JP2001027994A - Method and device for generating numeric data for calculation from analytic model by finite element method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To decrease the calculation quantity and memory capacity needed for a structure analysis by a finite element method, etc., even when the shape of a structure is complicated and elements and nodes are large in number. SOLUTION: An analytic model for the structure is roughly divided into rough divisional elements first and rough divisional elements which are arranged in one direction is set as one array to set the analytic model for the structure as multiple arrays 1 and 2; and the rough divisional elements are further divided into fine divisional elements FE1 to FE20, node numbers 1 to 15 and 1 to 21 are set to each of nodes of the fine divisional elements according to the arrays, and multiple arrays are integrated to obtain the whole analytic model. Then the node numbers at each of the nodes of the fine divisional elements are charged into node numbers of the whole analytic model.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a data generation method for generating numerical data for calculation from an analysis model used for structural analysis by the finite element method.

[0002]

2. Description of the Related Art Conventionally, when performing a structural analysis or the like by the finite element method, an analysis model of a structure to be analyzed is set, and numerical data for calculation is generated by the analysis model to perform a structural analysis. It is known. In general, when analyzing the motion or heat conduction of a structure using the finite element method, processing is generally performed according to the following procedure. (1) An analysis model of a structure is set, and the analysis model is divided into finite elements. (2) A serial number is assigned to each divided element and each node on each element. (3) the coordinates of each node, the number of each node on each element,
Generate numerical data including The above procedure is described in more detail as follows. First, an analysis model based on the finite element method is set depending on how the structure is analyzed, and the analysis model is divided into fine parts necessary for the analysis, and the elements (for example, a triangle or a quadrangle in the case of a two-dimensional model) are set. ｛= Quadrilateral｝ element, in the case of a three-dimensional model, a tetrahedron or hexahedron element)
A node number is assigned to each corner (node) of the element, an element matrix including the components of the peripheral node numbers is generated for each node number, and the entire matrix is generated by integrating the element matrices to perform analysis. Perform calculations. By the way, conventionally, when an analysis model is divided, the analysis model is divided at once into elements of fineness necessary for analysis, and node numbers are assigned to nodes in an arbitrary order.

However, when the node numbers are assigned in an arbitrary order, the difference between the maximum node number and the minimum node number in one element (for example, a quadrilateral element) increases,
There is a problem that the time and cost required for the analysis calculation are increased due to the increase in the half bandwidth described later. For example, even if an analysis model with the same number of nodes is divided in the same way, the calculation amount and the required memory amount in the finite element method analysis performed thereafter will differ due to the difference in the node number allocation method. It changes greatly. This is because the positions of the 0 element and the non-zero element in the matrix generated by the assignment of the node numbers are different. Generally, a matrix of non-zero elements generated by the finite element method is a band matrix including components of a predetermined width centered on diagonal components in the matrix, and the matrix is calculated by a half bandwidth of the band matrix. The amount and the amount of memory required for the calculation are determined. In order to solve the problem that the calculation time is increased by the way of assigning the node numbers, for example, a method called Cuthill-Mckee method is known as a method of replacing the node numbers of the subdivision elements. The Cuthill-Mckee method is described in the literature "EHCut
hill and JMMckee, Reducing the bandwidth of spar
se symmetric matrices. Proc. 24th National Confere
nce ACM, Bandon Systems Press, HJ, 1969, 157-172 ''
As described in (1), by applying a predetermined algorithm and changing the node number of each element, the calculation efficiency of the analysis can be increased and the time required for the calculation can be reduced. However, the Cuthill-Mckee method requires an enormous amount of calculation of the algorithm for rearranging the node numbers and requires a long processing time.Therefore, when the number of elements and the number of nodes are small, the time required for the calculation of the analysis is reduced. There is a case where it is effective as a method for solving the problem of reducing the number, but when the number of elements and the number of nodes are large, it is not suitable for solving the problem. Here, the fact that the amount of matrix calculation differs depending on how node numbers are allocated will be described using an actual example.

FIG. 7 is a diagram showing a matrix generally generated by the finite element method. A diagonal line from the upper left corner to the lower right corner of the matrix in FIG. 7 indicates a diagonal component in the matrix, and a band matrix of non-zero elements is formed on both sides of the diagonal component. Outside the band matrix in the matrix is a triangular matrix of 0 elements. In this matrix, the width from the diagonal component to the outermost element component of the band matrix is a half bandwidth. FIG.
FIG. 8 is a diagram illustrating a specific example of the matrix in FIG. 7. FIG. 8 (a)
FIG. 4 is a diagram showing a case where an analysis model having a rectangular parallelepiped shape is divided into six parts. The analysis model in FIG. 8A is divided into two in the vertical direction and into three in the left and right direction and divided into six. In each element of the divided analysis model, elements e1, e2, and e3 are arranged from the lower left to the right, and elements e4, e5, and e6 are arranged from the upper left to the right. FIG.
In the node number of (a), the node numbers located on the lower side of the elements e1 to e3 are 1, 2, 3, and 4 from the left, and the element e1
The node numbers located on the boundary side between the elements e4 to e3 and the elements e4 to e6 are 5, 6, 7, 8 in order from the left, and the node numbers located on the upper side of the elements e4 to e6 are 9, 10, 11, in the order from the left. 1
2. FIG. 8B is a diagram showing an element matrix at each node number of the element e1 in FIG. 8A. By allocating node numbers as shown in FIG. 8A, 1, 2, 5, 6 in the rows and columns in the element matrix of FIG.
Is allocated. All the elements in the element matrix of FIG. 8B are usually non-zero elements. FIG.
FIG. 14 is a diagram in which element matrices from element e2 to element e6 are generated according to the element matrix for element e1 shown in (b), and an overall matrix is created by integrating the element matrices. For example,
As shown in FIG. 8B, for the row of the node number 1, the element at the intersection with the columns of the node numbers 1, 2, 5, and 6 is non-zero.
Element. Similarly, for the row of the node number 2, in addition to the intersection with the column of the node numbers 1, 2, 5, and 6 similar to the node number 1, in addition to the node number 2, which is the node number of the element e2,
The intersection elements with the columns 3, 6, and 7 are non-zero elements. However, since the node numbers 2 and 6 are common to the elements e1 and e2, the node numbers 1, 2, 3, 5, 6, and 7 The element at the intersection with the column is a non-zero element. Hereinafter, the band matrix is formed by arranging non-zero elements in the rows of the node numbers 3 to 12 based on the respective element matrices. Assuming that the width from the diagonal element to the terminal element of the band matrix is a half bandwidth, FIG.
In (c), it becomes 6. Also, the half bandwidth in this case is
The difference between the maximum value and the minimum value of the node number for each element is the maximum value among all the elements extracted. The amount of calculation in the analysis of the structure using the finite element method changes depending on whether the half bandwidth is wide or narrow. In the case of FIG. 8C, the half bandwidth is 6, but when it becomes 7, the calculation amount increases, and when it becomes 5, the calculation amount decreases. To reduce this half bandwidth,
The node numbers are changed as described above.

FIG. 9 is a diagram showing a specific example in which the half bandwidth can be reduced by changing the node numbers of the analysis model of FIG. FIG. 9A shows FIG.
A case where the rectangular parallelepiped analysis model is divided into six in the same manner as (a) is shown, and the analysis model is divided into two in the vertical direction and divided into three in the horizontal direction and divided into six. Each element of the divided analysis model is e1 from the lower left to the right.
Elements e1, e12, and e13 are arranged, and elements e14, e15, and e16 are arranged from the upper left to the right. FIG.
In the node number of (a), the node numbers located on the left side of the elements e11 and e14 are 1, 2, and 3 in order from the bottom, and the element e1
The node numbers located at the boundary sides of 1 and e14 and the elements e12 and e15 are 4, 5 and 6 from the bottom, and the node numbers located at the boundary sides of the elements e12 and e15 and the elements e13 and e16 are 7 from the bottom. , 8, 9 and the elements e13 and e1
The node numbers located on the right side of 6 are 10, 11,
Twelve. FIG. 9B is a diagram showing an element matrix at each node number of the element e11 in FIG. 9A. FIG.
By assigning node numbers as shown in FIG.
In each of the rows and columns in the element matrix of FIG.
2, 4, and 5 are allocated. All elements in the element matrix of FIG. 9B are usually non-zero elements. FIG.
(C) is a diagram in which element matrices from element e12 to element e16 are generated according to the element matrix for element e11 shown in FIG. 9 (b), and an overall matrix in which the element matrices are integrated is generated. . For example, for the row of node number 1, FIG.
As shown in (b), the elements at the intersections with the columns of the node numbers 1, 2, 4, and 5 are non-zero elements. Similarly, for the row of the node number 2, the node numbers 1, 2,
In addition to the intersections with the columns 4 and 5, the intersection elements with the columns of the node numbers 2, 3, 5, and 6, which are the node numbers of the element e14, are non-zero.
The node numbers 2 and 5 are elements e11 and e1
4, the node numbers 1, 2, 3, 4, 5, 6
The element at the intersection with the column is a non-zero element. Hereinafter, the band matrix is formed by arranging non-zero elements in the rows of the node numbers 3 to 12 based on the respective element matrices. If the width from the element of the diagonal component to the element at the end of the band matrix is a half band width, it is 5 in FIG. 9C. FIG.
Since the half-band width in the case of (c) is 5, FIG.
In this case, the half band width 6 is narrower. Therefore,
By changing the node numbers from the case of FIG. 8C to the case of FIG. 9C, the calculation amount of the entire matrix is reduced.

[0006]

8 and 9 are diagrams.
In the case where the shape of the analysis model is simple and the number of elements and the number of nodes are small as in the case of (2), the node number can be easily changed as described above, but the shape of the analysis model is When the number of elements and the number of nodes are increased, the number of nodes cannot be easily changed. That is, in the case of a structure having a complicated shape or a large shape (that is, an analysis model), it is not easy to change the node numbers, and the Cuthill-Mckee method described above is also used to change the node numbers when there are many elements. Since the required amount of calculation increases, the amount of calculation and the required amount of memory cannot be reduced. If the computer cannot cope with the increase in the amount of calculation or the amount of memory, the analysis model must be roughly divided and the structure must be analyzed by the finite element method, resulting in a decrease in calculation accuracy. The present invention has been made in order to solve the conventional problems as described above, and it has been proposed that the analysis by the finite element method can be performed even when the structure of the structure is complicated and the number of elements and the number of nodes are large. An object of the present invention is to provide a data generation method for generating numerical data for calculation capable of reducing the amount of calculation and memory required for structural analysis such as the finite element method from a model.

[0007]

In order to achieve the above object, a data generating method for generating numerical data for calculation from an analytical model by the finite element method according to the present invention is characterized in that a plurality of structural model analytical models are provided. Numerical data for calculation is obtained from an analysis model by the finite element method that analyzes the behavior of the entire structure by dividing the elements into elements and assigning node numbers to the nodes of each element, and adding the numerical values representing the physical quantities at each node number. In the data generation method for generating, the processing of dividing the analysis model into elements includes a first step of roughly dividing the analysis model into coarsely divided elements, and a step of further dividing the coarsely divided elements into subdivided elements. It is characterized in that it is performed in two stages, the second stage and the second stage. According to a second aspect of the present invention, in the data generation method for generating numerical data for calculation from the analytic model by the finite element method according to the first aspect, the analysis model is arranged in one direction in a first stage division processing. The analysis model is constituted by a plurality of the coarsely divided element sequences by setting one coarsely divided element sequence for the plurality of the coarsely divided elements. According to a third aspect of the present invention, there is provided a data generation method for generating numerical data for calculation from an analysis model based on the finite element method according to the second aspect, wherein in each of the plurality of coarsely divided element columns, Along with this, a node number for each of the nodes is set as a node number for a coarsely divided column.

According to a fourth aspect of the present invention, there is provided a data generating method for generating numerical data for calculation from an analysis model by the finite element method according to the third aspect, wherein the analysis is performed by integrating the respective columns of the ancestor divided element columns. The method is characterized by returning to the overall shape of the model and resetting the node numbers of the entire analysis model to the integrated node numbers based on the order of the coarsely divided column contact numbers. A data generating apparatus for generating numerical data for calculation from an analysis model based on the finite element method according to the present invention includes an input device capable of inputting various characters and numerical values such as data and programs, and at least a finite element method for a structure. A storage device that stores an analysis model and stores a program and data for analyzing the behavior of the structure using the analysis model, and a processor that generates the numerical data for calculation from the analysis model by applying the program and the data A computing device having a display device, a printing device, an external storage device,
A data generating device for generating numerical data for calculation from an analytic model by a finite element method, comprising: an output device capable of outputting to a communication device or the like; Or a content for executing a data generation method for generating numerical data for calculation from an analysis model based on the finite element method described in item 1;
The calculation device generates numerical data for calculation from the analysis model by the data generation method. As described above, an analysis model of a structure is first divided roughly into coarsely divided elements, and then a plurality of the coarsely divided elements arranged in one direction is set as one row, thereby analyzing the structure. The model is made up of a plurality of columns, the coarsely divided elements are further subdivided into subdivided elements, and each node of each subdivided element is set with a node number along the row of the column. By integrating the columns into the entire analysis model, and by replacing the node numbers at each node of each subelement with the node numbers throughout the analysis model, the amount of computation and memory required for structural analysis such as the finite element method Allows you to reduce the amount.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described based on illustrated embodiments. FIG. 1 is a diagram illustrating an example of an analysis model of a structure. As shown in FIG. 1, this analysis model was a two-dimensional analysis model S1 having a pentagonal shape. The case where the analysis model S1 is divided into quadrilateral elements will be described below. As shown in FIG. 2, first, the analysis model S1 is roughly divided into quadrilateral coarse division elements RE1 to RE5. FIG. 3 is a diagram showing a case where a coarsely divided row is set in accordance with the arrangement of the coarsely divided elements in one direction in FIG. The coarse division element RE1 and the coarse division element RE2 are arranged in one direction on the left and right in the drawing (one-dimensional arrangement direction).
And coarsely divided element RE2 to set coarsely divided row 1. Similarly, the coarsely divided elements RE3 to RE5 are arranged in one direction on the left and right in the drawing (one-dimensional arrangement direction), and the coarsely divided row 2 is set by the coarsely divided elements RE3 to RE5. . FIG. 4 is a diagram showing a case where each of the coarsely divided elements in the coarsely divided row 1 and the coarsely divided row 2 in FIG. 3 is subdivided into subdivided elements required for analysis. The coarsely divided row 1 in FIG. 4 is further divided vertically into two, and each of the coarsely divided element RE1 and the coarsely divided element RE2 is also horizontally divided into two. That is, each of the coarsely divided element RE1 and the coarsely divided element RE2 is further divided into four, and each of the divided elements becomes a subdivided element. Coarse division row 1
Are FE1, FE2, FE3, and FE4 in order from the left, with the subdivision elements of the lower row divided into two vertically. In addition, the subdivision elements in the upper row are FE5, FE6,
FE7 and FE8. The node number is a subdivision element FE1,
The node numbers on the lower side of FE2, FE3, and FE4 are set to 1, 2, 3, 4, and 5 in order from the left. Node numbers above the subdivision elements FE1, FE2, FE3, and FE4 and below subdivision elements FE5, FE6, FE7, and FE8 are set to 6, 7, 8, 9, and 10 from the left. Further, regarding the upper node numbers of the subdivision elements FE5, FE6, FE7, and FE8, 11, 12, 1
3, 14, and 15 are set.

Since the coarsely divided row 2 in FIG. 4 cannot be simply divided into upper and lower parts, first, the coarsely divided elements RE3 and RE4 are divided into two parts. Further, the coarse division elements RE4 and RE5
Is divided into upper and lower parts. Then, the coarse division element RE4 is divided into four parts. The coarsely divided elements RE3 and RE5 have two left and right sides similarly to the coarsely divided elements RE1 and RE2.
To divide. By dividing in this manner, the coarsely divided row 2
Are divided into four, and each of the divided elements becomes a subdivided element. The subdivided elements of the lower row where the coarsely divided row 2 is vertically divided into two are sequentially assigned from left to
E9, FE10, FE11, FE12, and FE13. Further, the subdivision elements in the upper row are FE
14, FE15, FE16, FE17, FE18, FE
19 and FE20. The node number is a subdivision element FE9,
Node numbers on the lower side of FE10, FE11, FE12, and FE13 are set to 1, 2, 3, 4, and 5 in order from the left. Further, the subdivision elements FE9, FE10, FE11, FE
12, above FE13 and subdivided elements FE14, FE
15, FE16, FE17, FE18, FE19, FE
For the lower node numbers of 20, 20, 7, from the left,
8, 9, 10, 11, and 12 are set. Further, the subdivision elements FE14, FE15, FE16, FE17, FE18,
Regarding the node numbers on the upper side of FE19 and FE20, 13, 14, 15, 16, 17, 18, 19, 2
0 and 21 are set. FIG. 5 is a diagram showing that the coarsely divided columns of FIG. 4 are integrated and the node numbers are reset (replaced) for the entire analysis model. In FIG.
The coarsely divided row 1 and the coarsely divided row 2 are integrated to form an analysis model S1. The configuration of the subdivided elements FE1 to FE20 is the same as the configuration of FIG. 4 except that the coarsely divided row 1 and the coarsely divided row 2 are joined, but the node numbers in the coarsely divided row 2 of FIG. 4 are reset. . Node numbers 1 to 5 of coarsely divided row 2 in FIG.
With regard to, since the node numbers 11 to 15 of the coarsely divided row 1 are joined one-to-one by integration with the coarsely divided row 1, the node numbers 1 to 5 disappear using the node numbers 11 to 15. The node numbers 6 to 12 of the coarsely divided row 2 in FIG. 4 become the next node numbers of the node numbers 11 to 15 of the coarsely divided row 1 by integration with the coarsely divided row 1, so that the node numbers 6 to 12 Node numbers 16 to 22 are reset. The node numbers 13 to 21 of the coarsely divided row 2 in FIG. 4 become the next node numbers of the node numbers 16 to 22 of the coarsely divided row 2 by integration with the coarsely divided row 1, so that the node numbers 13 to 21 are Node numbers 23 to 31
Is reset.

FIG. 6 is a block diagram showing an embodiment of a data generating apparatus for generating numerical data for calculation from an analysis model according to the finite element method of the present invention. The data generation device 1 for generating numerical data for calculation from the analysis model by the finite element method of the present invention includes an input device 2 such as a keyboard and a digitizer, a calculation device 3 including a plurality of processors, and an analysis model by the finite element method. It comprises a storage device 4 for storing programs such as a data generation method for generating numerical data for calculation, various setting values, various data, and the like, and an output device 5 for outputting calculation results and the like by the calculation device 3. First,
The operator of the calculation device 1 inputs a program such as a data generation method for generating numerical data for calculation from an analysis model by the finite element method from the input device 2 and stores the program in the storage device 4 in advance. Next, the operator of the computing device 1 inputs various setting values, data, and the like using the input device 2. Computing device 3
Reads a program of a data generation method for generating numerical data for calculation from an analysis model based on the finite element method from the input various set values from the storage device 4 and performs calculations based on the input various set values and data. . The calculation result is output from the output device 5 of the calculation device 1. The calculation result output from the calculation device 1 is subjected to processing such as recognition by an operator by a display device, a printing device, or the like, storage in an external storage device, or output to a network by a communication device. . As described above, when a structure is analyzed by a computing device, data can be generated using a data generation method for generating numerical data for calculation from an analysis model by the finite element method of the present invention. The amount and the amount of memory required for calculations can be reduced. still,
In the present embodiment, a case where the coarsely divided elements are arranged in the left and right direction (horizontal direction in the drawing) is shown, but the present invention is not limited to this. It is sufficient that they are arranged in a line, and the present invention can be applied to a case where the lines are arranged vertically (in the vertical direction in the figure) or a line which is arranged diagonally, and the arrangement does not need to be strictly straight.

[0012]

As described above, according to the present invention, an analysis model of a structure is first divided roughly into coarsely divided elements, and then a plurality of coarsely divided elements arranged in one direction is set as one row. By doing, the analysis model of the structure is set in multiple columns,
Further, the coarsely divided element is subdivided into subdivided elements, and a node number is set for each node of each subdivided element according to the arrangement of the column,
Finally, the plurality of columns are integrated to form the entire analysis model, and the node numbers at each node of each subelement are replaced with the node numbers throughout the analysis model, which is necessary for structural analysis such as the finite element method. It is possible to make the difference between the node numbers in each element relatively small while performing fine element division. Therefore, it is possible to reduce the amount of calculation and the required memory when calculating the analysis of the analysis model using the finite element method.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating an example of an analysis model of a structure having a complicated shape.

FIG. 2 is a diagram showing a case where the analysis model of FIG. 1 is roughly divided into quadrilateral elements.

FIG. 3 is a diagram illustrating a case where a coarsely divided row is set in accordance with the arrangement of the coarsely divided elements in one direction in FIG. 2;

FIG. 4 is a diagram showing a case where each of the coarsely divided elements in the coarsely divided row 1 and the coarsely divided row 2 in FIG. 3 is subdivided into subdivided elements;

5 is a diagram showing that the coarsely divided columns of FIG. 4 are integrated and the node numbers are reset (replaced) for the entire analysis model.

FIG. 6 is a block diagram showing one embodiment of a data generation device for generating numerical data for calculation from an analysis model by the finite element method of the present invention.

FIG. 7 is a diagram showing a matrix generally generated by the finite element method.

8A, 8B, and 8C are diagrams showing specific examples of the matrix shown in FIG. 7;

FIGS. 9A, 9B, and 9C are diagrams showing specific examples in which the half bandwidth can be reduced by changing the node numbers of the analysis model in FIG. 8;

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Calculation device, 2 ... Input device, 3 ... Operation device, 4 ... Storage device, 5 ... Output device

 ──────────────────────────────────────────────────続 き Continued on the front page F-term (reference) 5B046 DA02 JA08 5B056 BB04

Claims (5)

[Claims] 1. An analysis model of a structure is divided into a plurality of elements, a node number is assigned to each node, and a numerical value representing a physical quantity at each node number is added to analyze the behavior of the entire structure. A data generation method for generating numerical data for calculation from an analysis model by a finite element method, wherein the processing of dividing the analysis model into elements is a first step of roughly dividing the analysis model into coarsely divided elements; A data generation method for generating numerical data for calculation from an analysis model by a finite element method, wherein the coarse division element is further subdivided into two sub-steps of subdividing into sub-elements. 2. A method according to claim 1, wherein in the first stage of the analysis model division processing, one coarse division element row is set for the plurality of coarse division elements arranged in one direction, so that the analysis model is divided into the plurality of coarse division elements. 2. The data generation method for generating numerical data for calculation from an analysis model based on the finite element method according to claim 1, wherein the data generation method includes a series of divided elements. 3. The method according to claim 2, wherein a node number for each of the nodes is set as a node number for a coarsely divided column along a direction in which the coarsely divided elements are arranged for each of the plurality of coarsely divided element columns. A data generation method for generating numerical data for calculation from an analytical model based on the finite element method described. 4. The method according to claim 1, further comprising: integrating the respective columns of the ancestral division element sequence to return to the overall shape of the analysis model; 4. The data generation method according to claim 3, wherein the node number is reset to a node number. 5. An input device capable of inputting various characters and numerical values such as data and programs, a program and data for storing at least an analysis model of a structure by a finite element method and analyzing behavior of the structure by the analysis model. A storage device for storing, a computing device including a processor or the like that generates the numerical data for calculation from the analysis model by applying the program and the data, a display device, a printing device, A data generation device for generating numerical data for calculation from an analysis model by a finite element method, the data generation device including an external storage device or an output device capable of outputting to a communication device or the like, wherein the program includes: Data generation for generating numerical data for calculation from the analytic model by the finite element method described in any one of the above items 3 to 3 Contents for executing the method are described, and in the computing device, the numerical data for calculation is obtained from the analysis model by the finite element method, wherein the numerical data for calculation is generated from the analysis model by the data generation method. The data generation device to generate.