Multi-phase material topological optimization method and equipment based on movable deformation holes

Abstract

The invention relates to the field of topological optimization, and discloses a multi-phase material topological optimization method and equipment based on movable deformation holes. According to the method, a boundary description parameter equation of a B spline hole is established; establishing a topology description function according to boundary information of the boundary description parameter equation, and determining a color interpolation format of the multiphase material according to the topology description function; and establishing a mathematical optimization model by using a color interpolation format, and obtaining the topological structure of the multiphase material based on sensitivity information obtained by calculation of the mathematical optimization model. The structural design flexibility is improved, middle density units of interfaces between materials are eliminated, and optimization of structural material distribution is achieved.

Description

Technical Field

[0001] This invention relates to the field of topology optimization, and in particular to a method and apparatus for topology optimization of multiphase materials based on movable deformable pores. Background Technology

[0002] Traditional multiphase material design methods often employ the density method, assigning two element densities as design variables to a finite element and using a multiphase material interpolation scheme to determine the material properties distributed within that finite element. This approach significantly increases the number of design variables as the number of elements increases, reducing computational efficiency. Furthermore, the interfaces of multiphase materials have numerous intermediate densities, posing challenges to the fabrication of multiphase material structures. Summary of the Invention

[0003] The purpose of this invention is to provide a method and apparatus for multiphase material topology optimization based on movable deformable holes. This method directly describes the hole boundaries using explicit B-spline hole boundary description parametric equations, enabling the optimized structure to have explicit geometric information while significantly reducing the number of design variables. Simultaneously, a color interpolation format based on the movable deformable hole method is proposed, assigning material properties to the overlapping parts of the holes, improving structural design flexibility, eliminating intermediate density units at material interfaces, optimizing the material distribution of the structure, and facilitating production.

[0004] To address the aforementioned technical problems, embodiments of the present invention provide a method for topology optimization of multiphase materials based on movable deformable pores, comprising: establishing boundary description parameter equations for B-spline pores; establishing a topology description function based on the boundary information of the boundary description parameter equations, and determining a color interpolation format for the multiphase material based on the topology description function; establishing a mathematical optimization model using the color interpolation format, and obtaining the topology of the multiphase material based on the sensitivity information calculated by the mathematical optimization model.

[0005] Embodiments of the present invention also provide an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the above-described multiphase material topology optimization method based on movable deformable pores.

[0006] Embodiments of the present invention also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for topology optimization of multiphase materials based on movable deformable pores.

[0007] Compared to existing technologies, this invention establishes boundary description parameter equations for B-spline holes; establishes topological description functions based on the boundary information of these equations; determines the color interpolation format for multiphase materials based on these functions; establishes a mathematical optimization model using the color interpolation format; and obtains the multiphase material topology based on the sensitivity information calculated from the mathematical optimization model. This improves the flexibility of structural design, eliminates intermediate density units at material interfaces, and optimizes the distribution of structural materials.

[0008] In addition, the color interpolation format is constructed using a unit step function.

[0009] Furthermore, the color interpolation format is: D(x)=(1-H ... 1 (x)))×H(χ 2 (x))×D 1 +(1-H(χ 2 (x)))×H(χ 1 (x))×D 2 +H(χ 1 (x))×H(χ 2 (x))×D 3 +(1-H(χ 2 (x)))×(1-H(χ 1 (x)))×D 4 Where D represents the material properties; x represents the location information; H represents the unit step function; and χ represents the topological description function.

[0010] In addition, the unit step function is specifically the Heaviside function.

[0011] In addition, the establishment of a mathematical optimization model using the color interpolation format includes: under the conditions of satisfying volume constraints and stress-strain relationship constraints, obtaining an objective function that minimizes compliance by adjusting the displacement field as the mathematical optimization model.

[0012] In addition, the mathematical optimization model includes: Min.: I=∫ s tudS;

[0013]

[0014] Where I represents compliance, u represents displacement field, f represents internal force, t represents external force, v represents associated displacement field, and V represents volume. ε represents volumetric constraints, ε represents strain, and S represents boundary information.

[0015] In addition, the sensitivity information is the sensitivity of compliance and volume constraint to the topological description function; specifically, the sensitivity information is obtained by calculating the derivatives of compliance and volume constraint with respect to the topological description function.

[0016] In addition, obtaining the multiphase material topology based on the sensitivity information calculated by the mathematical optimization model includes: incorporating the sensitivity information into the moving asymptote algorithm to obtain the multiphase material topology. Attached Figure Description

[0017] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations do not constitute a limitation on the embodiments, and unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0018] Figure 1 This is a flowchart of a multiphase material topology optimization method based on movable deformable pores according to an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of the boundary description parametric equation of the B-spline hole according to an embodiment of the present invention;

[0020] Figure 3 This is a schematic diagram of a color multiphase material interpolation format according to an embodiment of the present invention;

[0021] Figure 4 This is a schematic diagram of a simply supported beam according to an embodiment of the present invention;

[0022] Figure 5 This is a schematic diagram of the optimization process and results of the multiphase material topology optimization method based on movable deformable pores according to an embodiment of the present invention. Figure 6 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been presented in the various embodiments of the present invention to enable the reader to better understand this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various changes and modifications based on the following embodiments.

[0024] The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.

[0025] This invention relates to a multiphase material topology optimization method based on movable deformable pores, comprising: establishing boundary description parameter equations for B-spline pores; establishing a topology description function based on the boundary information of the boundary description parameter equations, and determining a color interpolation format for the multiphase material based on the topology description function; establishing a mathematical optimization model using the color interpolation format, and obtaining the multiphase material topology based on the sensitivity information calculated by the mathematical optimization model. This improves the flexibility of structural design, eliminates intermediate density units at the interfaces between materials, and optimizes the distribution of structural materials. The implementation details of the multiphase material topology optimization method based on movable deformable pores in this embodiment are described below. The following details are provided for ease of understanding and are not essential for implementing this solution.

[0026] In this embodiment, the multiphase material topology optimization method based on movable deformable pores is as follows: Figure 1 As shown, the method includes:

[0027] Step 101: Establish the boundary description parametric equations for the B-spline hole.

[0028] Specifically, such as Figure 2 As shown, the boundary description parametric equations for B-spline holes are established. P0, P1…P9 are the control points of the B-spline curve, and multiple control points together form a closed polygon. The closed curve inside the polygon is a hole formed based on the positions of the control points. With a sufficient number of control points, the deformation capability of the hole is stronger, and the deformation based on the hole can describe more complex topological structures, thus realizing the construction of the topological structure. To construct a closed curve, it is necessary to ensure that the control points are connected end-to-end, that is, the positions of P0 and P9 overlap. Furthermore, to ensure the continuity of the hole boundary and facilitate subsequent sensitivity information analysis, it is necessary to control the positions of P0 and P9 to be at the midpoint of line segment P1P8, i.e., P0 = P9 = (P1 + P8) / 2. In practical applications, the center point (x... c ,y c Then, the endpoints of the support radii (d1, d2, d3, d4, d5, d6, d7, d8) radiating from the center point at equal angles (θ) are used as control points (P1, P2, P3, P4, P5, P6, P7, P8). Simultaneously, the positions of P0 and P9 are determined based on the positions of P1 and P8, thus completing the construction of the B-spline curve. This construction method ensures that the control points can only move along the support radius direction, avoiding self-intersection phenomena that could affect the final topology optimization result.

[0029] based on Figure 2 The control point equations for the constructed B-spline hole are as follows:

[0030]

[0031] Among them, Pi Let x be the position coordinate of the i-th control point. c Let y be the x-coordinate of the center point. c Let d be the ordinate of the center point. i θ represents the distance from the center point to the i-th control point, i.e., the support radius mentioned above. The horizontal and vertical coordinates, along with the support radius, are design variables that control the deformation of the hole. θ is the fixed angle between adjacent support radii.

[0032] The explicit boundary description parametric equation C(u) for a B-spline hole is:

[0033]

[0034] N i，k (u) is derived from the nodal vector U = (u0, u1, ... u) m Create a vector, where U is a monotonically non-decreasing vector satisfying m = n + k + 2. a and b represent u0, u1, ..., u... m The upper and lower bounds of N. i，k For the k-th order basis function, the specific recursive expression is:

[0035]

[0036] Step 102: Establish a topological description function based on the boundary information of the boundary description parameter equation, and determine the color interpolation format of the multiphase material based on the topological description function.

[0037] The topological description function describes the hole from a mathematical perspective. Based on the boundary description parameter equation constructed in step 101 above, the topological description function χ is established according to the boundary information of the design region described by the boundary description parameter equation.

[0038]

[0039] Where Domain represents the design area, χ i (x) represents the topological description function of the i-th hole, x represents the coordinates of a point inside the design area, Ω i This represents the area occupied by the i-th hole. This represents the boundary of the i-th hole. From the topological description function above, we know that when the function value is less than 0, the coordinate point is located within the area occupied by the hole; when the function value is equal to 0, the coordinate point is located at the boundary of the hole; and for other function values ​​greater than 0, the coordinate point is located within the design area and is neither inside nor at the boundary of the hole.

[0040] The color interpolation scheme for multiphase materials is determined based on the topological description function. Specifically, the color interpolation scheme can be constructed using unit step functions, such as the Heaviside function. Figure 3As shown, D(x)=(1-H(χ) 1 (x)))×H(χ 2 (x))×D 1 +(1-H(χ 2 (x)))×H(χ 1 (x))×D 2 +H(χ 1 (x))×H(χ 2 (x))×D 3 +(1-H(χ 2 (x)))×(1-H(χ 1 (x)))×D 4 Where D represents the material properties; x represents the location information; H represents the unit step function; and χ represents the topological description function. Two layers of topological description functions can represent the distribution of three solid materials and one empty material region.

[0041] To simplify the mathematical formula for multiphase material interpolation, the parts of the color interpolation format related to the unit step function, excluding D, can be defined as follows: as follows:

[0042] φ 1 (x)=(1-H(χ 1 (x))*H(χ 2 (x));

[0043] φ 2 (x)=(1-H(χ 2 (x))*H(χ 1 (x));

[0044] φ 3 (x)=H(χ 2 (x)*H(χ 1 (x));

[0045] φ 4 (x)=(1-H(χ 1 (x))*(1-H(χ 2 (x));

[0046] Based on definition The abbreviation for color material interpolation format is:

[0047]

[0048] Step 103: Establish a mathematical optimization model using a color interpolation format, and obtain the multiphase material topology based on the sensitivity information calculated by the mathematical optimization model.

[0049] Specifically, under the conditions of satisfying volume constraints and stress-strain relationship constraints, the objective function that minimizes compliance can be obtained by adjusting the displacement field as a mathematical optimization model. The sensitivity information is obtained by calculating the derivatives of compliance and volume constraints with respect to the topological description function, and the established mathematical optimization model is as follows:

[0050] Min.:I=∫ s tudS;

[0051]

[0052] Where I represents compliance, u represents displacement field, f represents internal force, t represents external force, v represents associated displacement field, and V represents volume. ε represents volumetric constraints, ε represents strain, and S represents boundary information.

[0053] The volume constraints for the three solid materials are expressed as follows:

[0054] V 1 =(1-H(χ) 1 (x)))*H(χ 2 (x));

[0055] V 2 =(1-H(χ) 2 (x)))*H(χ 1 (x));

[0056] V 3 =H(χ) 1 (x))*H(χ 2 (x));

[0057] The optimization model employs a gradient-based optimization algorithm, requiring the calculation of the gradients of the objective function and constraint functions with respect to the design variables; this process is termed sensitivity calculation. Therefore, sensitivity calculation is performed based on the aforementioned mathematical optimization model, and the calculation process is as follows:

[0058]

[0059]

[0060] V n =[V 1 n V 2 n Let ] represent the normal velocity field along the boundary of the two-layer hole. Solve the above equation:

[0061] V n =δC(u)·n;

[0062] n·t=1;

[0063]

[0064] Where t represents the tangential unit vector, n represents the normal unit vector, and p x p y These represent the two coordinate values ​​of the control point.

[0065] The final sensitivity information calculation result is as follows:

[0066]

[0067] The sensitivity information is fed into a gradient-based optimization algorithm (moving asymptote algorithm) to obtain the topology of the multiphase material.

[0068] The steps of the various methods described above are only for clarity. In practice, they can be combined into one step or some steps can be split into multiple steps. As long as they include the same logical relationship, they are all within the protection scope of this invention. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the protection scope of this invention.

[0069] To verify the above-mentioned multiphase material topology optimization method based on movable deformable pores, a practical example is used below to test the effectiveness of the method.

[0070] like Figure 4 As shown, a simply supported beam has a length of 2 and a width of 1. The lower part of the beam is simultaneously subjected to three downward vertical forces of 1. The design region is divided into 120×60 elements. The initial design and optimization process and its results are as follows. Figure 5 The red material has a stiffness of 1, the green material has a stiffness of 5, and the blue material has a stiffness of 20. The volume constraint percentages are 10% for red material, 15% for green material, and 20% for blue material. The optimization results show that the green material regions with higher strength are distributed in the stress-bearing parts of the structure, while the other materials play a supporting role. This result is consistent with traditional optimization results, proving the effectiveness of the invented method.

[0071] Compared to traditional multiphase material optimization algorithms, this invention significantly reduces the number of design variables and improves computational stability and efficiency. The multiphase material color interpolation format based on movable deformable pores enhances algorithm flexibility. Furthermore, it provides detailed geometric information at structural boundaries and material interfaces, eliminating the need for post-processing and facilitating manufacturing.

[0072] This invention relates to an electronic device, such as... Figure 6As shown, it includes: at least one processor 601; and a memory 602 communicatively connected to at least one processor 601; wherein the memory 602 stores instructions executable by at least one processor 601, the instructions being executed by at least one processor 601 to enable at least one processor 601 to execute the above-described multiphase material topology optimization method based on movable deformable pores.

[0073] The memory and processor are connected using a bus, which can include any number of interconnected buses and bridges. The bus connects various circuits of one or more processors and memories. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits. These are all well known in the art and are therefore not described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over a wireless medium via an antenna. Furthermore, the antenna receives data and transmits it to the processor.

[0074] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0075] This invention relates to a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the method embodiments described above.

[0076] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0077] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A topology optimization method for multiphase materials based on movable deformable pores, characterized in that, include: Establish the boundary description parametric equations for the B-spline hole; A topological description function is established based on the boundary information of the boundary description parameter equation, and the color interpolation format of the multiphase material is determined based on the topological description function. A mathematical optimization model is established using the color interpolation format, and the topology of the multiphase material is obtained based on the sensitivity information calculated by the mathematical optimization model.

2. The multiphase material topology optimization method based on movable deformable pores according to claim 1, characterized in that, The color interpolation format is constructed using a unit step function.

3. The multiphase material topology optimization method based on movable deformable pores according to claim 2, characterized in that, The color interpolation format is as follows: D(x)=(1-H(x) 1 (x)))×H(x 2 (x))×D 1 +(1-H(x 2 (x)))×H(x 1 (x))×D 2 +H(x 1 (x))×H(x 2 (x))×D 3 +(1- H(x 2 (x)))×(1-H(x 1 (x)))×D 4 ; Where D represents the material properties; x represents the location information; H represents the unit step function; and χ represents the topological description function.

4. The multiphase material topology optimization method based on movable deformable pores according to claim 2, characterized in that, The unit step function is specifically the Heaviside function.

5. The multiphase material topology optimization method based on movable deformable pores according to any one of claims 1 to 4, characterized in that, The step of establishing a mathematical optimization model using the color interpolation format includes: Under the conditions of satisfying volume constraints and stress-strain relationship constraints, the objective function that minimizes compliance is obtained by adjusting the displacement field as the mathematical optimization model.

6. The multiphase material topology optimization method based on movable deformable pores according to claim 5, characterized in that, The mathematical optimization model includes: Min.: I=∫ s know; Where I represents compliance, u represents displacement field, f represents internal force, t represents external force, v represents associated displacement field, and V represents volume. ε represents volumetric constraints, ε represents strain, and S represents boundary information.

7. The multiphase material topology optimization method based on movable deformable pores according to claim 5, characterized in that, The sensitivity information refers to the sensitivity of compliance and volume constraint to the topological description function; Specifically, the sensitivity information is obtained by calculating the derivatives of compliance and volume constraint with respect to the topological description function.

8. The multiphase material topology optimization method based on movable deformable pores according to claim 1, characterized in that, The process of obtaining the multiphase material topology based on the sensitivity information calculated using the mathematical optimization model includes: The sensitivity information is then incorporated into the moving asymptote algorithm to obtain the multiphase material topology.

9. An electronic device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the multiphase material topology optimization method based on movable deformable pores as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the multiphase material topology optimization method based on movable deformable pores as described in any one of claims 1 to 8.

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