JP2007041630A - Structure design support program and structure design support apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a design support program and device of a structure for generating a properly shaped structure model with relative small calculation amounts only by setting a load value including loaded cyclic loading and a target value. <P>SOLUTION: This design support program is provided to execute first processing to calculate and set the stress value of each cell in design material information and loading information including cyclic loading, second processing to define a first cell in a design region as a target cell, and to compare the stress values of the target cell and the neighboring cell with the target stress value, third processing to set the target cell and an input value from the neighboring cell to the target cell based on the comparison result and input value conditions, fourth processing to add the total value of input values and a value calculated by performing an arithmetic operation to the current potential value of the target cell to calculate the new potential value of the cell, and fifth processing to compare the potential value of the calculation result with a predetermined threshold and sixth processing to set new design materials in the target cell based on the comparison result and to remove the design materials from the target cell, and to maintain the design materials. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to the field of designing a structure that satisfies a given design condition, and more particularly to a structure design support program and a structure design support apparatus suitable for supporting the design of a structure that receives a load. About.

  Conventionally, a simple concept of evolutionary structure optimization has been shown in which the shape of a structure evolves toward an optimal shape by gradually removing ineffective materials from the structure (see Non-Patent Document 1). This method can be regarded as a model of the concept of self-organization, for example, “the skeleton changes in response to the force field by interaction with the force field” (Non-patent Documents). 2). That is, cells that do not apply force disappear little by little, and by repeating such a process, a form that produces the maximum strength with a minimum amount of material is finally obtained.

However, it does not include a mechanism that “the part where the force is applied always grows and has the required strength”. On the other hand, a model in which a model including a growth mechanism is expressed using a cellular automaton and an application to optimization of a form has been devised (see Non-Patent Document 3). This exploits the intrinsic ability of self-organization that structures are generated autonomously by defining only simple local rules for cell appearance and disappearance. In order to determine the appearance and disappearance, it is necessary to set an upper limit stress value and a lower limit stress value as control parameters.

Xie, Y.M. and Steven, G.P .: Evolutionary Structural Optimization, Springer-Verlag, 1997 Darcy Thomson (Translated by Y. Yanagida and others): Biological Shape, University of Tokyo Press, 1981 Kazuo Mitsui: Autonomous generation and optimization of structural systems using cellular automata, Architectural Institute of Japan, 555, May 2000

However, in the method according to the conventional non-patent document 1, since the calculation process is started from a state in which the structure in the initial stage has the maximum volume, the amount of calculation becomes large.
Moreover, in the determination of the upper limit value and the lower limit value in the method of Non-Patent Document 3, it is necessary to obtain the values while repeating trial and error in some cases, which may be troublesome work.

  Furthermore, in each of the above examples, it has not been easy to apply to the design of a structural system that receives a load (periodic load) in which the magnitude and direction of the external force change periodically, such as a piston of a prime mover.

  Therefore, the present invention has been made by paying attention to such an unsolved problem of the conventional technology, and is appropriate only by setting a load value including a cyclic load to be loaded and a target value. It is an object of the present invention to provide a structure design support program and a structure design support apparatus that can generate a shape structure model and can generate the model with a relatively small amount of calculation.

  In order to achieve the above object, a structure design support program according to claim 1 of the present invention is a computer-executable program for generating a structure model having an appropriate shape based on given design conditions. And, as the design condition, at least information on a design material constituting the structure, a target stress value, load information including a periodic load applied to the structure, and the structure of the structure The design area information and the end condition are acquired, the process for dividing the design area into a plurality of virtual cells is performed, the support area and the load point are included in the design area, A process of initially arranging a structure model having a predetermined shape that can transmit a load applied to a load point to the support point and has a property of the design material under the design conditions is performed in association with the cell, A first process of calculating and setting each stress value for each cell corresponding to the structure model arranged in the design area based on the measured material information and the load information is performed. Cell is selected as a target cell, and a second process is performed for comparing the magnitude of the stress value of the target cell and the neighboring cells in the vicinity thereof with the magnitude of the target stress value. Based on the input value condition, a third process for setting input values from the target cell and the neighboring cells to the target cell is performed, and the total value of the input values and the current potential value of the target cell are attenuated. And a fourth process for calculating a new potential value of the target cell is performed, and the magnitude of the calculated potential value is compared with a predetermined threshold value. Based on the comparison result, a sixth process for setting a new design material in the target cell, removing the design material from the target cell, or maintaining the design material corresponding to the target cell is performed. The steps of performing the first to sixth processes on all cells capable of executing the processes are repeatedly performed until an end condition is satisfied.

  Accordingly, as design conditions, at least information on design materials constituting the structure, target stress values, load information applied to the structure, design area information of the structure, termination conditions, and design of the structure By acquiring the area information and the end condition, it is possible to transform the structure model arranged in the design area into an appropriate shape by repeating relatively simple operations until the end condition is satisfied. Is possible.

  Here, as described above, the structure model has information on the support point and the load point, and has the property that the load applied to the load point can be transmitted to the support point. It is a mathematical model with various information based on conditions. If each of these pieces of information is viewed as a functional unit, it can be said that the system has various functional units.

The design area can be acquired as a design condition by a user input or program setting. In the present invention, the design area is a design range of a structure. That is, within this range, the structure model that satisfies the end condition is generated by deforming the structure model.
The potential value indicates the energy of the cell regardless of the presence or absence of the design material. Normally, the higher this energy, the more likely new design material appears in the cell.

The current potential value is the potential value calculated in the previous step.
In addition, when calculating the potential value of the target cell as described above, a value obtained by attenuating the current potential value is used, but this is input from a cell with a nearby design material for a long time. This eliminates unnecessary material such as isolated design material, and enables generation of a more appropriately shaped structure model.

Further, as described above, the cell is a portion of each small area when the design area is divided into a set of a plurality of small areas.
The stress value (stress) is a resistance force generated inside the object according to the load when the object receives a load including a periodic load, and the strength is measured on both sides through an arbitrary unit area taken inside the object. It is expressed by the force that the parts exert on each other. Depending on how it appears, there are pressure, tension and shear stress.

  Although there is load information as a design condition, here, in addition to information on the magnitude, cycle, direction, etc. of the load applied to the structure, information on a support position that supports the load is also included.

  According to a second aspect of the present invention, in the structure design support program according to the first aspect, the comparison result between the stress values of the target cell and neighboring cells and the target stress value is the target stress value. When the stress value of the target cell is smaller than that, the input value to the target cell from the target cell and the neighboring cell is set to 0, and the magnitude of the stress value of the target cell and the neighboring cell and the target stress are set. When the comparison result with the magnitude of the value is greater in the stress value of the target cell and the neighboring cell than the target stress value, the input value from the target cell and the neighboring cell to the target cell is The new potential value is set to an increasing value.

The contents are reversed.
That is, when setting the input value to the own cell from the target cell and the neighboring cell, if the magnitude of the stress value of the target cell and the neighboring cell is smaller than the magnitude of the target stress value, 0 is set as the input value, When the magnitude of the stress value in the target cell and neighboring cells is larger than the magnitude of the target stress value, the new potential value of the target cell is set as the input value so that excessive stress occurs. The design material is likely to appear in the cell at the location where it is located, and the design material is easily removed from the cell where the sufficient stress is not generated, thus preventing the appearance and maintenance of useless design material. It becomes possible to perform efficient deformation.

According to a third aspect of the present invention, in the structure design support program according to the first or second aspect, the setting of the input value to the target cell in the second process is performed as von Mises as the stress value. The equivalent stress value of σ ^E is applied, the target stress value is σ ^E , the equivalent stress value of the target cell is σ ₀ , the input value to the own cell of the target cell is x ₀ , and the equivalent stress value of the neighboring cell is σ _i (i = 1, 2, 3,..., Where x _i (i = 1, 2, 3,...) Is an input value to a target cell of a neighboring cell, Yes.

In other words, the von Mises equivalent stress value is used as the stress value of the cell, and the input value is set according to the condition of the above formula. That is, when the input value from the target cell to the own cell is x ₀ and the input value from the neighboring cell to the target cell is x _i , for example, when considering a two-dimensional structure, it is adjacent to the target cell (up / down / left / right) If the four cells are set as neighboring cells and the input from these to the target cell is considered, the input values to the target cell are five values x ₀ , x ₁ , x ₂ , x ₃ , and x ₄ . Here, it is possible to consider inputs from cells that are diagonally spaced or two or more away from the target cell. Further, when expanding to three dimensions, the number of cells adjacent to the target cell increases, and each side of the cube When the input from the cell adjacent to (six planes) is considered, the input values to the target cell are seven values of x ₀ , x ₁ , x ₂ , x ₃ , x ₄ , x ₅ , x ₆ , Furthermore, when the cells in the oblique direction are taken into account, the total number of inputs to the target cell is 27. Of course, when the input from two or more cells is taken into account, the number of inputs further increases.

According to a fourth aspect of the present invention, in the design support program for a structure according to the third aspect, the calculation of the potential value in the third process is the current potential value calculated in the previous step. , Where u is _k (k is an integer), the attenuation constant is (1-λDt) (Dt is a time increment, and λ is a constant (0 <lDt <1)).

Here, the first term of the above equation means temporal addition to the potential of the input signal. When the potential u _k propagating in the next time step k + 1, so that the attenuated over time as it instead of propagating (1-LDT) multiplying it. From the second term onwards, it means spatial additivity. That is, a new potential value u _{k + 1} is calculated by using a value obtained by subtracting λΔt from 1 and the current potential value u _k for calculating a new potential value. It will be.

  The structure design support apparatus according to claim 5 of the present invention is an apparatus for generating a structure model having an appropriate shape based on a given design condition, and at least the structure as the design condition. Design condition setting means capable of setting information on a design material constituting the object, target stress value, load information applied to the structure, and design area information of the structure, and a plurality of virtual areas of the design area. A design area dividing means for dividing into a specific cell, a design area divided by the design area dividing means, including a support point and a load point, and a load applied to the load point can be transmitted to the support point; and Structure model placement means for initially placing a structure model of a predetermined shape having properties of the design material under design conditions in association with the cell, and the design based on the design material information and the load information A stress value setting means for calculating and setting each stress value for each cell corresponding to the structure model arranged in the area, and selecting one cell in the design area as the target cell, And a stress value comparison means for comparing the magnitude of the stress value of the neighboring cell in the vicinity thereof and the magnitude of the target stress value, and the target cell and the neighboring cell based on the comparison result and a preset input value condition Input value setting means for setting the input value to the target cell from each other, and the sum of the input values and the value obtained by attenuating the current potential value of the target cell are added together to obtain a new value for the target cell. Potential value calculating means for calculating the potential value, potential value comparing means for comparing the magnitude of the potential value of the calculation result with a predetermined threshold value, and the comparison result And a structure model deforming means for setting a new design material in the target cell, removing the design material from the target cell, or maintaining the design material corresponding to the target cell. .

  In such a configuration, the design condition setting means, as design conditions, at least information on the design material constituting the structure, the target stress value, load information applied to the structure, and the structure Design area information can be set, the design area dividing means can divide the design area into a plurality of virtual cells, and the structure model arranging means can be divided by the design area dividing means. Corresponding to the cell a structural model of a predetermined shape that includes a support point and a load point in the design area, can transmit the load applied to the load point to the support point, and has the properties of the design material under the design conditions The stress value setting means can correspond to the structure model arranged in the design area based on the design material information and the load information. It is possible to calculate and set the stress value for each cell, and select one cell in the design area as the target cell by the stress value comparison means, and the target cell and its nearby neighbors The magnitude of the stress value of the cell can be compared with the magnitude of the target stress value, and the target cell can be compared by the input value setting means based on the comparison result of the stress value comparison means and preset input value conditions. And the input value from the neighboring cell to the target cell can be set respectively, and the potential value calculation means adds the total value of the input values and the value obtained by attenuating the current potential value of the target cell. In addition, it is possible to calculate a new potential value of the target cell, by the potential value comparison means, by the potential value calculation means. It is possible to compare the magnitude of the generated potential value with a predetermined threshold value, and the structure model deforming means sets a new design material in the target cell based on the comparison result of the potential value comparing means, and the target It is possible to remove the design material from the cell or to maintain the design material corresponding to the target cell.

  Therefore, by providing at least the design material information constituting the structure, the target stress value, the load information applied to the structure, and the design area information of the structure as design conditions, it is relatively simple. By repeatedly performing the calculation, the structure model arranged in the design area can be transformed into an appropriate shape that satisfies the design conditions.

  According to a sixth aspect of the present invention, in the structure design support apparatus according to the fifth aspect, the input value setting means includes a magnitude of the stress value of the target cell and neighboring cells and the magnitude of the target stress value. When the comparison result shows that the stress value of the target cell is smaller than the target stress value, the input value to the target cell from the target cell and the neighboring cell is set to 0, and the stress of the target cell and the neighboring cell is set. When the comparison result between the magnitude of the value and the magnitude of the target stress value is larger in the stress value of the target cell and the neighboring cell than the target stress value, input from the target cell and the neighboring cell to the target cell A value is set to a value that increases the new potential value of the target cell.

  That is, regardless of the difference between the potential u and the threshold ε (ε is variable) (u−ε) (where u−ε ≧ 0, s = 1, that is, the material appears, and u−ε <0. When S = 0, that is, the material disappears, when the input values to the target cell from the target cell and the neighboring cell are set, the magnitude of the stress value of the target cell and the neighboring cell is the magnitude of the target stress value. When the value is smaller than 0, the input value is set to 0, and when setting the input value to the target cell from the target cell and the neighboring cell, the magnitude of the stress value of the target cell and the neighboring cell is larger than the magnitude of the target stress value. When it is large, the input value is set to a value that increases the new potential value of the target cell. Therefore, the design material tends to appear in the cell where excessive stress is generated, and sufficient stress is applied. A place where it does not occur Since easily removed design material from, it is possible to prevent the occurrence or maintenance of unnecessary design material, it is possible to perform efficient deformation.

  According to the structure design support program according to claim 1 of the present invention, as design conditions, at least information on a design material constituting the structure, a target stress value, and load information applied to the structure, By acquiring the design area information of the structure, it is possible to transform the structure model arranged in the design area into an appropriate shape by repeating relatively simple operations until the end condition is satisfied. Is possible.

  According to the structure design support program of claim 2, when setting the input value to the target cell from the target cell and the neighboring cell, the magnitude of the stress value of the target cell and the neighboring cell is the target stress. When the value is smaller than 0, the input value is set to 0, and when the input value from the target cell and the neighboring cell to the target cell is set, the magnitude of the stress value of the target cell and the neighboring cell is the target stress value. When the size is larger than the size, the input value is set to a value that increases the new potential value of the target cell. Therefore, the design material is likely to appear in the cell where excessive stress is generated. Since the design material is easily removed from the cell where no excessive stress is generated, it is possible to prevent the appearance and maintenance of useless design material and to perform efficient deformation. The

  Here, the structure design support apparatus according to claims 5 and 6 can be controlled by the structure design support program according to any one of claims 1 to 4, and the effects are duplicated. Therefore, the description is omitted.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. 1 to 16 are diagrams showing an embodiment of a structure design support apparatus according to the present invention.
First, the configuration of the design support apparatus according to the present invention will be described with reference to FIG. FIG. 1 is a block diagram showing a configuration of a design support apparatus according to the present invention.

The design support apparatus 1 includes a design support program 10, a CPU 11, a RAM 12, and a bus 13.
The design support program 10 includes a design condition setting unit 10a, a design region dividing unit 10b, a structure model arrangement unit 10c, a stress value setting unit 10d, a stress value comparison unit 10e, an input value setting unit 10f, a potential The value calculation unit 10g, the potential value comparison unit 10h, and the structure model deformation unit 10i are included. Note that ^{the first} design support program 10 constituted by these units is stored in a storage device (not shown), and is appropriately read and executed by the CPU 11.

Hereinafter, the processing contents of each unit at the time of program execution will be described.
The design condition setting unit 10a is for setting target stress value σ ^E , design region information, design material information, load information, and other information necessary for processing the program according to the structure to be designed. This information is provided in advance on the program side, selected by the user from the setting menu, or acquired manually by the user using an input device such as a keyboard. Here, the load information is information on the period, magnitude, and direction of the cyclic load applied to the weighting point of the structure to be designed, and the information necessary for the process is an end condition of the process (for example, a predetermined number of steps, A target value), a comparison value of potential values related to the appearance and disappearance of a design material, and the like.

The design area dividing unit 10b divides the design area set by the design condition setting unit 10a into a plurality of cells having a uniform size. Here, in this embodiment, it is assumed that the cell size can be varied.
The structure model arrangement unit 10c arranges a structure model having a predetermined shape having a property based on design material information in association with a cell in a design area divided into a plurality of cells. Can be evaluated for each cell.

  The stress value setting unit 10d performs stress analysis using the finite element method based on the set load information, and calculates the stress value of the design material corresponding to each cell of the structure model arranged in the design region. In this embodiment, von Mises equivalent stress value, which is often used as a criterion for isotropic materials, is applied, and calculation is performed according to the following number (1).

（１）

(1)

However, the two-dimensional coordinates are the x-axis and y-axis, σ _x is the stress value in the x-axis direction, σ _y is the stress value in the y-axis direction, and τ _xy is the shear stress value.
The stress value comparison unit 10e compares the magnitudes of the stress value σ ₀ and the target stress value σ ^E of the selected target cell, and also has cells in the vicinity of the target cell (for example, four cells adjacent in the vertical and horizontal directions). the magnitude of the stress value sigma _i and the target stress value sigma ^E) of even one that comparison, the comparative results will be stored therein is transmitted to the RAM12 via the bus 13.

Input value setting unit 10f is input value based on a result of comparison in the stress value comparison unit 10e, the input value x ₀ and the neighboring cells from the target cell to the local cell according to the following equation (2) to a target cell x _{1 to} x _i are respectively determined. The input value determined here is stored in the RAM 12.

（２）

(2)

Here, in order to determine whether or not a design material exists on a certain cell, it is a known method called a cellular automaton method to use a local rule related only to the vicinity of the cell.
Based on the determined input values x _{0 to} x _i and the current potential value u _k of the target cell, the potential value calculation unit 10g calculates a new potential value u _{k + 1} of the target cell according to the following number (3). Is to be calculated.

（３）

(3)

Here, the first term means temporal addition to the potential of the input signal. When the potential u _k propagates to the next time step k + 1, it does not propagate as it is, but attenuates with the passage of time by multiplying by (1-lDt). From the second term onwards, it means spatial additivity. That is, the new potential value u _{k + 1} is _obtained by multiplying the current potential value u _k by (1−λΔt), the input value x ₀ to the target cell's own cell, and a neighboring cell in the vicinity of the target cell. Input values x ₁ to x _i to the target cell from (for example, four cells adjacent vertically and horizontally) are added together.
The potential value comparison unit 10h compares the potential value u _{k + 1} calculated by the potential value calculation unit 10g with the comparison value related to the appearance and disappearance of the design material. The comparison result is stored in the RAM 12.

The structure model deforming unit 10i performs appearance, disappearance, and maintenance of the material in the target cell based on the comparison result of the potential value comparison unit 10h.
The CPU 11 reads each part of the design support program as appropriate into the RAM 12 and executes it based on data such as calculated values and comparison results stored in the RAM 12.

The RAM 12 mainly temporarily stores the processing results in the above-described units and temporarily stores the units of the design support program 10.
The bus 13 is a data transmission path for performing data transmission / reception between the above-described units and the CPU 11 and the RAM 12.
Hereinafter, a more specific operation of the design support apparatus 1 will be described with reference to FIGS. 2A to 2D are diagrams in which a structure model is arranged in a design area divided into a plurality of cells, and FIG. 3 shows a positional relationship between a target cell of a processing target cell group and its neighboring cells. FIG. 4 is a diagram showing a relationship between an input value and a potential value, and FIG. 5 is a diagram showing a step function for determining the appearance and disappearance of a design material. In the present embodiment, the process will be described by taking a two-dimensional structure model as an example for convenience of explanation.

  When the design condition described above is set by the design condition setting unit, a design area as shown by a lattice is set as shown in FIG. An initial shape is arbitrarily set in this. The load condition and the support condition include a cyclic load that varies periodically. When stress analysis is performed by the finite element method using each cell as an element, the stress value of each cell can be obtained. Based on this, the stress values in the vicinity are examined for all cells in the design space.

In this example, since all the cells and the vicinity thereof are examined, there are cases where the cells are not related to the structure as shown in FIG. The case where it is in contact with the structure as shown in FIG. 2C or the case where it is inside the structure as shown in FIG. In the actual calculation, there is no input in the case of FIG. The basic procedure of the structure design support apparatus according to this example is to repeat 3), 4) and 5) among the following five.

1) Divide the design area into uniform square lattices (cells).
2) Set up an arbitrary structural system that includes support points and load points in the design area and transmits the load to the support points.
3) In order to evaluate the response of the structure, perform stress analysis using the finite element method to obtain the stress of each cell.
4) Based on the stress obtained in 3), the state of the cell in the next time step, that is, whether or not material exists on the cell is determined, and the shape is updated.
5) Return to 3).

In the present invention, the calculation for determining whether or not material is present on the cell in 4) is essential. For this purpose, the stress state in the vicinity as shown in FIGS. 2B to 2D is examined for all cells. At this time, the following method is used.

FIG. 3 shows target cells and neighboring cells. Then, when a target stress value σ ^E is set in advance and there is a cell in the vicinity where the equivalent stress exceeds s ^E , an input signal +1 is input from the cell to the target cell. This is in accordance with number (5).

  Here, i = 0 means a target cell, and i = 1, 2, 3, 4 means neighboring cells. As a result, the sum of the input signals is added to the potential u of the target cell as in the second term of the number (3).

（４）

(4)

（５）

(5)

Here, u _k and u _{k + 1} are discrete times, potentials at k and k + 1, x ₀ is an input from the target cell, and x _i (i = 1, 4) is an input from a neighboring cell.
The first term of Equation 4 means temporal addition to the potential of the input signal. When the potential u _k propagating in the next time step k + 1, it decays with time as it instead of propagating (1-λΔt) multiplying it. From the second term onwards, it means spatial additivity. FIG. 4 shows the change in potential when the input +1 continues for 100 seconds and then the input becomes 0.

If the input continues, the potential reaches saturation. The saturation amount u _s can be adjusted by appropriately selecting w. The following equation is used to determine w.

（６）

入力がないときポテンシャルは時間と共に減衰する。ポテンシャルuが周期T(sec)の間にμからｍまで減衰するように設定するには数７によりlを決定すればよい。

(6)

When there is no input, the potential decays with time. In order to set the potential u to attenuate from μ to m during the period T (sec), l may be determined by Equation 7.

（７）

(7)

（８）

ここで、値については、u_s ＝10，ρ=ｍ/m =0.5とすると計算に好適である。解決すべき問題に周期Ｔは与えられるから、数(４)のλもωも数(５)(６)(７)により自動的に決定できる。また、時間増分Δｔは要求された解の精度によって任意に設定できる。

(8)

Here, the values are suitable for calculation when u _s = 10 and ρ = m / m = 0.5. Since the period T is given to the problem to be solved, both λ and ω of the equation (4) can be automatically determined by the equations (5), (6), and (7). Further, the time increment Δt can be arbitrarily set according to the accuracy of the requested solution.

  By doing so, as shown in FIG. 5, regardless of the difference u−ε between the potential u and the threshold value ε, when u−ε ≧ 0, s = 1, that is, the material appears, and u−ε. When <0, s = 0, that is, the material disappears. This means that the process is non-linear. These processes have the four basic properties of the binary nature of input / output signals and the above-described spatial addability, temporal addability, and nonlinearity.

Setting of the threshold ε is affected by setting the saturation amount u _s. The recommended value of the threshold ε when the saturation amount is set to 10 as described above is 1.

  More specifically, this process is performed by the design area dividing unit 10b to divide the set design area 20 into a plurality of cells 21 having a uniform size. And the structure which has the property of the set design material by the structure model arrangement | positioning part 10c after a division | segmentation process, and can transmit the periodic load concerning the periodic load point 24 to the support point 23 in a figure The object model 22 is arranged in association with the cell.

  Here, the structure model 22 is configured with the cell 21 as a minimum constituent unit. Therefore, it is possible to evaluate under the same conditions for each corresponding cell of the structure model. In the present embodiment, the property of the design material is determined by Young's modulus and Poisson's ratio, and here, occurrence of buckling is not considered. Moreover, the cell said here is a square lattice.

Further, the equivalent stress value σ of each cell 21 is calculated and set for the structure model 22 arranged in the design region 20 according to the above formula (1) based on the properties of the design material and the cyclic load information. When the equivalent stress value σ is set, the stress value comparison unit 10e performs a process of comparing the equivalent stress value σ set for the cell with the target stress value σ ^E according to Equation 2.

  Here, as shown in FIG. 3, the processing target cell group 30 to be processed includes the target cell 31, the target cell, and neighboring cells 31 a to 31 d in the vicinity adjacent to the top, bottom, left, and right (Neumann vicinity) (see FIG. 3). ) To select. That is, when the cell 31 corresponding to the structure model 22 in FIG. 2 is selected as the target cell, as shown in FIG. 3, the target cell 25 has the central cell 31 and the four neighboring cells 31a to 31d adjacent thereto. A cell that matches is selected as a processing target.

Therefore, the stress value comparison unit 10e first compares the equivalent stress value σ ₀ set in the target cell 31 with the target stress value σ ^E, and then compares the equivalent stress values σ _{1 to} σ _{4 of the} neighboring cell cells 31a to 31d. And the target stress value σ ^E are respectively compared.

  Therefore, in the input value setting unit 10f, the input value is set according to the above-described number (5) based on the comparison result between the target cell 31 subjected to the comparison process and the neighboring cell 31b.

For example, the target cell 31, the equivalent stress value sigma ₀ of neighboring cells 31a and 31b, when sigma ₁ and sigma ₂ is smaller than the target stress value sigma ^E, the input value x ₀ to the target cell 31, _{x 1} Contact call _{x 2} Is set to 0 according to the number (5), and the equivalent stress values σ ₃ and σ _{4 of} the neighboring cells 31c and 31d are larger than the target stress value σ ^E , the input values x ₃ and x to the target cell 31 ₄ is set to the value +1 according to the number (5). As a result, the potential of the target cell 31 increases by a value that is a constant multiple of these totals +2.

In the potential value calculation unit 10g, the potential value u _{k + 1} is calculated.

When the new potential value u _{k + 1 of} the target cell is calculated, the potential value comparison unit 10h compares the potential value u _{k + 1} with the comparison value of the potential value related to the appearance and disappearance of the design material. Processing is performed.
That is, the comparison value is a predetermined value (for example, 0) related to the appearance of a new design material, the disappearance of the design material (the part corresponding to the target cell of the structure model 22) (the design material is removed from the target cell), or the maintenance. is there.

When this comparison process is completed, if the potential value u _{k + 1} of the target cell is greater than or equal to the comparison value and there is no design material in the target cell, a new design material is placed in that cell. If the potential value u _{k + 1} of the target cell is equal to or greater than the comparison value and there is a design material in the target cell, a process of maintaining the design material as it is is performed, and the potential value u _{k + 1} Is smaller than the comparison value, and if there is already a design material in the target cell, a process of eliminating the design material from the target cell is performed.

That is, in the present embodiment, as shown in FIG. 5, if the value of (u−ε) is equal to or greater than “0” which is a comparison value, the new design material appearance process and the design material maintenance process are performed. On the other hand, if the value is smaller than the comparison value “0”, the design material disappearing process is performed (S = 0).
Therefore, in the potential value comparison process, if the potential value of the target cell is equal to or greater than the comparison value, the design material in the target cell is maintained, and if the potential value of the target cell 31 is equal to or greater than the comparison value, If the design material appears and the potential value of the target cell is smaller than the comparison value, the design material in the target cell disappears.

When the deformation process of the structure model is completed, the stress value setting unit 10d performs the calculation and resetting process of the equivalent stress value of each cell corresponding to the structure model 22 ′ after the deformation process according to the number (1). .
In the present embodiment, the above-described series of processing is performed on all cells for which potential values can be calculated, and this is repeated as one step until a predetermined condition is satisfied.

Further, when the step advances and the potential value u _{k + 1} of the target cell is calculated, the potential value for the step is calculated for each cell. For example, as the current potential value uk, the initial value “ It may have a numerical value other than “0”. Therefore, for example, if the potential value of the target cell is u _k = 10, in the calculation of a new potential value u _{k + 1} , the value _obtained by multiplying u _k = 10 by (1-lDt) is the input value x ₀ described above. It will be added together and ~x _4.

As described above, among the structures that support a given cyclic load, the problem is to find the structure with the smallest weight that satisfies the constraint condition that the stress value allowed in any part of the structure is less than or equal to the target stress value σ ^E. This is a minimum weight problem.

  Hereinafter, an example in which the present invention is applied to an actual minimum weight problem will be described with reference to FIGS. FIG. 6 is a diagram illustrating an example of design conditions, and FIG. 7 is a diagram illustrating a generation process of a structure model that satisfies an end condition when the present apparatus 1 is applied under the conditions of FIG. 8 is a diagram showing a volume change in the generation process of the structure shown in FIG. 7, and FIG. 9 is a graph showing an equivalent stress value in the generation process of the structure model that satisfies the termination condition when the apparatus 1 is applied under the conditions of FIG. It is a figure which shows transition. In addition, although the shading in the figure has shown the state of stress, in order to simplify description, suppose that the state of stress is not touched in the following description.

As shown in FIG. 6, the design support apparatus 1 is set with design conditions for generating a structure model that supports a periodic load of 800 N at a point 1000 mm from the wall surface in a 1000 mm × 2400 mm design region. The target stress value σ ^E : 0.25 Mpa, Young's modulus: 100 GPa, Poisson's ratio: 0.3, cell size: 40 mm × 40 mm, cell thickness: 10 mm, and the design material is linear elasticity such as steel. As a material, it was assumed that the characteristics can be given by Young's modulus and Poisson's ratio as described above.

  Next, as one of the cases where the external force fluctuates periodically, consider the case where the direction of the load changes periodically. This is a case where the direction of the load rotates clockwise from the initial state to 0 to p / 2 rad under the conditions shown in FIG. As the initial shape, a straight beam connecting the load point and the support point was selected from any shape that transmits the load to the left end.

  FIGS. 7A to 7J show the deformation process under this condition. FIG. 8 shows the change in volume during the generation process of the above example, averaged for each period. It can be seen that the shape changes autonomously with von Mises stress as the control parameter, and the volume converges accordingly.

Then, under the design conditions of FIG. 6, the design area is divided into a plurality of 25 × 60 cells, and a structure model whose initial shape is a cantilever shape as shown in FIG. In this case, by repeating the above-described steps of the design support program 10 on the structure model, as shown in FIGS. 7B to 7J, a new design material appears. The shape is deformed while eliminating unnecessary design materials, and finally (for example, after 160 steps), the equivalent stress value of the target stress value σ ^E corresponds to the structure model as shown in FIG. A model of a three-member frame structure that is distributed almost evenly in all cells is generated. In the generation process, the average value of the equivalent stress values σ in the corresponding cells of the structure model shows a transition as shown in FIG. 9 every time the step is repeated. That is, the local rule regarding the appearance and disappearance of the design material balances the stress value of each cell apart from the periodic load point where the stress is concentrated, and the average value is set as the set target stress value σ ^E = 0.25 Mpa. It can be seen that it has a function to induce

Further, FIGS. 10A to 10J show generation processes in other initial shapes under the conditions in FIG. In this example, it is possible to generate the same shape as in FIG. 7J by performing the same processing as in the above example assuming that the initial shape is different.
Thus, in the present invention, the same final shape can be obtained even with different initial shapes.

Next, the processing flow of the design support program will be described with reference to FIG. FIG. 11 is a flowchart showing the process of the design support program. However, the flowchart of FIG. 11 shows the flow of processing after setting the design conditions.
As shown in FIG. 13, first, the process proceeds to step S100 to determine whether the design condition is set and the process is started. If it is determined that the process is started (Yes), the process proceeds to step S102, and so on. If not (No), wait until it starts.

  When the process proceeds to step S102, the design area dividing unit 10b divides the set design area into a plurality of cells having a uniform size, and the process proceeds to step S104. In step S104, the structure model placement unit 10c places a structure model in the divided area, and the process proceeds to step S106. Here, in the present embodiment, the structure model to be arranged can transmit the cyclic load applied to the cyclic load point including the cyclic load point and the support point to the support point, and if the whole is within the design region, Arbitrary shapes can be arranged at arbitrary positions.

  In step S106, the stress value setting unit 10d performs stress analysis on the structure model arranged in the design region by using the finite element method, and based on the above number (1), the von Mises of each cell. The equivalent stress value σ is calculated and set in each corresponding cell, and the process proceeds to step S108. In step S108, the stress value comparison unit 10e selects a target cell and proceeds to step S110.

In step S110, the stress value comparison unit 10e, the target cells and the four and equivalent stress value sigma ₀ and sigma ₁ ～Shiguma ₄ neighboring cell and the target stress value sigma ^E, which is one of the design conditions in the vicinity thereof, respectively The comparison results are transmitted to the RAM 12 and the process proceeds to step S112.
In step S112, the input value setting unit 10f determines input values to the target cell according to the numbers (2) and (3) based on the comparison result by the stress value comparison unit 10e, and transmits them to the RAM 12. Then, the process proceeds to step S114.

In step S114, a new potential value u _{k + is} calculated according to the number (4) based on the input values x _{0 to} x ₄ and the current potential value u _k set by the input value setting unit 10f by the potential value calculation unit 10g. ₁ is calculated, and the process proceeds to step S116.
In step S116, the new potential value u _{k + 1 of} the target cell calculated by the potential value calculation unit 10g by the potential value comparison unit 10h and the comparison values related to the appearance and disappearance of the design material are shown in FIG. The comparison is performed according to the function, the comparison result is transmitted to the RAM 12, and the process proceeds to step S118.

In step S118, the structural model deforming unit 10i performs a deformation process on the structure model based on the comparison result in the potential value comparing unit 10h, and the process proceeds to step S120.
In step S120, the stress value comparison unit 10e determines whether all cells that can be processed have been selected. If it is determined that the cells have been selected, the process proceeds to step S122. If not, the process proceeds to step S108. Transition.

When the process proceeds to step S122, the stress value setting unit 10d determines whether or not the end condition is satisfied. When it is determined that the end condition is satisfied (Yes), the process ends, and when it is not (No) Proceeds to step S124.
When the process proceeds to step S124, the step indicating the passage of time is advanced by 1 and the process proceeds to step S106.

  As described above, according to the embodiment of the present invention, by giving the design conditions described above to the design support program 10, the structure model arranged in the design region divided into a plurality of uniform cells can be obtained. In accordance with local rules regarding the emergence and disappearance of design materials, design materials appear in areas where stress is required, while the design materials disappear from unnecessary areas. It is possible to generate a structure model that satisfies the end condition by deforming the equivalent stress value of the above to the target stress value.

Further, an example in which the present invention is applied to a three-dimensional structure will be described.
FIG. 12 is a diagram illustrating a three-dimensional processing target cell group including target cells and neighboring cells for application to a three-dimensional model, and FIG. 13 is a diagram illustrating an example in which the present embodiment is applied to a three-dimensional shape. a) is an initial shape, (b) is a diagram showing an optimized shape, FIG. 14 is a diagram showing another example in which this embodiment is applied to a three-dimensional shape, (a) is an initial shape, and (b) is an optimum shape. FIG. 15 is a diagram illustrating another example in which the present embodiment is applied to a three-dimensional shape, FIG. 16A is an initial shape, and FIG. 15B is a diagram illustrating an optimized shape.

  In this example, a cell to be processed is selected in the three-dimensional processing target cell group 40. The three-dimensional processing target cell group 40 includes seven target cells (not shown) and neighboring cells 41a to 41f (nearly neighboring cells 41f are not shown) in the vicinity (near Neumann) adjacent to the six faces thereof. One cell.

In this example, the three-dimensional processing target cell group 40 is used to perform the same processing as in the above example to optimize the three-dimensional structure.
In the example shown in FIG. 13, the initial structure of the three-dimensional structure having the initial shape shown in FIG. 13A has a vertical load of 5 KN / m ² and a seismic force with an inverted triangular seismic intensity distribution (C _B = 0.2) above each layer. ) Is optimized and the structure shown in (b) is obtained. In this example, the structure of (b) was obtained by the optimization process of 37 steps from the initial shape of (a).

In the example shown in FIG. 14, the concentrated load P = 100 KN is applied to the three-dimensional structure of the initial shape shown in FIG. The structure shown is obtained. In this example, the structure of (b) was obtained by the optimization process of 40 steps from the initial shape of (a).

The example shown in FIG. 16 has been optimized based on the optimization conditions shown in FIG. In this example, a vertical load and a horizontal load (0.2 times the vertical load) are applied to the horizontal plane (width 0.3 m) on the beam as a load to the three-dimensional structure shown in (a). In this example, as shown in FIG. 15, the design area 6 m × 6 m, Young's modulus 205 GPa, Poisson's ratio 0.3, cell size 0.1 ³ m ³ , σ ^L = 0.5 MPa, σ ^U = 1.0 MPa, P = 1000 N / nod, Q = 200 N / nod for optimization. From the state of FIG. 16 (a), the result of 9 optimization steps (b) and the result of 21 optimization steps (c) are obtained, and finally 41 optimization steps are performed. As a result, the structure of (d) was optimized.

  FIG. 17 shows the volume change in this process, and FIG. 18 shows the state of the average equivalent stress σ. From these graphs, it can be seen that as the optimization proceeds, the volume decreases and the average equivalent stress decreases, and the usefulness of the present embodiment is proved.

In the example shown in FIG. 19, the space portion of the three-dimensional structure having the initial shape shown in FIG. The structure shown in (b) is obtained. In this example, the structure of (b) was obtained by the optimization process of 20 steps from the initial shape of (a).

  As described above, according to the structure design support program and the structure design support apparatus according to the present invention, it is possible to obtain an optimum structure in a plane and a three-dimensional structure.

It is a block diagram which shows the structure of the design support apparatus which concerns on this invention. (A) is a figure which shows an example of a process target structure, (b)-(d) is a figure which shows the positional relationship of a process target structure, a target cell, and its vicinity cell. It is a figure which shows the process target cell group which consists of a target cell and a neighboring cell. It is a figure which shows the time change of a potential value. It is a figure which shows the step function which determines appearance and disappearance of a design material. It is a figure which shows an example of design conditions. (A)-(j) is a figure which shows an example which produces | generates the frame structure when the initial shape of a structure model is a cantilever in the design conditions of FIG. It is a figure which shows the volume change in the production | generation process of the structure shown in FIG. It is a figure which shows transition of the equivalent stress value in the production | generation process of the structure model which satisfies completion | finish conditions when this apparatus 1 is applied on the conditions of FIG. (A)-(j) is a figure which shows an example which produces | generates the frame structure when the initial shape of a structure model is made into another shape on the design conditions of FIG. It is a flowchart which shows the process of a design support program. It is a figure which shows the process target cell group which consists of a target cell and a neighboring cell for applying to a three-dimensional model. It is a figure which shows the example which applied a present Example to the solid shape, (a) is an initial shape, (b) is a figure which shows an optimization shape. It is a figure which shows the other example which applied the present Example to the solid shape, (a) is an initial shape, (b) is a figure which shows an optimization shape. It is a figure which shows the optimization conditions of the other example which applied the present Example to the solid shape. It is a figure which shows the optimization example shown in FIG. 15, (a) is an initial shape, (b), (c) is a figure of the production | generation process (d), and is a figure which shows an optimization shape. It is a figure which shows the volume change in the production | generation process of the structure shown in FIG. It is a figure which shows transition of the equivalent stress value in the production | generation process of the structure model shown in FIG. It is a figure which shows the other example which applied the present Example to the solid shape, (a) is an initial shape, (b) is a figure which shows an optimization shape.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Design support apparatus 10 Design support program 10a Design condition setting part 10b Design area division | segmentation part 10c Structure model arrangement | positioning part 10d Stress value setting part 10e Stress value comparison part 10f Input value setting part 10g Potential value calculation part 10h Potential value comparison part 10i Structure model deformation unit 20 Design area 21 Cell 22 Structure model 23 Support point 24 Periodic load point 30 Target cell group 31 Target cell 31a to 31d Neighbor cell 40 Three-dimensional cell group 41a to 41e Neighbor cell

Claims (6)

A computer-executable program for generating a structural model of an appropriate shape based on given design conditions,
As the design conditions, at least information on a design material constituting the structure, a target stress value, load information including a periodic load applied to the structure, design area information of the structure, and an end condition, The design area is divided into a plurality of virtual cells, the support area and the cyclic load point are included in the design area, and the periodic cyclic load applied to the cyclic load point is applied to the support point. An initial process is performed to initially arrange a structure model of a predetermined shape having a property of the design material in the design conditions that can be transmitted in association with the cell,
Performing a first process of calculating and setting each stress value for each cell corresponding to the structure model arranged in the design region based on the design material information and the load information,
Selecting one cell in the design area as a target cell, and performing a second process of comparing the magnitude of the stress value of the target cell and a neighboring cell in the vicinity thereof with the magnitude of the target stress value, respectively;
Based on the comparison result and a preset input value condition, perform a third process of setting the input value from the target cell and the neighboring cell to the target cell,
A fourth process for calculating a new potential value of the target cell by adding a value obtained by multiplying the sum of the input values by a constant and a value obtained by attenuating the current potential value of the target cell;
A fifth process for comparing the magnitude of the potential value of the calculation result with a predetermined threshold value is performed,
Based on the comparison result, a sixth process for setting a new design material in the target cell, removing the design material from the target cell, or maintaining the design material corresponding to the target cell is performed.
A structure design support program characterized in that the steps of performing the first to sixth processes on all cells capable of executing the processes are repeatedly performed until an end condition is satisfied.   When the comparison result between the magnitude of the stress value of the target cell and its neighboring cells and the magnitude of the target stress value is smaller than the stress value of the target cell and its neighboring cells, the target cell And the input value to the target cell from its neighboring cells is set to 0, and the comparison result between the magnitude of the stress value of the target cell and the neighboring cell and the magnitude of the target stress value is greater than the target stress value. When the stress value of the neighboring cell is larger, the input value from the target cell and the neighboring cell to the target cell is set to a value that increases the new potential value of the target cell. A structure design support program according to claim 1. In setting the input value to the target cell in the second process, the equivalent stress value of von Mises is applied as the stress value, the target stress value is σ ^E , the target cell equivalent stress value is σ ₀ , the target cell X ₀ , the equivalent stress value of the neighboring cell σ _i (i = 1, 2, 3,...), And the input value of the neighboring cell to the target cell x _i (i = 3. The structure design support program according to claim 1, wherein the structure design support program is executed according to the following formula.

The calculation of the potential value in the third process is performed by using the current potential value calculated in the previous step as u _k (k is an integer), the attenuation constant as (1-λDt) (Dt is a time increment, 4. The structure design support program according to claim 3, wherein λ is a constant (0 <lDt <1), and is performed according to the following equation.

An apparatus for generating a structural model of an appropriate shape based on given design conditions,
As the design conditions, at least information on a design material constituting the structure, a target stress value, load information including a period applied to the structure, design area information of the structure of the structure, A design condition setting means capable of setting an end condition;
Design area dividing means for dividing the design area into a plurality of virtual cells;
A predetermined shape including a support point and a load point in the design area divided by the design area dividing means, capable of transmitting the load applied to the load point to the support point, and having the properties of the design material under the design conditions A structure model placement means for initially placing the structure model in association with the cell;
Stress value setting means for calculating and setting the respective stress values for each cell corresponding to the structure model arranged in the design region based on the design material information and the load information;
Selecting one cell in the design region as a target cell, a stress value comparison means for comparing the target cell and the stress value of a neighboring cell in the vicinity thereof with the target stress value, respectively;
Input value setting means for setting input values from the target cell and the neighboring cells to the target cell based on the comparison result and a preset input value condition;
A potential value calculation means for adding a value obtained by multiplying the sum of the input values by a constant and a value obtained by attenuating the current potential value of the target cell to calculate a new potential value of the target cell;
A potential value comparing means for comparing the magnitude of the potential value of the calculation result with a predetermined threshold;
A structure model deformation means for setting a new design material in the target cell based on the comparison result, removing the design material from the target cell, or maintaining the design material corresponding to the target cell. A structure design support device characterized by the above. In the input value setting means, when the comparison result between the magnitude of the stress value of the target cell and the neighboring cell and the magnitude of the target stress value is smaller than the stress value of the target cell and the neighboring cell Sets the input value to the target cell from the target cell and the neighboring cell to 0, and the comparison result between the magnitude of the stress value of the target cell and the neighboring cell and the magnitude of the target stress value is the target stress. When the stress value of the target cell and the neighboring cell is larger than the value, the input value from the target cell and the neighboring cell to the target cell is set to a value that increases the new potential value of the target cell. The structure design support apparatus according to claim 6, wherein:

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