Voronoi porous structure topological optimization method for advanced construction

Abstract

The invention relates to a Voronoi porous structure topological optimization method for advanced construction, which comprises the following steps of: giving an initial structure design space R and a structure stress condition, assigning construction parameters of a Voronoi porous structure by a user, wherein the construction parameters comprise a preset volume fraction f, and setting the width t of a porous unit thin wall by combining a manufacturing process; establishing a relationship among the side length of the Delaunay triangle, the local volume fraction and the equivalent Young modulus; the optimal equivalent Young modulus is calculated according to the stress condition of the structure and the optimization target; constructing a gradient Delaunay triangle according to the local volume fractions of the grid units; and extracting vertexes of all the Delaunay triangles, generating a Voronoi polygon, endowing the Voronoi polygon with a width t, and generating a construction area. The gradient Voronoi porous structure is generated through Delaunay triangle reconstruction, the side length of the Delaunay triangle serves as a design variable, the Voronoi porous structure is constructed according to the optimal equivalent Young modulus obtained according to the maximum structural rigidity, and optimized layout of materials is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent construction, and in particular relates to a Voronoi porous structure topology optimization method for advanced construction. Background Art

[0002] The mechanical properties of porous structures mainly depend on the material distribution density. Topology optimization technology can optimally distribute structural materials within a given design space under known loads and boundary conditions, so as to achieve the best mechanical properties of the structure. The porous structure after optimized design is distributed in a gradient in space, and has obvious advantages in terms of structural load-bearing capacity, anti-buckling capacity and energy absorption characteristics. Topology optimization provides an efficient and accurate method for the design of porous structures, which can achieve lightweight structures while ensuring structural performance, and is an indispensable tool in modern engineering design.

[0003] Topology optimization usually involves a large number of iterative calculations, especially when dealing with complex engineering problems. Improving computational efficiency can reduce design cycles, reduce costs, and enable designers to respond quickly to design changes. The purpose of topology optimization is to seek the best distribution of structural materials within a given design domain to maximize or minimize certain design objectives, such as structural stiffness or weight, with better load-bearing capacity, which is critical to structural design.

[0004] The inventor's pending patent 2024108087736 discloses a topology optimization method for a high-performance Voronoi homogeneous gradient porous structure, which has low computational efficiency and relatively small stiffness, and further improvements are made in this regard. Summary of the invention

[0005] In view of the problems of low mechanical properties and low computational efficiency of existing Voronoi gradient porous structures, the technical solution to be solved by the present invention is to propose a topology optimization method for Voronoi homogeneous gradient porous structures for advanced construction.

[0006] The present invention solves the technical problem by adopting the following technical solution: A Voronoi porous structure topology optimization method for advanced construction, the method comprising the following steps: Step 1: Given the initial structural design space R and structural stress conditions, the user specifies the construction parameters of the Voronoi porous structure, including the preset volume fraction f and the porous unit thin wall width t set in combination with the manufacturing process; Step 2: Establish the relationship between the side length of the Delaunay triangle and the local volume fraction and the equivalent Young's modulus: Step 2-1 Define the side length of the Delaunay triangle as h, set the layout area A, and the area of ​​A is much larger than the area of ​​the triangle with side length h; fill area A with triangles with side length h, then extract the vertices of all triangles, generate a regular hexagonal skeleton in A based on the vertices, and give the skeleton a thin wall width l to generate the construction area R V , the local volume fraction W is R V The ratio of W to A =R V / A; Calculate the corresponding W for different Delaunay triangle side lengths h, and obtain the continuous function curve W representing the mapping relationship between W and h through curve fitting =f(h), the value range of W is (0, 1]; Step 2-2 On Curve W =f(h) uniformly select several points, each point corresponds to an h and W value, and the Young's modulus of the porous structure formed after the skeleton thin wall width t is determined according to h is E0. * =E0 / E S Determine the equivalent Young's modulus E * , where E S is the Young’s modulus of the construction material; Then the equivalent elastic modulus corresponding to different local volume fractions is obtained, and the expression E is obtained by curve fitting. * Continuous function curve E of the mapping relationship with the local volume fraction W * =g(W),E * The value range is [0, 1]; Step 3: Calculate the optimal equivalent Young's modulus according to the stress conditions and optimization objectives of the structure: Step 3-1 Use a grid cell S with a custom side length D i The discretization design domain, i represents the grid unit number, and the grid unit S i The center point is n i ; With the goal of maximizing the structural stiffness, the optimal equivalent Young's modulus E of the mesh unit is obtained by iterative calculation using the solid isotropic material penalty method i * ; At each iteration, pass E * Mapping relationship E with local volume fraction W * =g(W) to calculate each grid cell S i The local volume fraction W i The sum average of the local volume fractions of all grid cells is the porous structure volume fraction f. The porous structure volume fraction is controlled by iteration to obtain the optimal equivalent Young's modulus E of the grid cell corresponding to the preset volume fraction f. i * , and record the grid unit S at this timei The corresponding local volume fraction W i ; Step 3-2 artificially sets the deletion threshold Δ, deletes the area where the optimal equivalent Young's modulus value is less than the deletion threshold Δ, and the deleted area is defined as the new optimized structure space R 0 ; Step 4: construct a gradient Delaunay triangle according to the local volume fraction of the grid cell; Step 4-1 In the new optimized structure space R 0 The inner side of the grid is a Delaunay triangle with equal sides, i.e., an equilateral triangle, whose side length is smaller than the grid unit S. i The side length is D, and the vertex coordinates of the triangle are marked as v j , j is the triangle vertex number; Step 4-2 Based on the grid unit S i The corresponding local volume fraction is calculated for each grid cell S through the mapping relationship between W and h W = f(h) i Center point n i The Delaunay triangle at the constant side length h i ; Step 4-3 The center point of the Delaunay triangle is marked as p k , k is the triangle unit number, at the center point n of the grid unit i Find the horizontal and vertical coordinates and p k Points n' whose distances are all less than the grid unit side length D i , at this time, n' i The number of L is L, calculate p k to n' i The distance d l , l takes the value of 1, 2, ..., L, and uses n' i The corresponding constant side length h' i According to the distance d l Barycentric interpolation calculation p k The expected value of the side length of the Delaunay triangle at h k ; Step 4-4 Update the Delaunay triangle by adding, deleting, and adjusting the vertex coordinates v(m) j. After each update, execute step 4-3 to recalculate the expected value h(m) k of the side length at the center point p(m) k of the current Delaunay triangle, where m is the number of times step 4-3 is executed. When all the side lengths of the Delaunay triangle calculated for the mth time are close to the expected value h(m-1) k of the side length calculated for the m-1th time, that is, when the difference between all the side lengths of the Delaunay triangle and h(m-1) k is less than δ, stop changing the vertex coordinates v j , where δ is the set tolerance; Step 5: Extract the vertices of all Delaunay triangles, generate Voronoi polygons and assign them width t to generate the construction area.

[0007] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention proposes to use Delaunay triangle reconstruction to generate a gradient Voronoi porous structure, taking the side length of the Delaunay triangle as a design variable, and constructing the Voronoi porous structure according to the optimal equivalent Young's modulus obtained by maximizing the structural stiffness, thereby achieving an optimized layout of the material.

[0008] (2) When calculating the optimal equivalent Young's modulus, the present invention combines the relationship between the side length of the Delaunay triangle and the Voronoi porous structure to directly control the volume fraction of the final generated structure, thereby improving the calculation efficiency.

[0009] (3) The present invention can be combined with the manufacturing process to set optimization parameters to ensure manufacturing quality. The optimization method can be applied to new materials and new structures in intelligent manufacturing such as aerospace and automobiles. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a schematic diagram of the overall process of the Voronoi porous structure topology optimization method for advanced construction of the present invention; Figure 2 This is a schematic diagram of the design space and structural stress conditions of the three-point bending simply supported beam structure of Example 1; Figure 3 is the optimal equivalent Young's modulus cloud diagram; Figure 4 Schematic diagram of arranging regular triangles within a grid unit; Figure 5 Schematic diagram of calculating the expected side length of a Delaunay triangle for barycentric interpolation; Figure 6 This is the gradient Delaunay triangle calculation result diagram of Example 1; Figure 7 The gradient Delaunay triangle vertex graph of Example 1; Figure 8 This is the optimized topological structure diagram of Example 1; Fig. 9 Schematic diagram of structural design space and structural stress conditions of Example 2; Fig.10 This is a comparison chart of optimization results of different optimization methods; DETAILED DESCRIPTION

[0011] Specific embodiments are given below in conjunction with the accompanying drawings. The specific embodiments are only used to introduce the technical solutions of the present invention in detail and are not intended to limit the protection scope of the present application.

[0012] Example 1 The Voronoi porous structure topology optimization method for advanced construction of the present invention comprises the following steps: Step 1: Given the initial structural design space R and structural stress conditions, Figure 2 This is an example of a three-point bending simply supported beam structure. The size of the initial structural design space R is 160×40 mm. The user specifies the construction parameters of the Voronoi porous structure: including the preset volume fraction f, and the porous unit thin wall width l set in combination with the manufacturing process. In this example, the volume fraction f is 0.35, and the thin wall width l is 0.4 mm.

[0013] Step 2: Establish the relationship between the side length of the Delaunay triangle and the local volume fraction and the equivalent Young's modulus: Step 2-1 Define the side length of the Delaunay triangle as h, fill a larger area A (the area of ​​A is much larger than the area of ​​the triangle with side length h, A is the set value) with triangles with side length h, then extract the vertices of all triangles, generate a regular hexagonal skeleton in A based on the vertices, and give the skeleton a thin wall width l to generate the construction area R V , the local volume fraction W is R V The ratio of W to A =R V / A; Calculate the corresponding W for different Delaunay triangle side lengths h, and obtain the continuous function curve W representing the mapping relationship between W and h through curve fitting =f(h), the value range of W is (0, 1]; Step 2-2 Define the Young's modulus of the construction material as E S , the Young's modulus of the porous structure is E0, and the equivalent Young's modulus is E * For E0 and E S The ratio of E * =E0 / E S ; On curve W =f(h) uniformly select several points, each point corresponds to an h and W value, and the Young's modulus of the porous structure formed after the skeleton thin wall width t is determined according to h is E0. * =E0 / E S Determine the equivalent Young's modulus E * , Then the equivalent elastic modulus corresponding to different local volume fractions is obtained, and the expression E is obtained by curve fitting. *Continuous function curve E of the mapping relationship with the local volume fraction W * =g(W),E * The value range is [0, 1]; In this embodiment, the curve W =f(h) and 10 points are uniformly selected for data fitting.

[0014] Step 3: Calculate the optimal equivalent Young's modulus according to the stress conditions and optimization objectives of the structure: Step 3-1 Use a grid cell S with a custom side length D i The discretization design domain, i represents the grid unit number, and the grid unit S i The center point is n i ; With the goal of maximizing the structural stiffness, the optimal equivalent Young's modulus E of the mesh unit is obtained by iterative calculation using the solid isotropic material penalty method i * ; At each iteration, pass E * Mapping relationship E with local volume fraction W * =g(W) to calculate each grid cell S i The local volume fraction W i The sum average of the local volume fractions of all grid cells is the porous structure volume fraction f. The porous structure volume fraction is controlled by iteration to obtain the optimal equivalent Young's modulus E of the grid cell corresponding to the preset volume fraction f. i * , and record the grid unit S at this time i The corresponding local volume fraction W i ; The solid isotropic material penalty method is a well-known technique in the art. The solid isotropic material penalty method uses a dichotomy method to control E i * The sum of E and E cannot achieve the control of the volume fraction of the porous structure. i * The mapping relationship E = g(W) with the local volume fraction W is used to calculate each grid cell S i The local volume fraction W i , and then obtain the porous structure volume fraction f, thereby realizing the control of the porous structure volume fraction f. Figure 3 This is the optimal equivalent Young's modulus cloud diagram. The darker the color, the larger the value.

[0015] Step 3-2 Delete the area where the optimal equivalent Young's modulus value is close to 0. The deleted area is defined as the new optimized structure space R 0 ,Right now Figure 3The gray area in the figure; in this embodiment, close to 0 means less than the deletion threshold, that is, the optimal equivalent Young's modulus value is deleted when it is not greater than 0.05.

[0016] Step 4: construct a gradient Delaunay triangle based on the local volume fraction of the grid cell; Step 4-1 In the new optimized structure space R 0 The inner side of the grid is a Delaunay triangle with equal sides, i.e., an equilateral triangle, whose side length is smaller than the grid unit S. i The side length is D, and the vertex coordinates of the triangle are marked as v j , j is the triangle vertex number; Figure 4 A schematic diagram of several equilateral triangles arranged in four grid cells is given; Step 4-2 Based on the grid unit S i The corresponding local volume fraction is calculated for each grid cell S through the mapping relationship between W and h W = f(h) i Center point n i The Delaunay triangle at the constant side length h i ; Each center point corresponds to a constant side length, and the constant side length remains unchanged; Step 4-3 The center point of the Delaunay triangle is marked as p k , k is the triangle unit number, at the center point n of the grid unit i Find the horizontal and vertical coordinates and p k Points n' whose distances are all less than the grid unit side length D i , at this time, n' i The number of L is L, calculate p k to n' i The distance d l , l takes the value of 1, 2, ..., L, and uses n' i The corresponding constant side length h' i According to the distance d l Barycentric interpolation calculation p k The expected value of the side length of the Delaunay triangle at h k ,like Figure 5 As shown, Figure 5 The center point of the Delaunay triangle has four n' i .

[0017] Step 4-4 Update the Delaunay triangle by adding, deleting, and adjusting the vertex coordinates v(m) j. After each update, execute step 4-3 to recalculate the expected value h(m) k of the side length at the center point p(m) k of the current Delaunay triangle, where m is the number of times step 4-3 is executed. When all the side lengths of the Delaunay triangle calculated for the mth time are close to the expected value h(m-1) k of the side length calculated for the m-1th time, that is, when the difference between all the side lengths of the Delaunay triangle and h(m-1) k is less than δ, stop changing the vertex coordinates v j , where δ is the set tolerance; Figure 6 The calculation results of gradient Delaunay triangle are given; Step 5: Extract the vertices of all Delaunay triangles (see Figure 7 ), generate the Voronoi polygons and give them width t, and generate the construction area (see Figure 8 ).

[0018] Example 2 This embodiment adopts the topology optimization method of embodiment 1 to Fig. 9 The structure shown in the figure is optimized, the structural design space is 160×60 mm, the volume fraction f is 0.35, the component size is 160×40 mm, and the thin wall width l is 0.8 mm. The comparative example is the optimization method of document 1 in the background technology. The optimization results of the two methods are shown in Fig.10 , through finite element analysis, the running time of the two algorithms was tested using a Thinkpad T470P I7 laptop, as shown in Table 1, which is a comparison of the loading point displacement and calculation time of different optimization methods. The larger the displacement, the smaller the structural stiffness and the worse the mechanical properties; since this method directly controls the volume fraction of the porous structure in the solid isotropic material penalty method, it avoids complex iterative calculations and has higher processing efficiency. It can be seen that under the same material usage, the structure optimized by this method has better mechanical properties, higher calculation efficiency, denser materials, and more reasonable layout.

[0019]

[0020] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A Voronoi porous structure topology optimization method for advanced construction, characterized in that: The method comprises the following steps: Step 1: Given the initial structural design space R and structural stress conditions, the user specifies the construction parameters of the Voronoi porous structure, including the preset volume fraction f and the porous unit thin wall width t set in combination with the manufacturing process; Step 2: Establish the relationship between the side length of the Delaunay triangle and the local volume fraction and the equivalent Young's modulus: Step 2-1 Define the side length of the Delaunay triangle as h, set the layout area A, and the area of ​​A is much larger than the area of ​​the triangle with side length h; fill area A with triangles with side length h, then extract the vertices of all triangles, generate a regular hexagonal skeleton in A based on the vertices, and give the skeleton a thin wall width l to generate the construction area R V , the local volume fraction W is R V The ratio of W to A, that is, W = R V / A; Calculate the W corresponding to different Delaunay triangle side lengths h, and obtain the continuous function curve W=f(h) representing the mapping relationship between W and h through curve fitting. The value range of W is (0, 1]; Step 2-2 Select several points uniformly on the curve W=f(h), each point corresponds to an h and W value, and the Young's modulus of the porous structure formed by giving the skeleton thin wall width t is determined as E0 according to h. * =E0 / E S Determine the equivalent Young's modulus E * , where E S is the Young’s modulus of the construction material; Then the equivalent elastic modulus corresponding to different local volume fractions is obtained, and the expression E is obtained by curve fitting. * Continuous function curve E of the mapping relationship with the local volume fraction W * =g(W),E * The value range is [0, 1]; Step 3: Calculate the optimal equivalent Young's modulus according to the stress conditions and optimization objectives of the structure: Step 3-1 Use a grid cell S with a custom side length D i The discretization design domain, i represents the grid unit number, and the grid unit S i The center point is n i ; With the goal of maximizing the structural stiffness, the optimal equivalent Young's modulus E of the mesh unit is obtained by iterative calculation using the solid isotropic material penalty method i * ; At each iteration, pass E * Mapping relationship E with local volume fraction W * =g(W) to calculate each grid cell S i The local volume fraction W i The sum average of the local volume fractions of all grid cells is the porous structure volume fraction f. The porous structure volume fraction is controlled by iteration to obtain the optimal equivalent Young's modulus E of the grid cell corresponding to the preset volume fraction f. i * , and record the grid unit S at this time i The corresponding local volume fraction W i ; Step 3-2 artificially sets the deletion threshold Δ, deletes the area where the optimal equivalent Young's modulus value is less than the deletion threshold Δ, and the deleted area is defined as the new optimized structure space R 0 ; Step 4: construct a gradient Delaunay triangle according to the local volume fraction of the grid cell; Step 4-1 In the new optimized structure space R 0 The inner side of the grid is a Delaunay triangle with equal sides, i.e., an equilateral triangle, whose side length is smaller than the grid unit S. i The side length is D, and the vertex coordinates of the triangle are marked as v j , j is the triangle vertex number; Step 4-2 Based on the grid unit S i The corresponding local volume fraction is calculated for each grid cell S through the mapping relationship between W and h W = f(h) i Center point n i The Delaunay triangle at the constant side length h i ; Step 4-3 The center point of the Delaunay triangle is marked as p k , k is the triangle unit number, at the center point n of the grid unit i Find the horizontal and vertical coordinates and p k Points n' whose distances are all less than the grid unit side length D i , at this time, n' i The number of L is L, calculate p k to n' i The distance d l , l takes the value of 1, 2, ..., L, and uses n' i The corresponding constant side length h' i According to the distance d l Barycentric interpolation calculation p k The expected value of the side length of the Delaunay triangle at h k ; Step 4-4 Update the Delaunay triangle by adding, deleting, and adjusting the vertex coordinates v(m) j. After each update, execute step 4-3 to recalculate the expected value h(m) k of the side length at the center point p(m) k of the current Delaunay triangle, where m is the number of times step 4-3 is executed. When all the side lengths of the Delaunay triangle calculated for the mth time are close to the expected value h(m-1) k of the side length calculated for the m-1th time, that is, when the difference between all the side lengths of the Delaunay triangle and h(m-1) k is less than δ, stop changing the vertex coordinates v j , where δ is the set tolerance; Step 5: Extract the vertices of all Delaunay triangles, generate Voronoi polygons and assign them width t to generate the construction area.

Images