Design method of long-span spatial bridge structure based on bidirectional evolutionary topology optimization

Abstract

The application discloses a long-span space bridge structure design method based on bidirectional progressive topology optimization, obtains parameter data of all units, combines parameters of a set long-span space bridge structure model, and calculates unit sensitivity functions; then unit sensitivities of all units in an optimization region are calculated through the unit sensitivity functions, and a sensitivity threshold is calculated; finally, the optimization region is optimized based on the sensitivity threshold. The application can avoid unstable analysis numerical output, numerical error or algorithm failure and the like. The long-span space bridge structure model is set as two regions, one region is a model non-designable domain, and the other region is a model designable domain, the relationship between a volume fraction and a design variable is modified, and long-span space bridge structure optimization is more accurate. Parameter data of all units are quantified through functions in a numpy library, and the calculation speed of a unit node filtering function can be greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of structural topology optimization, and particularly relates to a long-span spatial bridge structure design method based on bidirectional evolutionary topology optimization. BACKGROUND

[0002] Structural topology optimization is an innovative structural optimization method, and a designer can quickly obtain the optimal distribution of materials in space by giving relevant conditions. Structural topology optimization is used to obtain the effective distribution of materials in a specified domain to achieve the best performance of the structure while meeting the defined constraints. In addition, topology optimization can be based on sensitivity. The sensitivity-based method generally has faster convergence speed and higher optimization efficiency, and is suitable for large-scale structural topology optimization, and especially using the second-order derivative can further improve the optimization convergence speed. The sensitivity analysis method proposed in the document "Arora JS, Haug E. Methods of design sensitivity analysis in structural optimization. AIAA Journal, 1979, 17(9): 970-974" includes the virtual load method, the state space method and the design space method, and they are different in expression.

[0003] The bidirectional evolutionary structural optimization algorithm proposed in the document "XIE Y M, STEVEN G P. A simple evolutionary procedure for structural optimization [J]. Computers & Structures, 1993, 49(5): 885-96." can be based on stiffness, mass and flexibility as the optimization target, and is a method for optimizing material distribution, which is a topology optimization method by deleting low-efficiency materials while increasing high-efficiency materials. The bidirectional evolutionary structural optimization has the advantages of high efficiency of structural optimization and accuracy of calculation and analysis, and is particularly suitable for nonlinear structure optimization analysis with maximum external force work as the main target. Under the condition of determined structural constraints, the volume of the structure is optimized by optimizing the external force work. However, it still has the following problems: "singularity" problem, local constraint problem, numerical instability problem, non-deterministic optimization problem and micro and macro optimization problem, and the "checkerboard" phenomenon is the key to causing this series of problems. The "checkerboard" phenomenon often occurs in the continuum of model optimization process, and the optimized unit appears alternately in the real and virtual units, which makes the analysis numerical output unstable and may cause numerical error or algorithm failure, and cannot produce actual guidance for structural design. SUMMARY

[0004] The purpose of the present application is to overcome the deficiencies of the prior art, and provide a large-span space bridge structure design method based on bidirectional progressive topology optimization.

[0005] To achieve the above object, the technical scheme provided by the present application is:

[0006] The large-span space bridge structure design method based on bidirectional progressive topology optimization comprises:

[0007] S1, a large-span space bridge structure model is established;

[0008] The large-span space bridge structure model is set as two regions, one region is a model non-designable domain, and the other region is a model designable domain. The model non-designable domain and the model designable domain are discretely optimized using a mesh division technique, and the two regions are divided into a plurality of hexahedrons. The model non-designable domain and the model designable domain are connected by Tie constraints to form an optimization region;

[0009] S2, parameters of the large-span space bridge structure model are set;

[0010] S3, the large-span space bridge structure model is imported into the abaqus software for finite element analysis, and parameter data of all elements constituting the large-span space bridge structure model are obtained;

[0011] S4, based on the obtained parameter data of all elements constituting the large-span space bridge structure model, and in combination with the set parameters of the large-span space bridge structure model, an element sensitivity function is solved, and a total external force work of the objective function is calculated;

[0012] S5, the element sensitivity of all elements in the optimization region is solved by the element sensitivity function, and a sensitivity threshold is solved;

[0013] S6, the optimization region is optimized based on the sensitivity threshold;

[0014] S7, a performance index is solved in combination with the total external force work of the objective function;

[0015] S8, steps S3 to S7 are repeated, and when the structure of the optimization region meets the change amount of the performance index, the optimization iteration is stopped, and thus an optimized large-span space bridge structure is obtained.

[0016] Further, when the model of the large-span space bridge structure is established, it further comprises:

[0017] The size of the model designable domain and the non-designable domain and the Young's modulus and Poisson's ratio of the material are set. The model non-designable domain is set to simulate the bridge deck, and full constraint fixation is applied to the short sides on both sides.

[0018] The bridge deck is divided into several equal-area planes, and static loads are symmetrically applied. Several analysis parts are applied to simulate the moving load driving on the bridge deck.

[0019] Further, the sensitivity function of the element is calculated, including:

[0020] The node sensitivity is calculated, and the formula is as follows:

[0021]

[0022] Wherein, M is the total number of elements connected to the jth node; ω i is the weight factor of the ith element, and r ij is the distance between the center of the ith element and the jth node. The closer the element is to the node, the higher the weight of the node sensitivity. The filter radius r min is set to determine the nodes covered around the ith element; α e is the average value of the element sensitivity of all elements;

[0023] The node sensitivity is projected to the subdomain, so that the node sensitivity is converted to smooth element sensitivity, thereby obtaining the element sensitivity function:

[0024]

[0025] The size of the subdomain does not change with the size of the grid, α i is the sensitivity of the ith element calculated for the nodes located in the subdomain Ω1; K is the total number of nodes in the subdomain Ω1; η j is the weight factor; ω(r ij ) is the weight function of the original sensitivity.

[0026] Further, the objective function total external force work includes the designable domain external force work W1 and the non-designable domain external force work W2.

[0027] The designable domain external force work W1 is:

[0028]

[0029] The non-designable domain external force work W2 is:

[0030]

[0031] F1 is the load vector of the designable domain; F2 is the load vector of the non-designable domain; U1 is the displacement vector of the designable domain; Y2 is the displacement vector of the non-designable domain;

[0032] The calculation formula of the objective function total external force work C is as follows:

[0033] C = W1 + W2.

[0034] Further, before the sensitivity function of each element is calculated and the total external force work of the objective function is calculated, the parameter data of all elements constituting the large-span spatial bridge structure model are quantified by using functions in the numpy library, including np.mean() and np.linalg.norm().

[0035] Further, the average of the maximum element sensitivity and the minimum element sensitivity of all elements in the to-be-optimized region is taken as the sensitivity threshold.

[0036] Further, the enumerate() function is used to traverse all elements in the to-be-optimized region, and the average of the maximum element sensitivity and the minimum element sensitivity of all elements in the to-be-optimized region is taken as the sensitivity threshold by using the binary search to dynamically update the threshold.

[0037] Further, the to-be-optimized region is optimized based on the sensitivity threshold, including:

[0038] The elements in the to-be-optimized region whose element sensitivity is less than or equal to the sensitivity threshold are deleted;

[0039] The elements in the to-be-optimized region whose element sensitivity is greater than the sensitivity threshold are added.

[0040] Further, the to-be-optimized region is optimized based on the sensitivity threshold, and further includes that the overall volume of the large-span spatial bridge structure model is basically unchanged after the elements are deleted and added in the structure optimization process.

[0041] The volume fraction expression is as follows:

[0042] V k+1 =V k 1-ER), k = 1, 2, 3,...

[0043] Wherein, ER is the evolution rate, V k is the volume fraction of the kth iteration, V k+1 is the volume fraction of the k+1th iteration, V1 = 1, when V k reaches the target volume constraint value V * , V k+1 = V * in the following iteration steps until the optimization model converges and stops; the elements are deleted and added in the structure optimization process, and V k+1 = V * .

[0044] Further, in step S8, the formula for stopping iteration is as follows:

[0045]

[0046] PIk-i+1 k-i+1 PIk-i+1 k-N+i-1 PIk-i+1 N is the number of iterations for the convergence of the objective function; i is a loop variable of N; tau is the allowed convergence error; PIk-i+1 k-i+1 PIk-i+1 k-N+i-1 PIk-i+1

[0047] Compared with the prior art, the technical principles and advantages of the scheme are as follows:

[0048] 1. Based on the obtained parameter data of all elements constituting the large-span spatial bridge structure model, the element sensitivity function is calculated in combination with the parameters of the large-span spatial bridge structure model. Then, the element sensitivity of all elements in the optimization region is calculated through the element sensitivity function, and the sensitivity threshold is calculated. Finally, the optimization region is optimized based on the sensitivity threshold.

[0049] The technical scheme can avoid the occurrence of unstable numerical value output, resulting in numerical error or algorithm failure, etc.

[0050] 2. The large-span spatial bridge structure model is set as two regions, one region is the model non-design domain, and the other region is the model design domain. The relationship between the volume fraction and the design variable is modified, so that the large-span spatial bridge structure optimization is more accurate.

[0051] 3. Before calculating the element sensitivity function and the total external force work of the objective function, the parameter data of all elements constituting the large-span spatial bridge structure model obtained through the function in the numpy library is quantified, which can greatly improve the calculation speed of the element node filtering function. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the services needed in the embodiment or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0053] Figure 1 It is the principle flow chart of the large-span spatial bridge structure design method based on the bidirectional progressive topology optimization of the present application;

[0054] Figure 2 It is the figure of the total external force work of the objective function and the volume fraction topology optimization changing with the number of iterations. DETAILED DESCRIPTION

[0055] The application will be further described below in combination with specific embodiments.

[0056] As shown in Figure 1 and Figure 2 The large-span space bridge structure design method based on the bidirectional progressive topology optimization in the embodiment includes the following steps:

[0057] S1, establishing a large-span space bridge structure model;

[0058] The large-span space bridge structure model is set as two regions, one region is a model non-design domain, and the other region is a model design domain. The grid division technology is used to discretize the optimization model non-design domain and the model design domain, and the two regions are divided into a plurality of hexahedrons. The model non-design domain and the model design domain are connected by Tie constraints to form an optimization region;

[0059] When the model of the large-span space bridge structure is established, it further includes:

[0060] The size of the model design domain and the non-design domain, the Young's modulus and the Poisson's ratio of the material are set. The model non-design domain is set to simulate the bridge deck, and the short sides on both sides are fixed by full constraint.

[0061] The bridge deck is divided into 11 equal-area planes, and static loads are symmetrically applied. Eleven analysis modules are applied to simulate the driving conditions of the moving load on the bridge deck.

[0062] S2, setting the parameters of the large-span space bridge structure model, including the target volume constraint value V * , evolution rate ER, and filter radius r min ;

[0063] S3, importing the large-span space bridge structure model into the abaqus software for finite element analysis to obtain the parameter data of all elements constituting the large-span space bridge structure model;

[0064] S4, quantifying the parameter data of all elements constituting the large-span space bridge structure model by using the functions in the numpy library; the functions in the numpy library include np.mean() and np.linalg.norm(); then, the element sensitivity function is calculated by combining the set parameters of the large-span space bridge structure model, and the total external force work of the objective function is calculated.

[0065] In this step, the element sensitivity function is calculated, including:

[0066] The node sensitivity is calculated, and the formula is as follows:

[0067]

[0068] wherein M is the total number of units connected to the jth node; ω i is the weight factor of the ith unit, and r ij is the distance between the center of the ith unit and the jth node, and the closer the unit is to the node, the higher the weight of the node sensitivity, and the filtering radius r is set min determines the nodes covered around the ith unit; α e is the average value of the unit sensitivity of all units;

[0069] project the node sensitivity to the sub-domain, so that the node sensitivity is converted into smooth unit sensitivity, thereby obtaining the unit sensitivity function:

[0070]

[0071] The size of the sub-domain does not change with the size of the grid, and α i calculates the sensitivity of the ith unit for the nodes located in the sub-domain Ω1; K is the total number of nodes in the sub-domain Ω1; η j is the weight factor; ω(r ij ) is the weight function of the original sensitivity.

[0072] The objective function total external force work includes the external force work W1 of the designable domain and the external force work W2 of the non-designable domain;

[0073] The external force work W1 of the designable domain:

[0074]

[0075] The external force work W2 of the non-designable domain:

[0076]

[0077] F1 is the load vector of the designable domain; F2 is the load vector of the non-designable domain; U1 is the displacement vector of the designable domain; U2 is the displacement vector of the non-designable domain;

[0078] The calculation formula of the objective function total external force work C is as follows:

[0079] C = W1 + W2.

[0080] S5, the unit sensitivity of all units in the to-be-optimized region is obtained by the unit sensitivity function, and the sensitivity threshold is obtained; specifically, the enumerate() function is used to traverse all units in the to-be-optimized region, the threshold is dynamically updated by binary search, and the average of the maximum unit sensitivity and the minimum sensitivity of all units in the to-be-optimized region is taken as the sensitivity threshold.

[0081] S6, optimizing the to-be-optimized region based on the sensitivity threshold, comprising:

[0082] 1) deleting a cell in the to-be-optimized region whose cell sensitivity is less than or equal to the sensitivity threshold;

[0083] 2) adding a cell whose cell sensitivity is greater than the sensitivity threshold into the to-be-optimized region;

[0084] 3) requiring the overall volume of the large-span spatial bridge structure model to be basically unchanged after deleting and adding cells in the structure optimization process;

[0085] The volume fraction expression is as follows:

[0086] V k+1 =V k (1-ER), k = 1, 2, 3, …

[0087] wherein, ER is the evolution rate, V k is the volume fraction of the kth iteration, V k+1 is the volume fraction of the k+1th iteration, V1 = 1, when V k reaches the target volume constraint value V * , V k+1 = V * is maintained in the following iteration steps until the optimization model converges and stops; the deletion and addition of cells in the structure optimization process both need to ensure that V k+1 = V * .

[0088] S7, obtaining the performance index by dividing the corresponding volume fraction by the total external force work of the corresponding algebra of the objective function;

[0089] S8, repeating steps S3 to S7, when the structure of the optimization region meets the change amount of the performance index, stopping the optimization iteration, thereby obtaining the optimized large-span spatial bridge structure.

[0090] The formula for stopping iteration is as follows:

[0091]

[0092] wherein, PI k-i+1 is the performance index of the k-i+1th generation; PI k-N+i-1 is the performance index of the k-N+i-1th generation; N is the iteration number for the convergence of the objective function; i is the loop variable of N; τ is the allowed convergence error; PI k-i+1 and PI k-N+i-1 are both obtained by dividing the corresponding volume fraction by the total external force work of the corresponding algebra of the objective function.

[0093] The above-described embodiments are only preferred embodiments of the present application, and are not intended to limit the scope of the present application. Any changes made in the shape, principle, and the like of the present application should be included in the scope of the present application.

Claims

1. A design method for long-span spatial bridge structures based on bidirectional progressive topology optimization, characterized in that, include: S1. Establish a structural model of a long-span spatial bridge; The large-span spatial bridge structure model is set into two regions: one region is the undesignable region and the other region is the designable region. The undesignable region and the designable region are discretized and optimized using mesh generation technology. The two regions are divided into several hexahedrons. The undesignable region and the designable region are connected by Tie constraints to form the region to be optimized. S2. Set the parameters of the long-span spatial bridge structure model; S3. Import the long-span spatial bridge structure model into Abaqus software for finite element analysis to obtain the parameter data of all elements constituting the long-span spatial bridge structure model. S4. Based on the parameter data of all elements constituting the large-span spatial bridge structure model, and combined with the parameters of the set large-span spatial bridge structure model, obtain the element sensitivity function and calculate the total external force work of the objective function. S5. Calculate the unit sensitivity of all units in the region to be optimized using the unit sensitivity function, and then calculate the sensitivity threshold. S6. Optimize the region to be optimized based on the sensitivity threshold; S7. Calculate the performance index by combining the total external force work of the objective function; S8. Repeat steps S3 to S7. When the structure of the optimization region meets the change of the performance index, stop the optimization iteration to obtain the optimized long-span spatial bridge structure. When building a model for a long-span spatial bridge structure, the following are also included: Set the dimensions and materials of the designable and non-designable domains of the model, as well as Young's modulus and Poisson's ratio; set the non-designable domains of the model, simulate the bridge deck, and apply full constraints to fix the two short sides; The bridge deck is divided into several planes of equal area, static loads are applied symmetrically, and several analysis units are applied to simulate the movement of moving loads on the bridge deck. To obtain the unit sensitivity function, the following steps are required: The formula for determining nodal sensitivity is as follows: Where M is the total number of units connected to the j-th node; ω i Let be the weight factor of the i-th unit, and r ij Let r be the distance between the center of the i-th cell and the j-th node. The closer a cell is to a node, the higher its weight in node sensitivity. Set the filter radius r. min Determine the nodes covered around the i-th cell; α e This is the average value of the unit sensitivity of all units; Projecting the nodal sensitivity onto a subdomain transforms the nodal sensitivity into a smoothed element sensitivity, resulting in the element sensitivity function: The size of the subdomain does not change with the size of the grid, α i Calculate the sensitivity of the i-th element for the node located in subdomain Ω1; K is the total number of nodes in subdomain Ω1; η i ω(r) is the weighting factor; ij ) is the weight function for the original sensitivity.

2. The design method for long-span spatial bridge structures based on bidirectional progressive topology optimization according to claim 1, characterized in that, The total external force work in the objective function includes external force work W1 in the designable domain and external force work W2 in the non-designable domain; Designable extraterrestrial force work W1: Undesignable extraterritorial work W2: F1 is the load vector of the designable domain; F2 is the load vector of the non-designable domain; U1 is the displacement vector of the designable domain; U2 is the displacement vector of the non-designable domain. The formula for calculating the total external work C of the objective function is as follows: C = W1 + W2.

3. The design method for long-span spatial bridge structures based on bidirectional progressive topology optimization according to any one of claims 1-2, characterized in that, Before obtaining the element sensitivity function and calculating the total external force work of the objective function, the parameter data of all elements constituting the long-span spatial bridge structure model are first obtained by quantizing using functions in the NumPy library, including np.mean() and np.linalg.norm().

4. The design method for long-span spatial bridge structures based on bidirectional progressive topology optimization according to claim 1, characterized in that, The average of the highest and lowest unit sensitivities among all units in the region to be optimized is used as the sensitivity threshold.

5. The design method for long-span spatial bridge structures based on bidirectional progressive topology optimization according to claim 4, characterized in that, The enumerate() function is used to traverse all cells in the region to be optimized. The threshold is dynamically updated by binary search, so that the average of the highest and lowest cell sensitivities in the region to be optimized is used as the sensitivity threshold.

6. The design method for long-span spatial bridge structures based on bidirectional progressive topology optimization according to claim 1, 4, or 5, characterized in that, Optimization is performed on the region to be optimized based on a sensitivity threshold, including: Delete cells in the region to be optimized whose sensitivity is less than or equal to the sensitivity threshold. Cells with sensitivity greater than the sensitivity threshold are added to the region to be optimized.

7. The design method for long-span spatial bridge structures based on bidirectional progressive topology optimization according to claim 6, characterized in that, The optimization of the region to be optimized is based on the sensitivity threshold, and it also includes the requirement that the overall volume of the large-span spatial bridge structure model remains basically unchanged after deleting and adding units during the structural optimization process. The volume fraction expression is as follows: V k+1 =V k (1-ER), k=1,2,3,… Where ER is the evolutionary rate, V k V represents the volume fraction in the k-th iteration. k+1 Let V1 be the volume fraction in the (k+1)th iteration, and V1 = 1. k Achieving the target volume constraint value V * V is maintained in subsequent iterations. k+1 =V * The optimization process continues until the model converges; during structural optimization, the deletion and addition of elements must ensure V. k+1 =V * .

8. The design method for long-span spatial bridge structures based on bidirectional progressive topology optimization according to claim 7, characterized in that, In step S8, the formula for stopping the iteration is as follows: Among them, PI k-i′+1 PI is the performance metric for generation ki′+1. k-N+i′-1 Let be the performance index for the k-N+i′-1 generation; N be the number of iterations used for convergence of the objective function; i′ be the loop variable of N; τ be the allowable convergence error; PI k-i′+1 and PI k-N+i′-1 All are obtained by dividing the corresponding volume fraction by the total external force work of the objective function of the corresponding algebra.

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