Hierarchical reduced rank matrix generating apparatus

Abstract

When model-based development is performed, a processing target is sometimes decomposed into local structures. In this case, if the degrees of freedom of each local structure are large, a large amount of calculation time and a large amount of computer resources are required. The present invention provides a hierarchical reduced order matrix generating apparatus (600) that generates a hierarchical reduced order matrix used for numerical analysis of a physical object, including a storage section (62) that stores physical object data representing characteristics of the physical object, and an arithmetic section (61) that generates a hierarchical reduced order matrix for a model of the physical object data, the arithmetic section (61) dividing the entire structure into a plurality of local structures, and calculating the reduced order matrix using an inherent mode and a static mode in each of the plurality of local structures obtained by the division.

Description

TECHNICAL FIELD

[0001] The present application relates to a numerical analysis technique related to Model Based Development. More particularly, it relates to a numerical analysis technique. The object of Model Based Development includes a control device such as a fuel injection valve. BACKGROUND

[0002] In the prior art, Model Based Development is sometimes used when developing a system or a component. In Model Based Development, model order-reduction is sometimes performed in order to suppress the cost of numerical analysis. As a prior art regarding order-reduction, there is Non-Patent Literature 1. In Non-Patent Literature 1, in a process of generating an order-reduced system matrix that is a residual region of a system matrix, the following processing is performed. A static mode is obtained by multiplying an inverse matrix of an internal region for removing degrees of freedom and a joint stiffness between the adjacent region and the boundary region and the internal region. Using the static mode and a unique mode of the internal region, the system matrix is order-reduced to a residual region in which degrees of freedom are to be left.

[0003] Prior Art Documents

[0004] Non-Patent Literature

[0005] Non-Patent Literature 1: "Finite Element Eigenvalue Analysis - Large-Scale Parallel Computation Method", Motoki Yagawa, Yuji Aoyama (October 2001), P102-P106 SUMMARY

[0006] PROBLEMS TO BE SOLVED BY THE INVENTION

[0007] In Non-Patent Literature 1, the local structure is decomposed in order to perform order-reduction. At this time, if the degrees of freedom of each local structure are large-scale, a large amount of calculation time and a large amount of computer resources are required. For example, it is known that in the case of calculating a static mode, inverse matrix calculation of an internal region is required. In the case where the degrees of freedom of a model of the entire structure that is a processing object are large-scale, an inverse matrix of a large-scale matrix is required. Therefore, a large amount of calculation time and a large amount of computer resources such as a memory of a computer are required.

[0008] MEANS OF SOLVING THE PROBLEMS

[0009] To solve the above problems, the present application provides a hierarchical reduced order matrix generating device which generates a hierarchical reduced order matrix for numerical analysis of a physical object, including a storage section which stores physical object data indicating characteristics of the physical object, and an arithmetic section which generates a hierarchical reduced order matrix for a model of the physical object data, wherein the arithmetic section divides an overall structure of the model of the physical object data into a plurality of local structures, and calculates the reduced order matrix using an inherent mode and a static mode in each of the plurality of local structures obtained by the division.

[0010] The present application also includes a program for executing the functions of the hierarchical reduced order matrix generating device and a medium in which the program is stored. Furthermore, the present application also includes a method for generating a reduced order matrix using the hierarchical reduced order matrix generating device.

[0011] Effects of the Invention

[0012] According to the present application, an increase in calculation time and computer resource consumption can be suppressed when model reduction is performed. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 is a flowchart illustrating the Craig-Bampton method.

[0014] Figure 2 is a flowchart illustrating the process of generating a reduced order system matrix in one embodiment of the present application.

[0015] Figure 3 is a flowchart illustrating the process of hierarchically dividing and hierarchically combining an overall structure including a boundary region.

[0016] Figure 4 is a schematic diagram illustrating the process of dividing each local structure of the reduced order system matrix when the overall structure is divided into, for example, 4 parts, for the purpose of illustrating the illustrated embodiment.

[0017] Figure 5 is a schematic diagram illustrating the process of combining each local structure of the reduced order system matrix when the overall structure is divided into, for example, 4 parts, for the purpose of illustrating the illustrated embodiment.

[0018] Figure 6 is a functional block diagram of the hierarchical reduced order matrix generating device of one embodiment of the present application.

[0019] Figure 7 is a hardware configuration diagram of the hierarchical reduced order matrix generating device of one embodiment of the present application. DETAILED DESCRIPTION

[0020] One embodiment of the present application will be described below using the drawings. Furthermore, as will be described later, the process described in this section is executed by the hierarchical reduced order matrix generating device 1 of one embodiment of the present application.Figure 6 The so-called computer execution is shown.

[0021] First, the Craig-Bampton method as a prior art of the present embodiment is explained.

[0022] [Explanation of Prior Art Method]

[0023] Figure 1 is a flowchart explaining the Craig-Bampton method. In the Craig-Bampton method, the overall structure is reduced to the degrees of freedom of the boundary region in the following manner. First, in step 101, physical object data as data in which information of a physical object is recorded is read. Next, a boundary region in which degrees of freedom are to be left is read. Then, in step 103, a system matrix of the overall structure is generated using the data read in steps 101, 102. Next, in step 104, for the generated system matrix, an inherent mode in a case where the degrees of freedom of the boundary region are fixed is calculated. Then, in step 104, for the system matrix, an inverse matrix of an internal region in which degrees of freedom are to be removed, and a product of a connection stiffness matrix of the internal region and the boundary region to be kept, that is, a static mode are calculated. Next, in step 106, a transformation matrix for generating a reduced matrix is generated. Then, in step 108, the generated transformation matrix is saved in an external storage region of a computer. Further, a reduced system matrix is calculated for the transformation matrix in step 107. Then, the reduced system matrix is saved in step 109.

[0024] Here, steps 101 to 103 among the above steps, which are related to the technical problem of the present embodiment, that is, increase in calculation time and computer resource consumption, are explained. First, the physical object data is saved in a memory of a computer by step 101, and the physical object data is classified into an internal region i and a boundary region b by step 102. Next, a system matrix of a mass matrix M, a stiffness matrix K, a damping matrix D, and a load vector F is generated based on the physical object data by step 103. This system matrix is expressed by a motion equation of the overall structure as shown in Expression 1.

[0025] The region in which degrees of freedom are to be left is defined, and the reduction calculation is performed.

[0026]

[0027] Further, the displacement u b of the boundary region in which degrees of freedom are to be left and the displacement u i of the internal region can be expressed as Expression 2.

[0028]

[0029] Further, the static mode matrix Gib is a vector, which is expressed by the product of the inverse matrix of the internal region to be removed from the degree of freedom, and the coupling stiffness matrix between the internal region and the boundary region to be maintained, as shown in Equation 3.

[0030] Further, the inherent mode matrix Φ i is an inherent mode calculated by the eigenvalue of Equation 4.

[0031]

[0032]

[0033] Thus, the transformation matrix T is expressed by Equation 5, and the reduced-order system matrix is generated by Equations 6, 7, and 8.

[0034]

[0035]

[0036]

[0037]

[0038] Thus, the displacement of the internal region can be expressed by the linear sum of the displacement of the boundary region and the inherent mode, and the dimension of the motion equation is reduced to the sum of the number of inherent modes and the degree of freedom of the boundary region.

[0039] However, in the above processing, in the case where the degree of freedom of all the local structures is large-scale, a large amount of computation and a large amount of computer memory capacity and external storage capacity and the like are required. In this case, in the case where the dimension of the motion equation is reduced, the inverse matrix calculation of the internal region as shown in Equation 3 is required. Therefore, as described above, in the case where the degree of freedom of the entire structure is large-scale, the inverse matrix of a large-scale matrix is required. Therefore, a large amount of computation time and a large amount of computer resources are required.

[0040] Further, in the process of generating the reduced-order matrix from the entire structure and in the process of restoring the response (for example, displacement) of the entire structure from the calculation result of the reduced-order matrix, a matrix (transformation matrix) which performs the mutual conversion between the entire structure system matrix and the reduced-order system matrix is required to be used. The size of the transformation matrix is the product of the degree of freedom of the entire structure and the boundary region. Further, the transformation matrix has a small number of non-zero elements. Therefore, in the case where the degree of freedom of all the local structures is large-scale, it sometimes exceeds several million degrees of freedom. Therefore, the calculation using these transformation matrices requires a large amount of computer resources and a large amount of computation.

[0041] [Generation method of hierarchical reduced-order matrix]

[0042] The following describes the method for generating the hierarchical reduction matrix in this embodiment to solve these problems. Specifically, using... Figures 2-4 , Figure 6 , Figure 7 This describes the process of hierarchically dividing the overall structure, which is the object of processing, into local structures and generating a reduced-order system matrix layer by layer. The overall structure represents a model of the physical object data, consisting of... Figure 4 The “level 0” is represented by this.

[0043] First, use Figure 6 The hierarchical reduction matrix generation device 600 used to generate the reduced-order system matrix is ​​described. Figure 6 This is a functional block diagram of a hierarchical reduced-order matrix generation device 600. The hierarchical reduced-order matrix generation device 600 includes an arithmetic unit 61, a storage unit 62, a display unit 63, a communication unit 64, an input unit 65, and a bus connection unit 66. The arithmetic unit 61 performs the process of hierarchically generating a reduced-order system matrix. For this purpose, the arithmetic unit 61 includes a data reading unit 611, a boundary region reading unit 612, an M, K, D, F matrix generation unit 613, an intrinsic pattern number reading unit 614, a static pattern reading unit 615, and a reduced-order system matrix generation unit 616. These units perform calculations according to a reduced-order system matrix generation program 601 stored in the storage unit 62. Note that the storage unit 62 also stores physical object data 602, intrinsic patterns 603, static patterns 604, and a reduced-order system matrix 605. These will be described later. Furthermore, at least a portion of the various information stored in the storage unit 62 can also be stored in other storage devices connected via the communication unit 64.

[0044] In addition, the display unit 63 displays the processing results of the arithmetic unit 61, information input via the input unit 65, etc. The communication unit 64 has the function of connecting to other devices, such as computers, via a network such as the Internet. The input unit 65 has the function of receiving user input. And the connection unit 66 has the function of connecting the above-mentioned units.

[0045] Here, using Figure 7 The hardware structure of the hierarchical reduced-order matrix generation device 600 is described below. The hierarchical reduced-order matrix generation device 600 is implemented by a so-called computer. The hardware of the hierarchical reduced-order matrix generation device 600 includes a CPU 6110, a storage device 620, a display 631, a display controller 632, a network interface 641, a keyboard 651, a mouse 652, and an I / O interface 653.

[0046] They and Figure 6 The functional block diagram shows the following relationships between the components.

[0047] CPU6110 Arithmetic Unit 61

[0048] Storage device 620 Storage unit 62

[0049] Display 631, display controller 632 Display section 63

[0050] Network interface 641 Communication section 64

[0051] Keyboard 651, mouse 652, I / O interface 653 Input section 65

[0052] Further, the storage device 620 stores Figure 6 various information as shown, and has a RAM 623 and a ROM 624 that receive access from the CPU 6110. Further, the storage device 620 includes a storage medium such as an HDD 621, a DVD / CD 622, and a disk controller 625 that controls access to the storage medium. In addition, the reduced-order system matrix generation program 601 and other various information are stored in the storage medium. Further, the storage device 620 loads the reduced-order system matrix generation program 601 into the ROM 610. Further, the RAM 608 is used as a work area.

[0053] In response thereto, the CPU 6110 accesses the storage device, and performs processing according to the reduced-order system matrix generation program 601. Details of the processing are described later. Figures 2-5

[0054] Further, the display 631 displays various information under the control of the display controller 632. Further, the network interface 641 is connected to other devices and the like via a network.

[0055] Further, the keyboard 651 and the mouse 652 receive input from a user. Then, the I / O interface 653 notifies the CPU 6110 and the like of the content of the input.

[0056] Next, Figure 2 is a flowchart 200 that illustrates one example of a method of hierarchically dividing a whole structure including a boundary region and hierarchically generating a reduced-order system matrix. Hereinafter, the functional block diagram of Figure 2 will also be used in the explanation of the flowchart below. Figure 6

[0057] First, in step 101, the data reading section 611 performs reading of physical object data. The data reading section 611 reads the physical object data 602 stored in the storage section 62. This physical object data 602 is a model that represents characteristics of a physical object that is a model development object. Further, the physical object data includes characteristics in control of a control device, a component. This step is the same processing as step 101 of the Figure 1 This is the same for steps 102 and 103 as well.

[0058] ​​Next, in step 102, the boundary region reading section 612 reads the boundary region in which the degree of freedom is to be left. That is, it means that the physical object data is divided into the internal region i and the boundary region b. In addition, the internal region i is a non-contact portion which does not contact with other models, and the boundary region b is a contact portion which contacts with other models.

[0059] Next, in step 103, the M, K, D, F matrix generating section 613 generates the system matrix of the entire structure using the results of steps 101 and 102. As a result, the system matrix of the mass matrix M, the stiffness matrix K, the damping matrix D, and the load vector F is generated as described above.

[0060] Next, in step 201, the natural mode number reading section 614 reads the natural mode number 603 stored in the storage section 62.

[0061] Next, in step 202, the static mode reading section 615 reads the natural mode number of the static mode (static mode 604).

[0062] Then, in step 300, the reduced system matrix generating section hierarchically generates the reduced system matrix using the natural mode number 603 and the static mode 604. The details of this step 303 are shown using the flowchart of FIG. 6. Figure 3 The details will be described.

[0063] Figure 3 is a flowchart showing the details of step 300.

[0064] First, in step 301, the reduced system matrix generating section 616 divides the entire structure corresponding to the physical object data into local structures. In order to perform this division, the reduced system matrix generating section 616 determines the level, that is, the number of divisions. In order to determine the level, information such as the computational load of the computer, the available memory area, and the like are used with respect to the degrees of freedom of the local structures. Thereby, it is possible to perform the computation with an appropriate number of divisions, and it is possible to reduce the computational load and the memory usage.

[0065] Here, the details of the division in this step will be described using Figure 4 The details of the division in this step will be described using

[0066] This example shows the case where the physical object data is divided into four local structures. The reduced system matrix generating section 616 divides the entire structure into four local structures A, B, C, and D at "level 2". In addition, hereinafter, the level on the side of each divided structure will be referred to as the upper level, and the level on the side after the division will be referred to as the lower level. That is, in this example, the upper level is "level 1", and the lower level is "level 2". Figure 4In the example of FIG. 6, "Level 0" is the uppermost level, and "Level 2" is the lowermost level. In addition, the partitioning of the local structures here can be performed in one step from Level 0 to Levels 1 and 2, or can be performed in stages by performing the partitioning to Level 1 and then to Level 2. By performing the partitioning in one step, the processing speed can be improved. In addition, by performing the partitioning in stages, load balancing can be achieved.

[0067] Next, in step 302, the reduced system matrix generating section 616 performs region determination on the local regions of each level. That is, for each local structure, it is determined which of the internal region, the boundary region, and the adjoining region it is. Here, the internal region refers to a region in which the degrees of freedom are to be removed. In addition, the boundary region refers to a region in which the degrees of freedom are to be left. Furthermore, the adjoining region refers to a region in which the local structures are adjacent to each other.

[0068] In Figure 4 In the example of FIG. 6, as the adjoining regions of Level 2, the adjoining region 2 between the local structure A and the local structure B, and the adjoining region 6 between the local structure C and the local structure D are determined. In addition, as the internal regions, the internal region 1 of the local structure A, the internal region 3 of the local structure B, the internal region 5 of the local structure C, and the internal region 7 of the local structure D are determined. Furthermore, as the boundary region, the boundary region 8 in the local structure D is determined. Then, the reduced system matrix generating section 616 stores this information in the storage section 62.

[0069] In addition, the reduced system matrix generating section 616 determines the adjoining region 4 between the local structure AB and the local structure CD as the adjoining region of Level 1. In addition, the reduced system matrix generating section 616 determines the boundary region 8 as the boundary region. Then, the reduced system matrix generating section 616 stores this information in the storage section 62 as well. Finally, as the information of the boundary region of Level 0, the reduced system matrix generating section 616 determines the boundary region 8 of the local structure ABCD. The reduced system matrix generating section 616 stores this information in the storage section 62 as well.

[0070] Next, in step 303, the reduced system matrix generating section 616 generates the mass matrix M and the stiffness matrix K of the entire structure according to Equations 9 and 10. Here, each local structure belongs to one of the local structure A, the local structure B, the local structure C, and the local structure D. In addition, the lower right subscript in Equations 9 and 10 indicates the number of the matrix of the entire structure. In addition, the upper left superscript indicates the local structure to which it belongs.

[0071]

[0072]

[0073] Furthermore, the reduced-order system matrix generation unit 616 calculates the system matrix of each local structure. Here, the reduced-order system matrix generation unit 616 divides the physical object into a finite number and obtains the nodes and elements at this time. Then, the reduced-order system matrix generation unit 616 uses the material physical property values ​​of the system matrix used in the numerical analysis to calculate the system matrix of the local structure based on the superposition principle. Other properties can also be used for the material physical property values. Specifically, the reduced-order system matrix generation unit 616 calculates the system matrix of local structure A according to Equations 11 and 12.

[0074]

[0075]

[0076] Then, in step 308, the order reduction system matrix generation unit 616 performs order reduction calculations on each local structure. For example, local structure A is classified in step 203 into an internal region 1 and an adjacent region 2 that is adjacent to local structure B in the previous layer. Therefore, the order reduction system matrix generation unit 616 performs order reduction calculations on the adjacent region 2 and the internal region 1, giving the adjacent region 2 only degrees of freedom.

[0077] The details of step 308 will be explained below, taking local structure A as an example, in steps 304 to 307.

[0078] First, in step 304, the reduced-order system matrix generation unit 616 calculates the static patterns of the adjacent surfaces and boundary surfaces of each local structure. Specifically, the reduced-order system matrix generation unit 616 calculates the static patterns of the adjacent regions and boundary regions in a manner that yields the system matrix of the adjacent region 2 in the layer above local structure A. Then, in step 305, the reduced-order system matrix generation unit 616 stores the calculated static patterns in the storage unit 62.

[0079] Next, in step 306, the reduced-order system matrix generation unit 616 calculates the intrinsic patterns of the internal region. At this time, the reduced-order system matrix generation unit 616 calculates the intrinsic patterns by performing intrinsic value decomposition on the internal region of the local structure A as described above. Then, in step 307, the reduced-order system matrix generation unit 616 stores the calculated intrinsic patterns in the storage unit 62.

[0080] Then, the reduced-order system matrix generation unit 616 uses Equation 13 to calculate the reduced-order matrix of the local structure A, and obtains Equations 14 and 15.

[0081]

[0082]

[0083]

[0084] The reduced system matrix generation section 616 also calculates reduced system matrices of the local structures B, C, and D through the same procedure.

[0085] In the case of the local structure B, the reduced system matrix generation section 616 calculates Equation 16 and Equation 17 as reduced system matrices. The local structure B has the internal region 3, the adjoining region 2 in the level 1, and the adjoining region 4 in the level 0. Therefore, the reduced system matrix generation section 616 reduces degrees of freedom so that only degrees of freedom of the adjoining region 2 in the level 1 and the adjoining region 4 in the level 0 exist. Then, the reduced system matrix generation section 616 calculates Equation 18 as a transformation matrix. Further, the reduced system matrix generation section 616 calculates reduced matrices of the local structure B by using Equation 18, to obtain Equation 19 and Equation 20.

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] Further, in the case of the local structure C, the reduced system matrix generation section 616 calculates Equation 21 and Equation 22 as system matrices. The local structure C has the internal region 5, the adjoining region 6 in the level 1 where the local structure C and the local structure D are adjacent to each other, and the adjoining region 4 in the level 0. Therefore, the reduced system matrix generation section 616 reduces degrees of freedom so that only degrees of freedom of the adjoining region 6 and the adjoining region 4 in the level 1 and the level 0 exist. Then, the reduced system matrix generation section 616 calculates Equation 23 as a transformation matrix. Further, the reduced system matrix generation section 616 calculates reduced matrices of the local structure C by using Equation 23, to obtain Equation 24 and Equation 25.

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] Further, in the case of the local structure D, the reduced system matrix generating section 616 calculates Equation 26 and Equation 27 as the system matrix. The local structure D has the internal region 7, the adjoining region 6 in the hierarchy 1, and the boundary region 8. Therefore, the reduced system matrix generating section 616 reduces the degrees of freedom so that only the degrees of freedom of the adjoining region 6 in the hierarchy 1 of the upper layer and the boundary region 8 exist. Then, the reduced system matrix generating section 616 calculates Equation 28 as the transformation matrix. Further, the reduced system matrix generating section 616 calculates the reduced matrix in the local structure D using Equation 28, resulting in Equation 29 and Equation 30.

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] Further, in the calculation of the local structures B, C, and D, the reduced system matrix generating section 616 performs Step 304 and Step 305.

[0104] As shown above, in each of the divided local structures, only the degrees of freedom of the adjoining region and the boundary region can exist. Since the entire structure is divided into each of the local structures, it is possible to reduce the computer resources and the amount of calculation. In the case where the calculation of the local structures is divided into a plurality of processors (CPU 6110) to perform the calculation, it is performed in the following manner. That is, the division method is determined in such a manner that the product of the sum of the boundary region and the adjoining region and the degrees of freedom of the local structure is as equal as possible. Thereby, the operation load and the computer resources of each CPU 6110 are dispersed, it is possible to make the time required for the operation of each processor equal, and it is possible to reduce the time each CPU waits for processing.

[0105] [Combination method of local structures]

[0106] Next, the combination method of the entire structure from each of the local structures in the present embodiment will be described using Figure 3 Figure 5 , in the present embodiment, since the degrees of freedom of the adjoining region remain in each of the local structures, it is possible to realize the combination of the physical coordinate system.

[0107] The combination method of the entire structure is performed in Figure 3 ​in step 315. First, in step 309 in step 315, the reduced system matrix generating section 616 combines (joins) the mass matrix, the matrix of each local structure on the adjoining surface. Specifically, the reduced system matrix generating section 616 uses the principle of superposition. For example, in the case where the local structure A and the local structure B are joined, the following processing is performed. The reduced system matrix generating section 616 performs the joining of the reduced mass matrix and the reduced stiffness matrix of the local structure A and the local structure B in accordance with the formula 32, the formula 33. Figure 5

[0108] In order to perform step 309, in step 310, the reduced system matrix generating section 616 reads the reduced system matrix of the local structure A and the local structure B from the storage section 62. The present reduced system matrix is represented by the formula 31.

[0109]

[0110]

[0111]

[0112] Next, in step 311, the reduced system matrix generating section 616 calculates the static reduced matrix. Here, the local structure obtained by the joining in step 309 is referred to as the local structure AB. The local structure AB is joined in a state where the adjoining region 4 in the level 0 is present. Therefore, in the level 0, the local structure A and B are joined in the adjoining region 4. Therefore, in the reduced system matrix generating section 616, as the previous stage, the degrees of freedom are reduced so that only the degrees of freedom of the adjoining region 4 in the level 0 are present, and the static reduced transformation matrix of the adjoining surface and the boundary surface of the next level shown in the formula 33 is calculated. Then, in step 312, the reduced system matrix generating section 616 stores the static mode determined based on the calculated static reduced transformation matrix in the storage section 62.

[0113] Next, in step 313, the reduced system matrix generating section 616 uses these transformation matrices to calculate the reduced mass matrix and the reduced stiffness matrix, and obtains the formula 34 and the formula 35. That is, the reduced system matrix generating section 616 calculates the eigenvalue in the case where the adjoining surface and the boundary surface of the next level are fixed. Then, in step 314, the reduced system matrix generating section 616 stores the calculated eigenvalue in the storage section 62.

[0114]

[0115]

[0116] Next, with respect to the local structure AB, the reduced system matrix generating section 616 performs the processing of steps 309 to 314. Figure 5 ​The example of combining local structure C and local structure D will be used for illustration. In step 309, the reduced-order system matrix generation unit 616 combines the reduced-order mass matrix and reduced-order stiffness matrix of local structure C and local structure D. Here, the reduced-order system matrix generation unit 616 similarly performs the combination according to Equations 36 and 37 using the superposition principle.

[0117]

[0118]

[0119] Next, in step 311, the reduced-order system matrix generation unit 616 calculates the static reduced-order matrix. Here, the combined local structure is referred to as the local structure CD. The local structure CD is combined in a state having the adjacent region 4 and the boundary region 8 as analyzed above. Therefore, the reduced-order system matrix generation unit 616 reduces the degrees of freedom so that only the degrees of freedom of the adjacent region 4 and the boundary region 8 required to generate the reduced-order system matrix of the overall structure exist, resulting in the transformation matrix represented by Equation 38.

[0120] Then, in step 313, the reduced-order system matrix generation unit 616 uses these transformation matrices to calculate the reduced-order mass matrix and the reduced-order stiffness matrix, obtaining Equations 39 and 40.

[0121]

[0122]

[0123]

[0124] Next, regarding Figure 5 The example of combining local structure AB and local structure CD will be used for illustration. In step 309, the reduced-order system matrix generation unit 616 combines the reduced-order mass matrix and reduced-order stiffness matrix of local structure AB and local structure CD. Here, the reduced-order system matrix generation unit 616 similarly performs the combination according to Equations 41 and 42 using the superposition principle.

[0125]

[0126]

[0127] Next, in step 311, the reduced system matrix generating section 616 calculates a static reduced matrix. Here, the resulting local structure will be referred to as local structure ABCD. The local structure ABCD has the boundary region 8 required to generate the reduced system matrix of the entire structure. Therefore, the reduced system matrix generating section 616 performs reduction so that only the degrees of freedom of the boundary region 8 exist, and obtains a transformation matrix represented by Equation 43. That is, in step 315, the reduced system matrix generating section 616 calculates the transformation matrix by performing reduction and combining of each local structure in order from the lower layer to the upper layer.

[0128] Further, in step 313, the reduced system matrix generating section 616 calculates the reduced mass matrix and the reduced stiffness matrix using the transformation matrix, and obtains Equations 44 and 45.

[0129]

[0130]

[0131]

[0132] The process proceeds from step 315 to step 316. In step 316, the reduced system matrix generating section 616 determines whether the level of the combining stage is greater than 0. That is, the reduced system matrix generating section 616 determines whether each local structure has been combined. In the case where it is greater than 0, the process returns to step 315, which is step 309. Thus, step 315 is repeated until the level is 0, that is, only the degrees of freedom of the boundary region exist, and each local structure is sequentially combined.

[0133] Here, with respect to the system matrix generated in the stage where the level is determined to be 0 in step 316, a reduced system matrix of a dimension of the sum of the degrees of freedom of the boundary region and the number of eigenvalues of the reduced portion is generated.

[0134] However, in the case where the degrees of freedom of the boundary region are very large, the size of the system matrix also becomes large.

[0135] Further, the memory required to retain the transformation matrix for restoring to the entire displacement is the product of the degrees of freedom of the entire structure and the degrees of freedom of the boundary region. Therefore, in the case where the degrees of freedom of the entire structure and the degrees of freedom of the boundary region are large, a large amount of memory is required.

[0136] To solve this problem, the process of step 317 is executed. In step 317, the reduced system matrix generating section 616 calculates the eigenmode of the residual region. Specifically, the reduced system matrix generating section 616 performs the calculation according to Equations 46 and 47. Here, the displacement of the contact portion is represented by the eigenmode {Φ8} obtained by the eigenvalue analysis of Equation 46. Also, if the displacement of the contact portion is represented using the eigenmode {Φ8}, it can be expressed by Equation 47.

[0137]

[0138]

[0139] Further, if the displacement of the reduced-order internal region i is expressed by the eigenmode {Φi} obtained by the eigenvalue analysis of the equation 48, since the connecting stiffness matrix of the reduced-order internal region i and the boundary region 8 is zero, the displacement of the reduced-order internal region i is the equation 49.

[0140]

[0141]

[0142] Thus, the reduced-order system matrix generating section 616 calculates the transformation matrix represented by the equations 50 to 54 as a transformation matrix for transforming from each local structure to the whole structure. In this way, by expressing the displacement of the contact portion by the eigenvector, it is possible to reduce the dimension of the transformation matrix used and held for restoration to the whole displacement, and it is possible to reduce the computer resources and reduce the number of operations.

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] Next, in step 318, the reduced-order system matrix generating section 616 calculates the reduced-order system matrix represented by the equations 55 to 58 as the final output using the transformation matrix of the equation 54.

[0149] In addition, the dimension of the obtained reduced-order system matrix is determined by the number of eigenvectors in the boundary region in the equation 46 and the number of eigenvectors in the residual region in the equation 48. Therefore, by changing the number of eigenvectors in the boundary region and the number of eigenvectors in the residual region according to the required calculation accuracy, it is possible to flexibly change the degree of freedom of the system matrix.

[0150]

[0151]

[0152]

[0153]

[0154] In addition, in the case of calculating the transformation matrix of the boundary region, by considering the computer resources, not all of the boundary regions of the boundary region are maintained but only a part is maintained, and the amount of operation and the memory consumption amount of the calculation of the eigenvector calculated by Expression 48 can be controlled.

[0155] In addition, in the present embodiment, a calculation example in the case where the number of levels is set to 2 and the number of divisions of the local structure is set to 4 is illustrated, but is not limited thereto, and the obtained effects do not change even in the case where the number of levels is increased or in the case where the number of levels is decreased. In addition, the entire structure is not necessarily divided into several.

[0156] Furthermore, the outline of the above processing is described as Figure 7 the processing on the hardware structure shown in FIG. 6 is described.

[0157] The static mode, the inherent mode, and the system matrix are stored in the HDD 621. Therefore, in step 300, the CPU 6110 is called again at the time of combining the local structure and is stored in the RAM 623. Then, the CPU 6110 uses them for the calculation.

[0158] These calls and writings are repeated until the reduced-order system matrix of the entire structure is generated, and the number of times of execution is the number of levels plus 1.

[0159] Here, a plurality of CPUs 611 can exist. In this case, each of the plurality of CPUs 6110 can reduce the capacity to be stored in the RAM 623 at one time by calculating the static mode and the inherent mode for the divided local structure. In addition, the operation of the inherent mode and the static mode by the CPU 6110 is divided by each CPU 6110, so the amount of operation of each CPU 6110 is reduced, and it can be executed at high speed.

[0160] Furthermore, the above processing can be executed cooperatively with another hierarchical reduced-order matrix generation device 600 (computer) connected via the network interface 641. In this case, each hierarchical reduced-order matrix generation device 600 shares data, and the calculation can be executed by each of the plurality of CPUs 6110. The plurality of CPUs 6110 execute step 300 of generating the above system matrix, and calculate the inherent mode and the static mode of the divided local structure.

[0161] Then, the CPU 6110 temporarily stores the operation result in the RAM 6238 of itself. Then, the CPU 6110 stores the result in the HDD 621 of itself or an external storage device.

[0162] The simulation environment exemplified in this embodiment is one example, and the present application can also operate using a plurality of other general-purpose or dedicated simulation system environments or structures. That is, the present application is not limited to the environment described in the embodiment.

[0163] Reference Signs

[0164] 61 … arithmetic unit, 611 … data reading unit, 612 … boundary region reading unit, 613 … M, K, D, F matrix generating unit, 614 … inherent mode number reading unit, 615 … static mode reading unit, 616 … reduced-order system matrix generating unit, 62 … storage unit, 601 … reduced-order system matrix generating program, 602 … physical object data, 603 … inherent mode, 604 … static mode, 605 … reduced-order system matrix, 63 … display unit, 64 … communication unit, 65 … input unit, 66 … connection unit.

Claims

1. A hierarchical reduced-order matrix generation device, which generates hierarchical reduced-order matrices for numerical analysis of physical objects, characterized in that, include: The storage unit stores physical object data representing the characteristics of the physical object; and The computation unit generates a hierarchical reduced-order matrix for the model of the physical object data. Wherein, the arithmetic unit, Using information representing the computational load and available memory area of ​​the computer-based hierarchical reduction matrix generation device, the number of partitions representing the hierarchy is determined. The overall structure of the model of the physical object data is divided into multiple local structures according to the determined number of segmentations. The reduced-order matrix is ​​calculated using the intrinsic and static patterns in each of the multiple local structures obtained from the segmentation. The arithmetic unit, For each of the multiple local structures obtained from the segmentation, they are classified into internal regions where degrees of freedom need to be removed, boundary regions where degrees of freedom need to be retained, and adjacent regions between local structures. Calculate the inherent pattern of the internal region. Calculate the static patterns of the adjacent regions and the boundary regions. The reduced-order matrix is ​​calculated using the inherent patterns of the internal regions, the static patterns of the adjacent regions, and the boundary regions, wherein... When the computation of the local structure is divided into multiple processors, the division method is determined in such a way that the product of the sum of the boundary region and the adjacent region multiplied by the degrees of freedom of the local structure is as equal as possible.

2. The hierarchical reduction matrix generation device as described in claim 1, characterized in that: The arithmetic unit, The overall structure is divided into multiple local structures in stages. The reduced-order matrix is ​​calculated by reducing and combining each of the local structures in order from the lower to the upper levels of the hierarchy.

3. The hierarchical reduction matrix generation device as described in claim 1 or 2, characterized in that: The computation unit performs the segmentation from the overall structure to the multiple local structures in stages.

4. The hierarchical reduced-order matrix generation device as described in claim 1 or 2, characterized in that: The computation unit performs the division from the overall structure to the multiple local structures in one operation.

5. A storage medium storing a program for enabling a computer to function as a hierarchical reduced-order matrix generation device, the hierarchical reduced-order matrix generation device generating hierarchical reduced-order matrices for numerical analysis of physical objects, characterized in that: The computer has a storage unit that stores physical object data representing the characteristics of the physical object. The program causes the computer to perform the following steps: The step of determining the number of partitions representing the hierarchy using information representing the computational load and available memory area of ​​the hierarchical reduction matrix generation device; The step of dividing the overall structure of the model of the physical object data into multiple local structures according to the determined number of divisions; and The step of calculating the reduced-order matrix is ​​performed using the intrinsic and static patterns in each of the multiple local structures obtained from the segmentation, and... The program causes the computer to perform the following steps: For each of the multiple local structures obtained by segmentation, the steps are classified into internal regions where degrees of freedom are to be removed, boundary regions where degrees of freedom are to be retained, and adjacent regions between local structures. The steps for calculating the inherent pattern of the internal region; The steps for calculating the static patterns of the adjacent regions and the boundary regions; The step of calculating the reduced-order matrix using the inherent pattern of the internal region, the static pattern of the adjacent region, and the boundary region; and When the computation of the local structure is divided into multiple processors, the step of determining the partitioning method is to make the product of the sum of the boundary region and the adjacent region multiplied by the degrees of freedom of the local structure as equal as possible.

6. The storage medium as described in claim 5, characterized in that, The program causes the computer to perform the following steps: The steps of dividing the overall structure into multiple local structures in stages; and The step of calculating the reduced-order matrix is ​​to reduce and combine each of the local structures in order from the lower to the upper levels of the hierarchy.

7. The storage medium as described in claim 5 or 6, characterized in that: The program causes the computer to perform a phased process of segmenting the overall structure into the multiple local structures.

8. The storage medium as described in claim 5 or 6, characterized in that: The program causes the computer to perform a step of dividing the overall structure into the multiple local structures in one go.

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