indicates the fiber orientation in the model shown in Figure 10. As can be seen from the comparison between arrow 2B and arrow 2D, the fiber orientation in region 102B is rotated by 90° relative to the original orientation. In this case, the stiffness in the X direction of each element in region 102B is k = 2.91 × 10⁻¹⁰. 2 Let the stiffness be [N / m], and the stiffness in the Y direction be k = 6.56 × 10⁻⁶. 3 It is expressed as [N / m].

[0117] Figure 21 shows the index U in the model shown in Figure 19. * This figure shows the distribution of . Figure 22 shows index A in the model shown in Figure 19. * This figure shows the distribution of [the index]. In Figure 21, the index U * The broken line shown in the distribution diagram indicates the load transfer path obtained by drawing a line with a gentle slope in the distribution of the load transfer index. By aligning the fiber orientation in region 102B shown in Figure 20 with the displacement direction of the load point, the load transfer path changes to follow the direction of the fiber from the load point. Furthermore, in region 102C enclosed by a dashed line, index U * The value of increases. That is, the connection between any point in region 102C and the load point is stronger than the connection between any point in other regions and the load point.

[0118] In Figure 22, the region 102D enclosed by a dashed line corresponds to region 102B shown in Figure 19. Comparing Figure 18 and Figure 22, by aligning the fiber orientation in region 102B with the displacement direction of the load point, index A * This value decreases compared to the original value. This indicates that by aligning the fiber orientation in region 102B with the displacement direction of the load point, the contribution of the analyzed structure to the stiffness in this region increased.

[0119] As described above, according to the embodiments of the present invention, the effect of the anisotropy of an anisotropic material on the overall rigidity of a structure can be analyzed by numerical calculation. Therefore, by utilizing these analysis results, it is possible to fabricate a structure with higher rigidity or to reinforce a structure to increase its rigidity.

[0120] Recently, the use of fiber composite materials to manufacture structures using 3D printers has become widespread. According to an embodiment of the present invention, for example, the fiber orientation of the fiber composite material can be optimized in advance on a computer. By manufacturing the structure using a 3D printer in accordance with that fiber orientation, it becomes possible to produce a highly rigid structure.

[0121] Furthermore, in the case of sheet-like intermediate materials, such as chopped sheets, which are made by randomly decomposing and welding chopped material, which is made by cutting thin-layer prepreg into strips, the fibers are randomly oriented within the resin. According to the embodiment of the present invention, when reinforcing such existing fiber composite materials, it is possible to determine on a computer where and with which fiber orientation patches should be applied. Therefore, reinforcement work can be carried out efficiently.

[0122] In the structural analysis example above, a fiber-reinforced composite material was used as the structure (anisotropic material) to be analyzed. However, according to the embodiment of the present invention, the anisotropic material to be analyzed is not limited to fiber-reinforced composite materials. A model is set up in which the direction of the material axis vectors at all arbitrary points necessary for the analysis of the structure is defined. By setting the values ​​of the necessary parameters and performing the analysis according to the method described above, structural analysis is possible even for structures containing anisotropic materials other than fiber-reinforced composite materials.

[0123] While embodiments and examples of the present invention have been described, the embodiments disclosed herein should be considered in all respects to be illustrative and not restrictive. The scope of the present invention is defined by the claims, and all modifications within the meaning and scope equivalent to the claims are intended to be included. [Explanation of Symbols]

[0124] 1 Structure, 2 Material axis, 2A~2D Arrows, 10 Analysis device, 11 Control unit, 12 Data acquisition unit (input unit), 14 Storage unit, 16 Index calculation unit, 18 Output unit, 21 Finite element method calculation unit, 22 Stiffness matrix calculation unit, 23 Position change unit, 24 Work / displacement calculation unit, 25 A * Calculation section, 26 U * Calculation Department, 27 F * Calculation unit, 31 Processor, 32 Primary memory, 33 Secondary memory, 34 External device interface, 35 Input interface, 36 Output interface, 37 Communication interface, 38 Bus, 41 Keyboard, 42 Mouse, 43 Display, 101,102,101A~101C,102A~102D Areas, A,B,C Points, d A d B d C ,d' A ,d' B ,d' C Displacement, K AC ,K AC (Δθ) Components of the stiffness matrix, P A ,P B ,P C ,P' A ,P'B ,P' C Load, n vector, S11~S18, S21~S25, S31~S33 steps, U first work, U' second work.

Claims

1. A structural analysis method performed by a computer, The steps include assigning calculation points to the structural data, The steps include assigning material properties, including anisotropy, to the data of the aforementioned structure, The steps include: arranging a load point, a support point, and an arbitrary point at the aforementioned calculation point; The first work required for the displacement of the load point when the material axis vector at the aforementioned arbitrary point is set according to the anisotropy of the material properties, The second work required for the displacement of the load point when the direction of the material axis vector is rotated to coincide with the displacement direction of the load point, A step of calculating a first index based on the ratio of, A step of calculating the distribution of the first index in the data of the structure by changing the arbitrary point, A structural analysis method comprising the following features.

2. With the material axis vector set according to the anisotropy, the work required for the displacement of the load point when the arbitrary point is constrained is, The work required for the displacement of the load point when the aforementioned arbitrary point is not constrained, The structural analysis method according to claim 1, further comprising the step of calculating a load transfer index based on the ratio of while changing the arbitrary point, and calculating the distribution of the load transfer index in the data of the structure.

3. The structural analysis method according to claim 2, further comprising the step of calculating the distribution of the second index in the data of the structure by calculating a second index which is the product of the first index and the load transfer index for the arbitrary point.

4. A program for causing a computer to perform the structural analysis method described in any one of claims 1 to 3.

5. A computer-readable recording medium having the program described in claim 4 recorded on it.

6. A data acquisition unit that receives structural data and material properties including anisotropy, Calculation points are assigned to the data of the aforementioned structure, The aforementioned calculation point is given a load point, a support point, and an arbitrary point. Assign the material properties to the data of the aforementioned structure, An index calculation unit calculates an index related to the stiffness of the aforementioned structure data, An output unit that outputs the results calculated by the index calculation unit, Equipped with, The aforementioned index calculation unit, The first work required for the displacement of the load point when the material axis vector at an arbitrary point in the data of the structure is set according to the anisotropy of the material properties, The second work required for the displacement of the load point when the direction of the material axis vector is rotated to coincide with the displacement direction of the load point, A structural analysis device configured to calculate a first index based on the ratio of a given point, while changing the arbitrary point, and to calculate the distribution of the first index in the data of the structure.

7. The aforementioned index calculation unit further, With the material axis vector set according to the anisotropy, the work required for the displacement of the load point when the arbitrary point placed in the data of the structure is constrained, The work required for the displacement of the load point when the arbitrary point of the anisotropic material is not constrained, The structural analysis apparatus according to claim 6, configured to calculate a load transfer index based on the ratio of the load transfer index, while changing the arbitrary point, and to calculate the distribution of the load transfer index in the data of the structure.

8. The aforementioned index calculation unit further, The structural analysis apparatus according to claim 7, configured to calculate the distribution of the second index in the data of the structure by calculating a second index which is the product of the first index and the load transfer index for any given point.

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