Voronoi porous structure topology optimization method for advanced construction

Abstract

The application is a Voronoi porous structure topology optimization method for advanced construction, which comprises the following steps: given an initial structure design space R and a structure stress condition, a user specifies the construction parameters of the Voronoi porous structure, including a preset volume fraction f, and sets the porous unit thin wall width t in combination with a manufacturing process; a relationship between the Delaunay triangle side length and the local volume fraction and the equivalent Young's modulus is established; the optimal equivalent Young's modulus is calculated according to the stress condition and the optimization target of the structure; the gradient Delaunay triangle is constructed according to the local volume fraction of the grid element; the vertices of all Delaunay triangles are extracted, the Voronoi polygon is generated and is given a width t, and the construction area is generated. The gradient Voronoi porous structure is generated by adopting the Delaunay triangle reconstruction, the Delaunay triangle side length is taken as a design variable, the Voronoi porous structure is constructed according to the optimal equivalent Young's modulus obtained by the maximum structure stiffness, and the optimization layout of the material is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent construction, and particularly relates to a Voronoi porous structure topology optimization method for advanced construction. BACKGROUND

[0002] The mechanical properties of the porous structure mainly depend on the material distribution density. The topology optimization technology can optimally distribute the structural material in the given design space under the known load and boundary conditions, so that the mechanical properties of the structure are optimized. The porous structure after optimization design is gradiently distributed in space, and has obvious advantages in structural load-bearing capacity, buckling resistance and energy absorption characteristics. The topology optimization provides an efficient and accurate method for porous structure design, can realize the lightweight of the structure while ensuring the performance of the structure, 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 the calculation efficiency can reduce the design cycle, reduce the cost, and enable designers to quickly respond to design changes. The purpose of topology optimization is to seek the optimal distribution of structural material in the given design domain to maximize or minimize certain design objectives such as structural stiffness or weight, and has better load-bearing capacity, which is crucial for structural design.

[0004] The inventor of document 1 has a pending patent 2024108087736, which discloses a topology optimization method for high-performance Voronoi homogeneous gradient porous structure. The calculation efficiency is low, and the stiffness is relatively small. Further improvement is needed. SUMMARY

[0005] In view of the problems of low mechanical properties and low calculation efficiency of the existing Voronoi gradient porous structure, the technical solution of the application is to propose a Voronoi homogeneous gradient porous structure topology optimization method for advanced construction.

[0006] The application solves the technical problem by adopting the following technical solution:

[0007] A Voronoi porous structure topology optimization method for advanced construction, the method comprising the following steps:

[0008] Step 1, given the initial structure design space R and the structure stress condition, 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 combined with the manufacturing process;

[0009] Step 2, establish the relationship between the Delaunay triangle side length and the local volume fraction, equivalent Young's modulus:

[0010] Step 2-1 defines the edge length of the Delaunay triangle as h, sets the arrangement area A, and the area of A is much larger than that of the triangle with edge length h; the area A is filled with triangles with edge length h, and then the vertices of all the triangles are extracted, a regular hexagonal skeleton is generated according to the vertices in A, and a skeleton thin wall width l is given to generate a construction area R V , the local volume fraction W is the ratio of R V to A, that is, W =R V / A; the corresponding W is calculated when the edge length h of different Delaunay triangles is calculated, and a continuous function curve W =f(h) representing the mapping relationship between W and h is obtained by curve fitting, and the value range of W is (0, 1];

[0011] Step 2-2 uniformly selects several points 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 after the skeleton thin wall width t is determined according to h is E0, the equivalent Young's modulus E * is determined according to E S =E0 / E * , wherein E S is the Young's modulus of the construction material;

[0012] Further, the corresponding equivalent elastic modulus when the local volume fraction is different is obtained, and a continuous function curve E * =g(W) representing the mapping relationship between E * and the local volume fraction W is obtained by curve fitting, and the value range of E * is (0, 1];

[0013] Step 3, calculate the optimal equivalent Young's modulus according to the stress condition and optimization target of the structure:

[0014] Step 3-1 discretizes the design domain by using a grid element S i with a user-defined edge length D, i represents the grid element number, and the center point of the grid element S i is n i ; taking the maximum structural stiffness as the target, the optimal equivalent Young's modulus E i of the grid element is calculated by using the solid isotropic material penalty method to iteratively calculate the optimal equivalent Young's modulus E * ; in each iteration, the local volume fraction W of each grid element S * is calculated by the mapping relationship E * =g(W) between E i and the local volume fraction W i, the average of the sum of the local volume fraction of all grid cells is the volume fraction f of the porous structure, the control of the volume fraction of the porous structure is achieved by iteration, and the optimal equivalent Young's modulus E of the grid cell corresponding to the preset volume fraction f is obtained i * , and the grid cell S i at this time is recorded i ;

[0015] Step 3-2: Manually set a deletion threshold Δ, delete the region with an optimal equivalent Young's modulus value less than the deletion threshold Δ, and define the region after deletion as a new optimized structure space R 0 ;

[0016] Step 4: Construct a gradient Delaunay triangle according to the local volume fraction of the grid cell;

[0017] Step 4-1: Arrange Delaunay triangles with equal side lengths, i.e. equilateral triangles, in the new optimized structure space R 0 , the side length of which is less than the side length D of the grid cell S i , and the coordinates of the vertices of the triangle are marked as v j , and j is the vertex number of the triangle;

[0018] Step 4-2: According to the local volume fraction of the grid cell S i , calculate the constant side length h i of the Delaunay triangle at the center point n i of each grid cell S i through the mapping relationship W=f(h) between W and h;

[0019] Step 4-3: Mark the center point of the Delaunay triangle as p k , and k is the triangle number. Find the point n' i in the center point n i of the grid cell whose horizontal and vertical coordinates are both less than the distance between p k and the grid cell side length D; i At this time, the number of n' i satisfying the condition is L, the distance d l between p k and n' i is calculated, l takes values 1, 2, …, L, and the constant side length h' i corresponding to n' i is used to calculate the expected value h k of the Delaunay triangle side length at p k according to the distance d l ;

[0020] Step 4-4 updates the Delaunay triangle by increasing, deleting or adjusting the vertex coordinate v(m) j, and after each update, step 4-3 is performed to recalculate the edge length expectation value h(m) k at the current Delaunay triangle center point p(m) k, m is the number of times step 4-3 is performed; when the edge length of all Delaunay triangles in the mth time is close to the edge length expectation value h(m-1) k in the (m-1) th time, that is, the difference between the edge length of all Delaunay triangles and h(m-1) k is less than δ, stop changing the vertex coordinate v j , wherein δ is a set tolerance;

[0021] Step 5, extract all the vertices of the Delaunay triangle, generate the Voronoi polygon and assign it a width t, and generate the construction area.

[0022] Compared with the prior art, the beneficial effects of the present application are:

[0023] (1) The present application proposes to generate a gradient Voronoi porous structure by using Delaunay triangle reconstruction, taking the Delaunay triangle edge length as a design variable, and constructing a Voronoi porous structure according to the optimal equivalent Young's modulus obtained by maximizing the structural stiffness, which realizes the optimal layout of the material.

[0024] (2) The present application combines the relationship between the Delaunay triangle edge length and the Voronoi porous structure when calculating the optimal equivalent Young's modulus, directly controls the volume fraction of the finally generated structure, and improves the calculation efficiency.

[0025] (3) The present application can set optimization parameters in combination with manufacturing processes to ensure manufacturing quality, and the optimization method can be applied to the fields of intelligent manufacturing of new materials and new structures in aerospace, automobiles, etc. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 It is a whole flowchart of the Voronoi porous structure topology optimization method for advanced construction of the present application;

[0027] Figure 2 It is a three-point bending simply supported beam structure design space and structure stress condition schematic diagram of Example 1;

[0028] Figure 3 It is an optimal equivalent Young's modulus cloud chart;

[0029] Figure 4 It is a schematic diagram of arranging equilateral triangles in a grid element;

[0030] Figure 5 It is a schematic diagram of calculating the expected edge length of the Delaunay triangle by barycentric interpolation;

[0031] Figure 6 This is the gradient Delaunay triangle calculation result diagram of Example 1;

[0032] Figure 7 The gradient Delaunay triangle vertex graph of Example 1;

[0033] Figure 8 This is the optimized topological structure diagram of Example 1;

[0034] Figure 9 Schematic diagram of structural design space and structural stress conditions of Example 2;

[0035] Figure 10 A comparison chart of optimization results of different optimization methods; DETAILED DESCRIPTION

[0036] 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 scope of protection of the present application.

[0037] Example 1

[0038] The Voronoi porous structure topology optimization method for advanced construction of the present invention comprises the following steps:

[0039] 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 initial structural design space R has dimensions of 160 × 40 mm. The user specifies the construction parameters of the Voronoi porous structure, including a preset volume fraction f and a porous unit thin-wall width l, which is set based on the manufacturing process. In this example, the volume fraction f is 0.35, and the thin-wall width l is 0.4 mm.

[0040] Step 2: Establish the relationship between the side length of the Delaunay triangle and the local volume fraction and the equivalent Young's modulus:

[0041] Step 2-1: Define the Delaunay triangle with a side length of h. Fill a larger area A (the area of ​​A is much larger than the area of ​​a triangle with side length h, A is a set value) with triangles with side length h. Then extract the vertices of all triangles and generate a regular hexagonal skeleton in A based on the vertices. Then give the skeleton a thin wall width of 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 W corresponding to 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];

[0042] 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 E * For E0 and E S The ratio of E * =E0 / E S ;

[0043] 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 to be E0 according to h. * =E0 / E S Determine the equivalent Young's modulus E * ,

[0044] Then the equivalent elastic modulus corresponding to different local volume fractions is obtained, and the E * Continuous function curve E of the mapping relationship with the local volume fraction W * =g(W),E * The value range is [0, 1];

[0045] In this embodiment, the curve W =f(h) and evenly select 10 points for data fitting.

[0046] Step 3: Calculate the optimal equivalent Young's modulus based on the structural stress conditions and optimization objectives:

[0047] Step 3-1 Use a grid cell S with a custom side length D i Discretize the design domain, i represents the grid unit number, grid unit S i The center point is n i ; With the goal of maximizing the structural stiffness, the solid isotropic material penalty method is used to iteratively calculate the optimal equivalent Young's modulus E of the grid element 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 iThe corresponding local volume fraction W i ;

[0048] Solid isotropic material penalization method is a known technology in the art, in which the bisection method is used to control E i * The sum of E i * The local volume fraction W i of each grid cell S i is calculated according to the mapping relationship E = g(W) between W and the local volume fraction W 0 , and then the porous structure volume fraction f is obtained to realize the control of the porous structure volume fraction f. Figure 3 The optimal equivalent Young's modulus cloud chart, the darker the color, the larger the value.

[0049] Step 3-2 deletes the area with an optimal equivalent Young's modulus value close to 0, and the area after deletion is defined as a new optimization structure space R 0 , that is, the gray area in Figure 3 ; In this embodiment, close to 0 means less than the deletion threshold, that is, the optimal equivalent Young's modulus value is not greater than 0.05.

[0050] Step 4, constructing a gradient Delaunay triangle according to the local volume fraction of the grid cell;

[0051] Step 4-1 arranging Delaunay triangles with equal side length, that is, equilateral triangles, in the new optimization structure space R 0 , the side length of which is less than the side length D of the grid cell S i , and the coordinates of the vertices of the triangle are marked as v j , and j is the vertex number of the triangle; Figure 4 A schematic diagram of several equilateral triangles arranged in four grid cells is given;

[0052] Step 4-2 calculating the constant side length h i of the Delaunay triangle at the center point n i of each grid cell S i according to the mapping relationship W = f(h) between W and h according to the corresponding local volume fraction of the grid cell S i ; Each center point corresponds to a constant side length, and the constant side length is always unchanged;

[0053] Step 4-3 marking the center point of the Delaunay triangle as p k , and k is the triangle number, and the horizontal and vertical coordinates of the center point n i of the grid cell are searched for p kPoints n' whose distance is 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 .

[0054] Step 4-4 updates 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;

[0055] Step 5. Extract all the vertices of the Delaunay triangle (see Figure 7 ), generate Voronoi polygons and assign them width t, generate the construction area (see Figure 8 ).

[0056] Example 2

[0057] This embodiment adopts the topology optimization method of embodiment 1 to Figure 9 The structure shown in the figure is optimized, with a structural design space of 160×60 mm, a volume fraction f of 0.35, a component size of 160×40 mm, and a thin wall width l of 0.8 mm. The comparison example is the optimization method of reference 1 in the background technology. The results of the two methods are shown in Figure 10, the running time of the two algorithms is tested by finite element analysis and Thinkpad T470P I7 notebook computer, see table 1, and table 1 is the displacement of loading point and the comparison data of calculation time of different optimization methods.The greater the displacement represents that the structural stiffness is smaller, and the mechanical performance is poorer;Since the volume fraction of the porous structure is directly controlled in the solid isotropic material penalty method, the complex iterative calculation is avoided, and the processing efficiency is higher.Therefore, under the condition that the material consumption is the same, the mechanical performance of the structure optimized by the method is better, the calculation efficiency is higher, the material is denser, and the layout is more reasonable.

[0058]

[0059] The unmentioned part of the application is 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 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. According to h, the Young's modulus of the porous structure formed after the skeleton thin wall width t is determined as E0. According to E * =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 based on the structural stress conditions and optimization objectives: Step 3-1 Use a grid cell S with a custom side length D i Discretize the design domain, i represents the grid unit number, grid unit S i The center point is n i ; With the goal of maximizing the structural stiffness, the solid isotropic material penalty method is used to iteratively calculate the optimal equivalent Young's modulus E of the grid element 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 area after deletion is defined as the new optimized structure space R 0 ; 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 Delaunay triangle is an equilateral triangle with equal sides, and its 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 W=f(h) between W and 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 distance is 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 updates 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.

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