A cross-shaped specimen optimization design method based on parametric modeling

Abstract

The present invention discloses a cross-shaped specimen optimization design method based on parametric modeling, the method comprising the following steps: adopting a variety of geometric optimization forms, designing a cross piece that can generate a larger central area stress in biaxial stretching according to requirements, and determining the geometric parameters of the cross piece to be optimized and their value ranges; writing a parametric modeling script to realize the parametric modeling process of the cross piece; adopting a genetic algorithm to optimize the geometric parameters of the cross piece, and finally obtaining a cross piece with the largest central area stress by promoting the continuous increase of the population fitness function value, and determining the size of each shape parameter thereof; adopting the ratio of the difference between the maximum and minimum stresses in the central area to the maximum stress to test the stress uniformity of the central area of ​​the cross piece. The present invention defines a fitness function that reflects the stress level of the central area of ​​the cross piece, adopts a genetic algorithm based on binary coding, and successfully obtains the optimal specimen with a larger central area stress. The optimization program converges quickly and has a good optimization effect.

Description

Technical Field

[0001] The invention relates to a cross-shaped test piece optimization design method based on parameterized modeling, and belongs to the technical field of computer simulation. Background Art

[0002] In the actual engineering field, many parts are subjected to multiple cyclic loads during service and are in a complex stress state. Most of their failure forms are multi-axial fatigue failure. Although some parts are only subjected to a single load, they also have multi-axial stress states locally due to complex structural forms such as bosses, grooves, circular holes, and slits. In order to improve the safety and reliability of parts in actual engineering, it is necessary to predict and analyze their multi-axial fatigue life. Cross pieces can effectively simulate multi-axial stress states, and are therefore widely used in material parameter determination and life prediction analysis of parts. However, conventional cross pieces are prone to the situation where the stress at the arm angle is greater than the stress in the center area, resulting in the arm angle breaking earlier than the center area, causing the test to fail, and thus failing to accurately and effectively simulate the load state of the component. At present, there is no unified standard for the shape of cross pieces in the world, nor are there corresponding design specifications and processes, which also brings certain difficulties to the shape design and parameter optimization of cross pieces. Summary of the invention

[0003] In order to obtain a cross-piece with the largest possible stress in the central area and a more uniform stress distribution, it is necessary to optimize its parameters after designing its shape. The present invention uses a genetic algorithm to optimize the geometric parameters of the cross-piece. The genetic algorithm simulates the process of natural selection in nature and can realize the function of automatic optimization of multiple parameters. The optimization process is as follows: first, the fitness of individuals in the population is calculated (i.e., the optimization target: the stress level in the central area), and individuals are selected as the parents of the next generation population according to the fitness; the next generation population is generated by the crossover and mutation of chromosomes (i.e., the combination of parameters to be optimized) between the parents; by promoting the continuous improvement of the fitness of the population, individuals with the best fitness are finally obtained, so they are very suitable for parameter optimization of the cross-piece. The parametric modeling analysis can serve as a bridge between the genetic algorithm and the specific cross-piece stress analysis. The fitness required by the genetic algorithm is calculated through the geometric parameters given by the genetic algorithm, and the cross-piece optimization design is finally completed in cooperation with each other.

[0004] The purpose of the present invention is to overcome the technical defects of the prior art, solve the above-mentioned technical problems, and propose a cross-shaped specimen optimization design method based on parametric modeling, so as to realize the optimization of the geometric parameters of the cross piece with the goal of maximizing the stress in the center area and more uniform stress distribution, which is used in the biaxial tensile test of the cross piece to achieve the design purpose of rupture of the center area first, so as to obtain better test results.

[0005] The present invention specifically adopts the following technical solution: a cross-shaped specimen optimization design method based on parametric modeling, comprising the following steps:

[0006] Step SS1: adopting various geometric optimization forms, designing a cross piece that can generate a larger central stress in biaxial stretching according to requirements, and determining the geometric parameters to be optimized of the cross piece and their value ranges;

[0007] Step SS2: writing a parametric modeling script to implement the parametric modeling process of the cross piece involved in step SS1, so that the cross piece designed in step SS1 can automatically complete the modeling, loading, calculation, and stress analysis operations in the finite element analysis under any shape parameter combination;

[0008] Step SS3: Genetic algorithm is used to optimize the geometric parameters of the cross-piece, wherein the binary number converted from the shape parameters of the cross-piece is used as the chromosome, the maximum stress in the center area of ​​the cross-piece minus the maximum stress in other areas is used as the fitness, and the excellent cross-pieces in the population are selected as the parents of the next generation population based on the fitness size, and the random exchange of fragments and changes in individual bits between binary numbers are used as the crossover and mutation of chromosomes. By promoting the continuous increase of the fitness function value of the population, the cross-piece with the maximum stress in the center area is finally obtained, and the size of each of its shape parameters is determined;

[0009] Step SS4: Use the ratio of the difference between the maximum and minimum stresses in the center area to the maximum stress to check the stress uniformity in the center area of ​​the cross piece.

[0010] As a preferred embodiment, step SS1 specifically includes: according to design requirements, the cross piece is geometrically designed by center thinning, center opening, arm corner chamfering, arm thinning or slits, so that the maximum stress of the cross piece in biaxial stretching appears in the center area as much as possible.

[0011] As a preferred embodiment, the step SS3 specifically includes: the fitness function in the genetic algorithm is defined as follows:

[0012]

[0013] Where Δσ is the fitness of a certain parameter cross-piece, is the maximum stress in the center of the cross piece, It is the maximum stress in all high stress areas outside the center area of ​​the cross piece.

[0014] As a preferred embodiment, is the maximum stress near the center of the slit head, is the maximum stress at the tail of the slit away from the center, is the maximum stress at the chamfer of the arm corner. If the shape of the cross piece is changed or other cross pieces are used for optimization, then The number and meaning of also change accordingly.

[0015] As a preferred embodiment, the step SS3 specifically includes: using the roulette method and retaining the best individual in the genetic algorithm to obtain the cross-piece with higher fitness in one generation of population as the parent generation of the next generation of population.

[0016] As a preferred embodiment, the step SS4 specifically includes: defining the stress uniformity of the central area as follows:

[0017]

[0018] In the formula, α is an index to measure the stress uniformity in the central area. is the maximum stress in the center of the cross piece, It is the minimum stress in the center area. The smaller α is, the better the uniformity of the center area of ​​the cross piece is.

[0019] The beneficial effects achieved by the present invention are as follows: first, the present invention aims at the defects of fewer parameters and lower optimization efficiency in existing cross piece optimization research, realizes genetic algorithm optimization of the geometric parameters of the cross piece, and improves the optimization efficiency for multiple shape parameters at the same time. Through this optimization method, a cross piece that meets the design requirements and has good simulation effect is finally obtained smoothly; second, a fitness function that reflects the stress level in the central area of ​​the cross piece is proposed, so as to explicitly express the optimization degree of the cross piece, facilitate comparison between cross pieces, and improve the optimization efficiency of the geometric parameters of the cross piece; third, the genetic algorithm is combined with parametric modeling to realize full-automatic optimization of the shape parameters of the cross piece, thereby increasing the optimization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flow chart of the cross piece parameter optimization method of the present invention;

[0021] Figure 2 This is a schematic diagram of the designed cross-piece shape;

[0022] Figure 3 for Figure 2 AA sectional view of FIG.

[0023] Figure 4 Flowchart for obtaining the best cross piece for the genetic algorithm;

[0024] Figure 5 is a schematic diagram of a binary gene;

[0025] Figure 6 Schematic diagram of the transformation of binary genes and shape parameters;

[0026] Figure 7 Schematic diagram of the chromosome exchange (crossover) process;

[0027] Figure 8 Schematic diagram of the chromosome mutation process;

[0028] Fig. 9 This is a schematic diagram of the optimal fitness of each generation obtained by the genetic algorithm changing with the number of generations;

[0029] Fig.10 Schematic diagram of stress cloud phase of the optimal cross piece. DETAILED DESCRIPTION

[0030] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0031] Embodiment 1: A cross-shaped specimen optimization design method based on parametric modeling, comprising the following steps:

[0032] Step SS1: adopting various geometric optimization forms, designing a cross piece that can generate a larger central stress in biaxial stretching according to requirements, and determining the geometric parameters to be optimized of the cross piece and their value ranges;

[0033] Step SS2: writing a parametric modeling script to implement the parametric modeling process of the cross piece involved in step SS1, so that the cross piece designed in step SS1 can automatically complete the modeling, loading, calculation, stress analysis and other operations in the finite element analysis under any shape parameter combination;

[0034] Step SS3: Genetic algorithm is used to optimize the geometric parameters of the cross-piece, wherein the binary number converted from the shape parameters of the cross-piece is used as the chromosome, the maximum stress in the center area of ​​the cross-piece minus the maximum stress in other areas is used as the fitness, and the excellent cross-pieces in the population are selected as the parents of the next generation population based on the fitness size, and the random exchange of fragments and changes in individual bits between binary numbers are used as the crossover and mutation of chromosomes. By promoting the continuous increase of the fitness function value of the population, the cross-piece with the maximum stress in the center area is finally obtained, and the size of each of its shape parameters is determined;

[0035] Step SS4: Use the ratio of the difference between the maximum and minimum stresses in the center area to the maximum stress to check the stress uniformity in the center area of ​​the cross piece.

[0036] As a preferred embodiment, the step SS1 specifically includes: according to the design requirements, the geometric shape of the cross piece is designed by center thinning, center opening, arm corner chamfering, arm thinning or slits, so that the maximum stress of the cross piece in biaxial stretching appears in the central area as much as possible, so as to achieve better test results.

[0037] As a preferred embodiment, the step SS3 specifically includes: the fitness function in the genetic algorithm is defined as follows:

[0038]

[0039] Where Δσ is the fitness of a certain parameter cross-piece, is the maximum stress in the center of the cross piece, is the maximum stress of each high stress area outside the center area of ​​the cross piece. In the specific embodiment of this article (such as Figure 2 shown), where is the maximum stress near the center of the slit head, is the maximum stress at the tail of the slit away from the center, is the maximum stress at the chamfer of the arm corner. If the shape of the cross piece is changed or other cross pieces are used for optimization, then The number and meaning of also change accordingly. The greater the fitness, the higher the stress level in the center of the cross-piece compared to other areas, the easier it is for the center to break first under biaxial tension, and the easier it is for the genes to be passed on to the next generation, resulting in a better individual.

[0040] The step SS3 specifically includes: the crossover and mutation steps in the genetic algorithm adopt a binary number method to control the change of the geometric parameters of the cross piece.

[0041] As a preferred embodiment, the step SS3 specifically includes: using the roulette method and retaining the best individual in the genetic algorithm to obtain the cross-piece with higher fitness in one generation of population as the parent generation of the next generation of population.

[0042] As a preferred embodiment, the step SS4 specifically includes: defining the stress uniformity of the central area as follows:

[0043]

[0044] In the formula, α is an index to measure the stress uniformity in the central area. is the maximum stress in the center of the cross piece, It is the minimum stress in the center area. The smaller α is, the better the uniformity of the center area of ​​the cross piece is.

[0045] The present invention proposes a cross-shaped specimen optimization design method based on parametric modeling, such as Figure 1 As shown in the figure, this method is used to carry out shape design and geometric parameter optimization of the cross piece. First, the cross piece shape is designed according to the cross piece design conditions and design requirements (this optimization method is also applicable to any existing cross piece shape), and the geometric parameters to be optimized and their value ranges are determined.

[0046] The design conditions of the cross piece are as follows:

[0047] (1) Basic geometry: The two arms of the cross are 100 mm long, 22 mm wide and 6 mm thick;

[0048] (2) Material parameters: nickel-based high-temperature alloy GH4169, elastic modulus of 198.5 GPa, Poisson's ratio of 0.3, strength coefficient of 1579.7 Mpa, strain hardening exponent of 0.06;

[0049] (3) Load and constraint: The cross member is subjected to an equibiaxial tensile load of 400 MPa (each arm bears a uniformly distributed load of 400 MPa).

[0050] The design requirements for the cross piece are as follows:

[0051] (1) The maximum stress in the central area is at least 20% higher than the stress in any other area;

[0052] (2) The difference between the maximum and minimum stresses in the central area is less than 2%;

[0053] (3) Avoid stress concentration as much as possible.

[0054] The cross piece designed in this embodiment has a shape as follows Figure 2 and Figure 3 As shown, the length of the two arms is L, the width of the arms is D, and the thickness is H; the thickness of the central thinning zone decreases linearly from H at the outer circle of the thinning zone to h at the central test section, the radius of the test section is RR, and there is also a chamfer of radius R between the test section and the linear thinning zone to further reduce the stress concentration in the central zone; a slit is introduced on each arm to release the lateral stiffness on the arm and improve the uniformity of stress distribution in the central zone. The chamfer radii at both ends of the slit are different to uniformly weaken the lateral stiffness on the arm; a chamfer is introduced between two adjacent arms to reduce stress concentration. In this cross-piece, the geometric parameters to be optimized are: the thickness of the central thinning zone h, the outer diameter of the central thinning zone Ra, the distance w from the slit head to the outer edge of the thinning zone, the slit length lf, the chamfer radius Rb of the slit head, the chamfer radius Rc of the slit tail, and the chamfer radius Rd of the arm corner. The specific value range and step size are shown in Table 1.

[0055] Table 1 Cross-piece parameters to be optimized and their value ranges

[0056] Parameters to be optimized Value range (mm) Step length (mm) Thickness of the central thinning area h 0.5-1 0.2 Outer diameter of central thinning area Ra 12.5-14 0.1 Distance w from the slit to the outer edge of the thinning area 1.5-3 0.1 Slit length lf 18-25.5 0.5 Slit head fillet radius Rb 2.5-4 0.1 Slit tail rounding radius Rc 2.5-4 0.1 Arm corner chamfer radius Rd 6-10.5 0.3

[0057] Write a parametric modeling script for the designed cross piece. Select any geometric parameter within the value range, and run the script to automatically complete the modeling, loading, segmentation, meshing, stress calculation, data extraction and other operations of the parametric cross piece in the finite element software, and finally obtain relevant data reflecting the stress level of the central area.

[0058] Write a genetic algorithm script and combine it with parametric modeling technology to optimize the geometric parameters of the cross piece. The process of genetic algorithm optimization of cross piece parameters is as follows: Figure 4 As shown in the figure, firstly, randomly select values ​​within the parameter range as the geometric parameters of the cross-piece to generate the first generation of cross-piece population, then calculate the fitness of each cross-piece through the parameterized modeling script, and use the roulette method to select the better individuals as the parent generation according to the fitness. The next generation population is generated through the crossover mutation of chromosomes (the best individuals do not participate in the crossover mutation), and through continuous genetic iteration, the fitness is finally continuously increased, the automatic optimization of multiple parameters is realized, and the parameter optimization design of the cross-piece is realized.

[0059] The relationship between the cross parameter and chromosome is as follows Figure 5 As shown in the figure, each parameter is converted into a binary number with a length of n1 to n7 as a gene segment, and then arranged in order to form a chromosome. The conversion between each parameter of the cross and the gene segment, that is, the encoding and decoding of the gene, is as follows Figure 6 As shown, according to the multiple relationship between the range of geometric parameters and the range of converted binary numbers, the parameters are mapped one-to-one with the binary numbers, thereby realizing the encoding and decoding of genes.

[0060] Crossover and mutation of genes are Figure 7 and Figure 8 As shown, crossover is the random exchange of a binary number between chromosomes, and mutation is the conversion between 1 and 0 on random individual bits of chromosomes.

[0061] The final relationship between the maximum fitness of each generation and the genetic number of generations is shown in the following figure: Fig. 9 As shown in (50 generations of inheritance, 50 cross pieces in each generation), it can be seen from the line graph that the genetic algorithm based on binary coding has a fast convergence speed and good optimization effect. The final maximum fitness is 344.8Mpa, and the shape parameters of the cross piece are shown in Table 2.

[0062] Table 2 Optimal cross-piece geometric parameters

[0063] parameter Optimal size (mm) Thickness of the central thinning area h 0.5 Outer diameter of central thinning area Ra 14 Distance w from the slit to the outer edge of the thinning area 1.9 Slit length lf 24.5 Slit head fillet radius Rb 2.5 Slit tail rounding radius Rc 1 Chamfer radius between arms Rd 9

[0064] The stress analysis of the cross piece is carried out separately, and the stress cloud diagram is obtained as follows Fig.10 As shown. According to calculations, the stress in the central area is more than 40% higher than that in other areas, far exceeding the previously set target of 20%, proving that the cross-piece has indeed achieved the design target of higher stress in the central area than in other areas, which is conducive to the central area breaking before other areas under biaxial tension; the difference between the maximum and minimum stresses in the central area is only 0.4% of the maximum stress, proving that the stress uniformity in the central area is relatively high and meets the design requirements.

[0065] It can be seen that by taking the maximum stress level in the center area as the optimization goal, a specific combination of cross-piece shape parameters can be obtained. By performing biaxial tensile finite element analysis on the cross-piece under this shape parameter, the maximum stress level in the center area can be obtained and the stress uniformity in the center area is good.

[0066] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0067] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A cross-shaped specimen optimization design method based on parametric modeling, characterized in that: The steps include: Step SS1: adopting various geometric optimization forms, designing a cross piece that can generate central zone stress in biaxial stretching according to requirements, and determining the geometric parameters to be optimized of the cross piece and their value ranges; Step SS2: writing a parametric modeling script to implement the parametric modeling process of the cross piece involved in step SS1, so that the cross piece designed in step SS1 can automatically complete the modeling, loading, calculation, and stress analysis operations in the finite element analysis under any shape parameter combination; Step SS3: Genetic algorithm is used to optimize the geometric parameters of the cross-piece, wherein the binary number converted from the shape parameters of the cross-piece is used as the chromosome, the maximum stress in the center area of ​​the cross-piece minus the maximum stress in other areas is used as the fitness, and the excellent cross-pieces in the population are selected as the parents of the next generation population based on the fitness size, and the random exchange of fragments and changes in individual bits between binary numbers are used as the crossover and mutation of chromosomes. By promoting the continuous increase of the fitness function value of the population, the cross-piece with the maximum stress in the center area is finally obtained, and the size of each of its shape parameters is determined; Step SS4: Use the ratio of the difference between the maximum and minimum stresses in the center area to the maximum stress to check the stress uniformity in the center area of ​​the cross piece.

2. The cross-shaped specimen optimization design method based on parametric modeling according to claim 1 is characterized in that: The step SS1 specifically includes: according to the design requirements, the geometric shape of the cross piece is designed by adopting the form of center thinning, center opening, arm corner chamfering, arm thinning or slits, so that the maximum stress of the cross piece in biaxial stretching appears in the central area as much as possible.

3. The cross-shaped specimen optimization design method based on parametric modeling according to claim 1 is characterized in that: The step SS3 specifically includes: the fitness function in the genetic algorithm is defined as follows: Where Δσ is the fitness of a certain parameter cross-piece, is the maximum stress in the center of the cross piece, It is the maximum stress in all high stress areas outside the center area of ​​the cross piece.

4. The method for optimizing the design of a cross-shaped specimen based on parametric modeling according to claim 3, characterized in that: in is the maximum stress near the center of the slit head, is the maximum stress at the tail of the slit away from the center, is the maximum stress at the chamfer of the arm corner.

5. The cross-shaped specimen optimization design method based on parametric modeling according to claim 1 is characterized in that: The step SS3 specifically includes: using the roulette method and retaining the best individual in the genetic algorithm to obtain the cross pieces with higher fitness in one generation of population as the parents of the next generation of population.

6. The method for optimizing the design of a cross-shaped specimen based on parametric modeling according to claim 1, characterized in that: The step SS4 specifically includes: defining the stress uniformity of the central area as follows: In the formula, α is an index to measure the stress uniformity in the central area. is the maximum stress in the center of the cross piece, It is the minimum stress in the center area. The smaller α is, the better the uniformity of the center area of ​​the cross piece is.

Images