KR101703450B1 - Structural topology optimization method using bigbang-bigcrunch algorithm - Google Patents
Structural topology optimization method using bigbang-bigcrunch algorithm Download PDFInfo
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Abstract
A phase optimization design method of a structure includes dividing a design area of the structure into a plurality of elements, calculating a sensitivity value of each of the elements by finite element analysis, and calculating a fitness from the sensitivity value ; Creating a virtual design area extending in the design area and having an arbitrary area; And executing the large explosion-versus-shrink algorithm in each of the execution regions by arbitrarily setting the execution regions in the reference region unit over the entire region including the design region and the virtual design region.
Description
The present invention relates to a method of optimizing a topology of a structure, and more particularly, to a method of optimizing a topology of a structure using a large explosion-large contraction algorithm.
The Bigbang-Bigcrunch Algorithm is an algorithm inspired by the process of the birth and extinction of the universe, in which a myriad of planets are created at the birth of the universe, which, as the universe expands, It is a method to search the solution through the process of converging to the center of gravity by increasing the gravity of the part and disappearing. It has been confirmed that this large explosion - contraction algorithm is efficient in finding the global solution value faster than other algorithms in the optimization process.
On the other hand, the purpose of structural optimization is to obtain the shape of a structure that can draw the smallest static compliance value while satisfying the constraints such as the stress limit, the deformation limit, and the volume condition of the structure. According to the requirements of the designer, the structure optimization is divided into sizing, shape, and topology optimization. Conventional techniques include solid isotropic material with penalization (SIMP) and bi-directional evolutionary structural optimization (BESO ), Ant colony optimization (ACO), artificial bee colony algorithm (ABCA), and Harmony Search Algorithm (HS) all provide a similar optimal phase.
Among the phase optimization algorithms, SIMP has a gray area in phase, which makes it difficult to clearly define the optimized phase boundary and is slow. BESO requires a process to match target volume, so convergence is slow and ACO is also slow. The fastest ABCA of the prior art has the fastest convergence speed in the process of sending the employment bee to a better position for quick search, but it still needs to improve the convergence speed. Also, in the case of phase optimization using the HS (Harmonic Search) method, if the target volume is decreased below a certain amount, there is a limit that the optimum phase can not be found.
Although there is a case where the above-described large explosion-shrinkage algorithm is applied to the size optimization design of a structure, there is no case where the phase optimization is applied. This is because the large explosion-versus-contraction algorithm finds only one optimal solution for the center of gravity (contraction) of the candidate solutions, so that the general boundary-contraction algorithm can not find the boundary of the structure.
The present invention provides a method of performing a topology optimization design of a structure using a large explosion-versus-shrink algorithm.
According to an embodiment of the present invention, a method for optimizing a topology of a structure includes dividing a design area of the structure into a plurality of elements, calculating a sensitivity value of each of the elements by finite element analysis, Calculating a fitness from the sensitivity value; Creating a virtual design area extending in the design area and having an arbitrary area; And executing the large explosion-versus-shrink algorithm in each of the execution regions by arbitrarily setting the execution regions in the reference region unit over the entire region including the design region and the virtual design region.
Also, the reference area may be an area in which the elements are arranged in a matrix of m x n (m and n are natural numbers), and the virtual design area may be extended in the design area at a certain rate of the m x n matrix.
Also, the virtual design area may be extended to the upper and lower sides of the design area by a row of the elements corresponding to 1/2 of m, and may be extended to both sides of the design area Respectively.
The step of performing the large explosion-contraction algorithm in the execution regions may further include: randomly selecting a candidate solution among the elements; Dividing the execution region into a solid region including the candidate solution and a void region not including the candidate solution; Performing the large explosion-versus-shrink algorithm in the solid region, and selecting an element having the highest fitness in the solid region; Performing the large explosion-versus-shrink algorithm in the void region, and selecting an element having the lowest fitness in the void region; Comparing the element having the highest fitness and the element having the lowest fitness; And when the fitness of the element with the highest fitness is greater than the fitness of the element with the lowest fitness, the position of the element with the highest fitness and the one with the lowest fitness are not exchanged, Of the element having the highest degree of fidelity is larger than the degree of fidelity of the element having the highest degree of fidelity.
Also, the number of times the position of the element having the highest fitness and the element having the lowest fitness is not counted is counted until the number of consecutive times is repeated at a preset number of times, May be repeated.
The topology optimization design method of a structure according to another embodiment of the present invention designs an optimum phase of the structure by executing a large explosion-large shrinkage algorithm.
Calculating a sensitivity value of the elements by a finite element analysis on a design area of the structure and calculating a fitness from the sensitivity value; Executing the large explosion-versus-shrink algorithm in the entire area including the design area and a virtual design area extending therefrom to an arbitrary area; And classifying the elements having a high value of the fitness and the elements having a low value of the fitness by executing the large explosion-large contraction algorithm.
Also, the large explosion-to-shrink algorithm may be performed in units of execution regions where the elements are included in a predetermined area, and the virtual design region may be extended from the design region at a certain rate of the execution region.
The step of performing the large explosion-contraction algorithm in the entire region may include: selecting a candidate solution among the elements; Dividing the execution region into a solid region including the candidate solution and a void region not including the candidate solution; Performing the large explosion-versus-shrink algorithm in the solid region, and selecting an element having the highest fitness in the solid region; And performing the large explosion-versus-shrink algorithm in the void region, and selecting an element having the lowest fidelity in the void region, wherein the element having a high value of the fidelity and the element having a low value of the fidelity Wherein the classifying step compares the element having the highest fitness with the element having the lowest fitness and if the fitness of the element having the highest fitness is greater than the fitness of the element having the lowest fitness, If the position of the element with the lowest degree of fit is not replaced and if the degree of fit of the element with the lowest degree of fit is larger than that of the element with the highest degree of fit, Exchangeable.
Also, the number of times the positions of the elements having the highest fitness and the elements having the lowest fitness are not counted are counted, and a large-explosion-shrinkage algorithm is performed in all the regions until the number of consecutive times is repeated a preset number of times. May be repeated.
According to another embodiment of the present invention, a method for optimizing a topology of a structure includes defining a design area of the structure, creating a virtual design area extending from the design area to an arbitrary area, And performs a large explosion-versus-shrink algorithm on the entire region including the region.
According to the present invention, the design method using the large explosion-shrinkage algorithm improves the convergence speed than the conventional design method.
1 is a flow chart illustrating a method for optimizing a topology of a structure according to an embodiment of the present invention.
2 is a view showing an example of a structure to which a topology optimization design method according to an embodiment of the present invention is applied.
FIGS. 3 and 4 are views illustrating a process of creating a virtual design area according to an embodiment of the present invention.
5 to 9 are views showing an example of executing a large explosion-large contraction algorithm according to an embodiment of the present invention.
FIGS. 10 and 11 are views showing an example of a phase optimization design of a structure to which a large explosion-shrinkage algorithm according to an embodiment of the present invention is applied.
12 is a diagram showing an experimental example according to a conventional phase optimization design method.
Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. However, the technical spirit of the present invention is not limited to the embodiments described herein but may be embodied in other forms. Rather, the embodiments disclosed herein are provided so that the disclosure can be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
In this specification, when an element is referred to as being on another element, it may be directly formed on another element, or a third element may be interposed therebetween. Further, in the drawings, the thicknesses of the films and regions are exaggerated for an effective explanation of the technical content.
Also, while the terms first, second, third, etc. in the various embodiments of the present disclosure are used to describe various components, these components should not be limited by these terms. These terms have only been used to distinguish one component from another. Thus, what is referred to as a first component in any one embodiment may be referred to as a second component in another embodiment. Each embodiment described and exemplified herein also includes its complementary embodiment. Also, in this specification, 'and / or' are used to include at least one of the front and rear components.
The singular forms "a", "an", and "the" include plural referents unless the context clearly dictates otherwise. It is also to be understood that the terms such as " comprises "or" having "are intended to specify the presence of stated features, integers, Should not be understood to exclude the presence or addition of one or more other elements, elements, or combinations thereof. Also, in this specification, the term "connection " is used to include both indirectly connecting and directly connecting a plurality of components.
In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear.
1 is a flow chart illustrating a method for optimizing a topology of a structure according to an embodiment of the present invention.
Referring to FIG. 1, a method of optimizing a topology of a structure includes steps of defining a design domain and a design parameter (S10), inputting a boundary and a load condition of the structure (S20), finite element analysis Calculating a sensitivity value of each element (S30), calculating a fitness from the obtained sensitivity values of each element (S40), generating a virtual design area of an arbitrary area with respect to the design area In step S50, the execution regions are defined as a reference region unit over the entire region including the design region and the virtual design region, the large-explosion-contraction algorithm is repeatedly executed in each of the execution regions, (S60) of replacing elements having small fitness values, and evaluating the obtained structure (S70).
Step S10 of defining the design area and the design parameters will be described with reference to Fig. FIG. 2 is a diagram illustrating a Cantilever beam. In step S10 of defining a design region and a design variable, a target volume of a designed structure is defined as a design region, and variables that can occur in the design of the structure are defined.
Step S20 of inputting the boundary and load condition of the structure inputs information about the structure required for the phase optimization. The input information may include boundary condition, load acting position, load magnitude, load acting direction, and the like.
In the step S30 of calculating the sensitivity number of each element by performing the finite element analysis, the defined design region is divided into a plurality of elements, and the sensitivity value of each element is calculated through a finite element analysis .
The step of calculating the fitness from the sensitivity values of the obtained elements (S40) calculates the fitness from the sensitivity values. Fit is the reciprocal of the sensitivity, and the elements with low fit are interpreted as the area where the structure is located and the elements with high fitness are the areas where the structure is not located.
The step (S50) of creating a virtual design area of an arbitrary area with respect to the design area creates a virtual design area and expands the design area. In the case of the existing large-explosion-contraction algorithm, there is no restriction on the boundary because it finds the candidate solution with its center of gravity by randomly causing a large explosion in the infinite region to find the solution. However, Therefore, we can not find the boundary of the structure by using the characteristics of the algorithm that finds the optimal solution with the center of gravity intact. Therefore, in order to solve the problem, an arbitrary virtual design area is added to a desired design area. And we propose a method to find boundary of design area by expanding explosion area to virtual design area.
FIGS. 3 and 4 are views illustrating a process of creating a virtual design area according to an embodiment of the present invention.
Referring to FIG. 3, the
Referring to FIG. 4, an expanded
The
Referring again to FIG. 1, step S60 of executing the large explosion-large contraction algorithm may be performed by setting execution regions on a per-reference-area basis over the entire region including the design region and the virtual design region, - Executes a major contraction algorithm.
The step S60 of executing the large explosion-large contraction algorithm includes generating (S110) execution regions on the basis of the reference region in the entire region, arbitrarily setting a candidate solution among elements included in the design region, (S120) dividing an execution region including the candidate solution into solid regions and dividing an execution region not including the candidate solution into void regions (S120), executing a large explosion-to-contraction algorithm in the solid region, (S140), selecting the element having the highest fitness in the void region (S140), executing the large explosion-contraction algorithm in the void region (S140), selecting the element having the highest fitness And comparing the value of the fitness value of the lowest fitness factor with the fitness value of the lowest fitness factor (S150). If the fitness value of the element having the highest fitness is smaller than the fitness value of the element having the lowest fitness, the positions of the elements are exchanged (S160). If the fitness value of the element having the highest fitness is greater than the fitness value of the element having the lowest fitness, the positions of the corresponding elements are not exchanged (S170).
FIGS. 5 to 7 sequentially illustrate the steps of executing the large explosion-to-contraction algorithm according to the embodiment of the present invention.
Referring to FIG. 5, the
The process of executing the above-described large explosion-large contraction algorithm is repeated by resetting the
In the execution step (S60) of the large explosion-large contraction algorithm, the final large contraction point is designated as the optimal candidate solution, and a large explosion occurs in the vicinity of the large contraction point, thereby selecting a plurality of large explosion points near the candidate solution. And exchanging the data. This is based on the fact that several candidate solutions are gathered near the structure. As shown in FIG. 8, the
While the above-described large explosion-to-shrink algorithm execution step is repeated, the number of elements to be exchanged gradually decreases, and the number of non-exchanged elements gradually increases.
Referring again to FIG. 1, the repetition of step S60 of executing the large explosion-major contraction algorithm is repeated until the non-exchanged successively reaches a preset value. If it is determined that the fitness of the elements in the solid region is higher than the fitness of the elements in the void region, the number of times of non-replacement is increased by one (S170). Alternatively, if the fit of the elements in the solid region is less than the fit of the elements in the void region, then the exchange of elements takes place and the pre-counted number of unchanged times is initialized (S160). When the number of unexchanged cycles is counted in the course of execution of the large explosion-to-contraction algorithm, the execution of the large explosion-contraction algorithm ends when the counted number of unexchanged cycles reaches a predetermined value.
When the execution of the large explosion-major shrink algorithm is terminated, a step S70 of evaluating the obtained structure is performed. The evaluation step S70 calculates the objective function for the obtained structure, and calculates the sensitivity number according to the calculated objective function (S210). Then, it is determined whether the objective function of the structure according to the interation is converged (220). When the convergence condition is satisfied, the calculation is terminated. Otherwise, if the convergence condition is not satisfied, the above-described processes are repeated from the step of calculating the sensitivity number of each element by performing the finite element analysis.
FIGS. 10 and 11 are views showing an example of a phase optimization design of a structure to which a large explosion-shrinkage algorithm according to an embodiment of the present invention is applied. FIG. 10 is a view illustrating a phase optimization designing process for a cantilever beam structure, and FIG. 11 is a diagram illustrating a phase optimization designing process for an MBB beam structure. The phase optimization design process for the cantilever beam structure shows 26 convergence speeds, and the phase optimization design process for the MBB beam structure shows 27 convergence speeds.
12 is a diagram illustrating an experimental example according to a conventional phase optimization design method. In the phase optimization design of the cantilever beam, a Harmony Search Algorithm (HS), an artificial bee colony algorithm (ABCA), a bi-directional evolutionary structural optimization Respectively.
Referring to FIG. 10 and FIG. 12, the result obtained through the design method according to the present invention and the conventional design methods are represented by a topology structure having the same shape. On the other hand, the design method according to the present invention shows 27 convergence speeds, whereas the HS design method shows 33 times, the ABCA design method shows 41 times, and the BESO design method shows 63 times and 71 times convergence speed respectively. Accordingly, the phase optimization design method according to the present invention can be expected to have a speed efficiency as compared with the conventional design method.
While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the scope of the present invention is not limited to the disclosed exemplary embodiments. It will also be appreciated that many modifications and variations will be apparent to those skilled in the art without departing from the scope of the invention.
10: Design area
11: Element
20: Virtual design area
30: reference area, execution area
30a: solid area
30b: void area
41: Candidate
42: The element with the highest fitness
43: The lowest fit
Claims (11)
Computing a sensitivity value of each of the elements by finite element analysis and calculating a fit from the sensitivity value;
Creating a virtual design area extending in the design area and having an arbitrary area; And
Determining execution regions on a per-reference-area basis over the entire region including the design region and the virtual design region, and executing a large-size contraction algorithm in each of the execution regions,
Wherein performing the large explosion-to-contraction algorithm in the execution regions comprises:
Arbitrarily selecting a candidate solution among the elements;
Dividing the execution region into a solid region including the candidate solution and a void region not including the candidate solution;
Performing the large explosion-versus-shrink algorithm in the solid region, and selecting an element having the highest fitness in the solid region;
Performing the large explosion-versus-shrink algorithm in the void region, and selecting an element having the lowest fitness in the void region;
Comparing the element having the highest fitness and the element having the lowest fitness; And
Wherein when the fitness of the element with the highest fitness is greater than the fitness of the element with the lowest fitness, the position of the element with the highest fitness and the one with the lowest fitness are not exchanged, and the fitness of the element with the lowest fitness And replacing the location of the element with the highest fitness and the location of the element with the lowest fitness when the fitness is greater than the fitness of the element with the highest fitness.
Wherein the reference region is an area in which the elements are arranged in a matrix of mxn (m and n are natural numbers)
Wherein the virtual design area extends in the design area at a constant rate of the mxn matrix.
Wherein the virtual design area is extended to upper and lower sides of the design area by a row of the elements corresponding to 1/2 of m and each of the elements is expanded to both sides of the design area by a row of the elements corresponding to 1/2 of n Topology Optimization Design Method of Structures.
A large explosion-to-contraction algorithm is executed in the execution regions until the number of times the element having the highest fitness and the element having the lowest fitness are not replaced is repeated a predetermined number of times consecutively A phase optimization design method for a structure in which the steps are repeated.
Calculating a sensitivity value of the elements by a finite element analysis on a design area of the structure and calculating a fitness from the sensitivity value;
Executing a large explosion-versus-shrink algorithm in the entire area including the design area and a virtual design area extending therefrom to an arbitrary area;
Classifying the elements having a high value of the fitness and the elements having a low value of the fitness by execution of the large explosion-contraction algorithm,
Wherein the large explosion-versus-shrink algorithm is performed on an execution region unit in which the elements are included in a predetermined area, the virtual design region is extended from the design region at a predetermined ratio of the execution region,
Wherein performing the large explosion-versus-shrink algorithm in the entire region comprises:
Arbitrarily selecting a candidate solution among the elements;
Dividing the execution region into a solid region including the candidate solution and a void region not including the candidate solution;
Performing the large explosion-versus-shrink algorithm in the solid region, and selecting an element having the highest fitness in the solid region; And
Performing the large explosion-versus-shrink algorithm in the void region, and selecting an element having the lowest fidelity in the void region,
Wherein the step of classifying elements having a high value of the goodness of fit and elements having a low value of the goodness value includes:
When the element having the highest fitness is compared with the element having the lowest fitness and the fitness of the element having the highest fitness is greater than that of the element having the lowest fitness, The position of the element is not exchanged,
Wherein the position of the element with the highest fitness and the element with the lowest fitness are exchanged when the fitness of the element with the lowest fitness is greater than the fitness of the element with the highest fitness.
A large explosion-versus-shrink algorithm is executed in all the regions until the number of times the element having the highest fitness and the element having the lowest fitness are not replaced is repeated a predetermined number of times consecutively A phase optimization design method for a structure in which the steps are repeated.
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| CN110261154A (en) * | 2019-06-21 | 2019-09-20 | 广州大学 | A kind of Structural Damage Identification and device |
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