A topology optimization method for traveling bridge structure based on multi-dimensional equivalent dynamic load theory

Abstract

The present invention discloses a topology optimization method for a traveling bridge structure based on a multi-dimensional equivalent dynamic load theory, comprising: using a dynamic analysis method to determine the stress condition of a mechanism to be optimized under actual dynamic continuous working conditions; obtaining a key stress section of the mechanism to be optimized where the load position does not change for a certain period of time under continuous working conditions, anchoring the unit time of the equivalent process analysis step according to the characteristics of the mechanism to be optimized; using the relative density of each unit of the nonlinear finite element model of the key components of the mechanism to be optimized as a design variable, and using a variable density method to perform topology optimization on the finite element analysis results of each equivalent working condition; combining the system equivalent coefficient Q i The continuous dynamic working conditions of the mechanism to be optimized are converted to equivalent static conditions, and then the structural topology optimization is performed to generate the optimized results. The optimal mechanical bridge topology obtained by this method is highly lightweight while meeting actual working conditions and can be widely used to guide production practices.

Description

Technical Field

[0001] The present invention relates to the technical field of traveling bridge structures, and in particular to a traveling bridge structure topology optimization method based on multi-dimensional equivalent dynamic load theory. Background Art

[0002] As a typical method for optimizing continuum structures in the initial stages of engineering design and providing design assistance, topology optimization has been widely used in various sub-fields. Taking the most widely used material interpolation model variable density method as an example, its key concept is to transform the optimization of various component structures into the redistribution of internal materials of the components. Based on finite element analysis, the relative density of each finite element unit of the component is used as the design variable, and the flexibility, displacement field or stress field of the component under actual working conditions can be defined as the design objective function or design constraint. This working condition can be single or multiple.

[0003] Currently, topology optimization methods are mainly used to solve engineering and technical problems under static working conditions. For the optimization problems of dynamic systems, the basic idea of ​​the ESL method proposed by Park et al. is to apply a series of static loads to the engineering model for linear static analysis, so that it produces the same displacement field as the dynamic analysis, ensuring the equivalence of the linear static working condition model and the dynamic working condition model used for subsequent optimization. However, this method is mostly used for size optimization and shape optimization. In the field of topology optimization, the equivalent static working condition analysis model obtained by applying this method at a discrete time point is often the equivalent time point of the maximum displacement field. In actual dynamic system optimization problems, it is necessary to consider not only the displacement field, but also the influence of the stress field and the duration of the working condition. The current existing technology for the analysis of bridge structures has the following defects: the optimization of traveling bridge structures is often based on the analysis of a single working condition of static stiffness, lacking a comprehensive optimization analysis process under dynamic continuous working conditions. The optimization of bridge structures is often mainly based on size optimization and morphology optimization. Traveling bridge structures using topology optimization as the main optimization method are very rare. Summary of the Invention

[0004] In view of the problems existing in the prior art, the present invention discloses a topology optimization method for a traveling bridge structure based on multi-dimensional equivalent dynamic load theory, which specifically includes the following steps:

[0005] Establish a nonlinear finite element model of the mechanism to be optimized with kinematic degrees of freedom, and use dynamic analysis methods to determine the stress conditions of the mechanism to be optimized under actual dynamic continuous working conditions;

[0006] Obtain the key stress section where the load position does not change for a period of time under continuous working conditions for the mechanism to be optimized, and anchor the unit time of the equivalent process analysis step according to the characteristics of the mechanism to be optimized;

[0007] Based on unit time, the dynamic continuous working conditions of the mechanism to be optimized are converted into multiple unit working conditions;

[0008] Judge the working condition number, if i=N max , then skip this step and proceed to subsequent calculations. If i is not equal to N max , update the working condition number i=i+1, analyze the finite element under this working condition number, and when reaching the critical stress period time domain, merge all the unit working conditions in this time domain, and use the merged working condition as the research object for finite element analysis;

[0009] According to the material properties of the key components of the mechanism to be optimized, all equivalent working conditions are equivalently processed from three dimensions: stress, displacement and time domain;

[0010] The weights of different force-bearing sections in the full working condition of the mechanism to be optimized are controlled to meet actual requirements, and the system equivalent coefficient is calculated. The larger the system equivalent coefficient, the more important the equivalent working condition is in the continuous dynamic working condition of the mechanism to be optimized.

[0011] The relative density of each unit of the nonlinear finite element model of the key components of the mechanism to be optimized is used as the design variable, and the variable density method is used to perform topological optimization on the finite element analysis results of each equivalent working condition;

[0012] Set a penalty factor. Set a suitable value for the penalty factor to control the unit density of the mechanism to be optimized to be as close to 0 or 1 as possible, thereby converting the originally discrete nonlinear finite element model into an easy-to-solve continuous optimization model for calculation;

[0013] Combined with the system equivalent coefficient Q i , the continuous dynamic working conditions of the optimized mechanism are transformed into equivalent static conditions, and then the structural topology optimization is performed to generate the optimization results.

[0014] Furthermore, according to the material properties of the key components of the mechanism to be optimized, the stress threshold S is set. max and displacement threshold D max , for all equivalent working conditions, from the stress S i , displacement D i Time domain T i Equivalence processing is performed in three dimensions. According to the needs of equivalent analysis, all parameters are first unified:

[0015] Stress parameter L si =S i / S max

[0016] Displacement parameter L di =D i / D max

[0017] Time domain parameters

[0018] Furthermore, in the process of converting complex continuous dynamic conditions into equivalent static conditions, different unit conditions at different times correspond to different weight coefficients, and the equivalent coefficient is calculated in the following way:

[0019]

[0020] L si represents the stress parameter, L di represents the displacement parameter, L ti represents the time domain parameter, V i It represents the volume of the tetrahedron surrounded by stress parameter, displacement parameter, time domain parameter and three coordinate axes under working condition i, where the three coordinate axes are stress parameter, displacement parameter and time domain parameter respectively.

[0021] Furthermore, through the established comprehensive objective function, the structural topology optimization of the continuous dynamic working conditions of the optimized mechanism is performed to obtain the optimization results, where the comprehensive objective function is as follows:

[0022]

[0023] Where F(ρ) is the structural synthesis objective function, C i (ρ) is the structural flexibility value under the i-th working condition, C max and C min Represent the maximum and minimum flexibility of the structure, F i is the resultant force vector of the structure under the i-th working condition, K i is the stiffness matrix of the structure under the i-th working condition, U i is the displacement array of the structure under the i-th working condition, V0 is the initial volume of the structural design area, V is the volume after structural optimization, f is the structural volume fraction constraint parameter, ρ min is the minimum relative density of the unit.

[0024] Due to the adoption of the above-mentioned technical solution, the present invention provides a bridge structure topology optimization method based on multi-dimensional equivalent dynamic load theory. This method can be widely applied to the field of bridge design under linear dynamic loads. The complex bridge dynamic system working condition is equivalent to several static load working conditions that consider stress fields and displacement fields, and the influence of time effects is taken into account, thereby converting it into a multi-condition bridge structure topology optimization problem under multi-dimensional conditions, thereby solving the bridge optimization problem under complex dynamic system working conditions. The resulting optimal mechanical bridge topology structure has a high degree of lightweight while meeting actual working conditions and can be widely used to guide production practice activities. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0026] Figure 1 This is a flow chart of the bridge structure topology optimization method based on multi-dimensional equivalent dynamic load theory disclosed in the present invention.

[0027] Figure 2 A simplified three-dimensional model of a bridge mechanism provided in an embodiment of the present invention.

[0028] Figure 3 This is a schematic diagram of the actual use of the bridge by workers in an embodiment of the present invention.

[0029] Figure 4 This is an equivalent variable density cloud diagram of the optimization results of the embodiment based on the multi-dimensional equivalent dynamic load theory provided in the embodiment of the present invention.

[0030] Figure 5 This is a schematic diagram of a three-dimensional model of a movable tripod reconstructed according to optimization results and specific usage conditions in an embodiment of the present invention.

[0031] Figure 6 Schematic diagram comparing stress cloud diagrams of the movable tripod before and after optimization under the same working conditions in an embodiment of the present invention.

[0032] Figure 7 Schematic diagram showing the comparison of displacement cloud diagrams of the movable tripod before and after optimization under the same working conditions in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] To make the technical solutions and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention:

[0034] like Figure 1 The topology optimization method of the traveling bridge structure based on the multi-dimensional equivalent dynamic load theory shown in the figure specifically includes the following steps:

[0035] Step 1: For the mechanism to be optimized, a nonlinear finite element model with kinematic degrees of freedom is established, and the force conditions of the mechanism under actual dynamic continuous working conditions are determined through dynamic analysis.

[0036] Step 2: Through the analysis in the previous step, obtain the key stress section where the load position does not change in a certain period of time under the continuous working condition. At this time, anchor the equivalent process analysis step unit time t (in seconds) according to the characteristics of the mechanism to be optimized.

[0037] Step 3: Based on the unit time t, the dynamic continuous working condition of the mechanism to be optimized is converted into multiple unit working conditions. The total number of unit working conditions is N. max =T / t (T is the total duration of the dynamic working condition of the mechanism to be optimized), set the initial working condition i to 1, use finite element software to analyze the stress conditions of the mechanism to be optimized under the initial working condition, obtain the stress field and displacement field of the key components of the mechanism to be optimized under the initial working condition, and record the maximum stress value S1 and displacement value D1 corresponding to the N1 working condition (i=1).

[0038] Step 4: Determine the working condition number. If i=N max , skip step 4 and proceed to subsequent calculations. If i is not equal to N max , update the working condition number i=i+1 and continue the finite element analysis under the corresponding working condition number. When reaching the critical stress period time domain, all unit working conditions in the time domain need to be merged, and the merged working condition is used as the research object for finite element analysis.

[0039] Step 5: Set the stress threshold S according to the material properties of the key components of the mechanism to be optimized max and displacement threshold D max , for all equivalent working conditions, from the stress S i , displacement D i Time domain T i The three dimensions are equivalently processed. Due to the need for equivalent analysis, all parameters should be unified first:

[0040] Stress parameter L si =S i / S max

[0041] Displacement parameter L di =D i / D max

[0042] Time domain parameters

[0043] Step 6: Introduce the concept of system equivalent coefficient. In the process of converting complex continuous dynamic working conditions into equivalent static conditions, different unit working conditions correspond to different weight coefficients over time. To ensure that the weights of different load-bearing sections in the full working conditions of the optimized mechanism are in line with reality, the equivalent coefficient is calculated using the following equation:

[0044]

[0045] Equivalent coefficient Q iThe larger the L is, the more important the equivalent working condition is in the continuous dynamic working condition of the mechanism to be optimized. In the subsequent topology optimization process, its structural influence on the key components of the mechanism to be optimized should be considered. si represents the stress parameter, L di represents the displacement parameter, L ti represents the time domain parameter, V i It represents the volume of the tetrahedron surrounded by stress parameters, displacement parameters, time domain parameters and three coordinate axes under working condition i.

[0046] Step 7: Using the relative density ρ of each unit of the finite element model of the key components of the mechanism to be optimized as the design variable, the variable density method is used to perform topology optimization based on the finite element analysis results of each equivalent working condition. The optimization objective is set as:

[0047]

[0048] Where C(P) is the total flexibility of the structure, F is the force vector, U is the displacement matrix, K is the total stiffness matrix of the structure, V0 is the initial volume of the structural design area, V is the volume after structural optimization, f is the structural volume fraction constraint parameter, ρ min is the minimum relative density of the unit. In the variable density method, the material density is distributed in [0,1]. i = 0 means that the unit has no material, and the corresponding unit stiffness matrix is ​​0, which will lead to a singular structural stiffness matrix and is difficult to solve. Therefore, ρ is introduced min Instead of ρ i ≤ρ min The units represented by , mean that there is no material at the unit, and often these units have very small stiffness values, and their replacement has little effect on the overall calculation accuracy.

[0049] Step 8: In order to minimize the number of units with intermediate material density, we introduce the concept of a penalty factor. The penalty factor p is used to force the density of structural units to approach 0 or 1 as much as possible by setting an appropriate value for it, thereby converting the originally discrete optimization model into an easily solved continuous optimization model for calculation:

[0050]

[0051] In the formula K (ρ) is the structural penalty stiffness, K is the actual stiffness of the structure, E (ρ) is the structural penalty elastic modulus, E is the actual elastic modulus of the structure, ρ is the structural density, and p is the penalty factor, which is always greater than 1.

[0052] Step 9: Combine the equivalent coefficient Q i, the structural topology optimization after equivalent static transformation of the continuous dynamic working condition of the optimized mechanism is carried out, and the comprehensive objective function established is as follows:

[0053]

[0054] Where F(ρ) is the structural comprehensive objective function, C i (ρ) is the structural flexibility value under the i-th working condition, C max with C min Represent the maximum and minimum flexibility of the structure, F i is the resultant force vector of the structure under the i-th working condition, K i is the stiffness matrix of the structure under the i-th working condition, U i is the displacement array of the structure under the i-th working condition, V0 is the initial volume of the structural design area, V is the volume after structural optimization, f is the structural volume fraction constraint parameter, ρ min is the minimum relative density of the unit, and its meaning has been explained in step 7.

[0055] Example:

[0056] like Figure 2 As shown in the figure, a 3D model of the bridge mechanism was established, and fillets that did not affect the structural analysis were removed. Connections and power transmission components, such as hinges, were deleted and replaced with couplings, constraints, and loads to promote convergence of the calculation and analysis. The traveling platform 1 is connected to the movable tripod 3 via platform tie rods 2, and the movable tripod 3 and the traveling platform 1 are each connected to the bridge body 4 via hinge constraints. Finite element analysis software was used to perform finite element meshing on the cleaned-up bridge mechanism. The model material was defined as Q355B, and material properties such as elastic modulus, density, and Poisson's ratio were assigned.

[0057] Based on the actual use of the bridge by workers, such as Figure 3 As shown, the worker will move from point a to point b at a constant speed, and stop at point b to observe the situation ahead. Only after determining a safe path will he continue to move forward. Therefore, the dynamic movement condition of the worker on the bridge platform can be divided into several equivalent static conditions. For this embodiment, the unit time t = 1s is defined. The worker carries a heavy object (taking the limit value of 500kg) and moves from point a to point b for a total of 11s, of which the stay time at point b is 6s. Then, this dynamic continuous condition is equivalent to six unit conditions. The key component of the bridge is analyzed, the movable tripod, which has a mass of 23.46kg. The stiffness analysis is performed on each equivalent static condition to obtain the initial calculation data of the movable tripod:

[0058]

[0059] According to the material properties of the key components of the mechanism to be optimized, the stress threshold S is setmax The material yield strength of Q355B is 355 MPa, and the displacement threshold D is taken according to design experience. max =4mm, and all parameters are standardized:

[0060] Working conditions Stress parameters Time domain parameters Displacement parameters Working conditions Stress parameters Time domain parameters Displacement parameters 1 0.02 0.09 0.07 4 0.08 0.09 0.35 2 0.04 0.09 0.14 5 0.11 0.09 0.46 3 0.06 0.09 0.23 6 0.14 0.55 0.57

[0061] Obtain the equivalent coefficient Q under each working condition i , the structural topology optimization after equivalent static transformation of the continuous dynamic working condition of the optimized mechanism is carried out. The implementation flow chart based on the multi-dimensional equivalent dynamic load theory is as follows Figure 1 shown.

[0062] After 10 optimization iterations, the equivalent density cloud map of the optimization result provided by this embodiment of the present invention is obtained as follows: Figure 4 As shown, according to the optimization results, the movable tripod structure of this embodiment is reconstructed, and the new movable tripod structure is as follows Figure 5 As shown in Figure 2, the mass of the optimized tripod is 20.74 kg. Comparison of stress cloud diagrams of the tripod before and after optimization under the same working conditions Figure 6 As shown in the figure, the displacement cloud diagram of the movable tripod before and after optimization under the same working conditions is compared. Figure 7 shown.

[0063] The stiffness cloud diagram obtained after static analysis of the reconstructed mechanism under the same working conditions is shown in the following table:

[0064]

[0065]

[0066] It can be seen that the mass of the movable tripod of the bridge mechanism obtained by optimizing this method is reduced by 11.6%, and the stiffness is basically unchanged, and the deformation is still within the allowable range.

[0067] The method disclosed in the present invention cleverly transforms the dynamic working condition optimization problem of the bridge into a static multi-working condition optimization problem, so that the originally complex dynamic optimization problem of the bridge can be better solved. In addition, by proposing a multi-dimensional concept, the equivalent dynamic load not only considers the spatial changes of the working conditions in the equivalence process, but also takes into account the influence of the time domain, and aggregates the equivalent processes of each key stress section into a key working condition section, which greatly shortens the time for the overall dynamic system to be handed over to the computer for calculation after equivalence; by proposing system equivalent parameters, the equivalent value of each key stress section is made more reasonable in the overall continuous optimization process, and then the topological optimization analysis results after the overall equivalence of the dynamic working conditions of the optimized mechanism are more in line with the original intention of the engineering design, saving the design time of engineering designers and improving design efficiency.

[0068] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A topology optimization method for traveling bridge structure based on multi-dimensional equivalent dynamic load theory, characterized by include: Establish a nonlinear finite element model of the mechanism to be optimized with kinematic degrees of freedom, and use dynamic analysis methods to determine the stress conditions of the mechanism to be optimized under actual dynamic continuous working conditions; Obtain the key stress section where the load position does not change for a period of time under continuous working conditions for the mechanism to be optimized, and anchor the unit time of the equivalent process analysis step according to the characteristics of the mechanism to be optimized; Based on the unit time, the dynamic continuous working conditions of the mechanism to be optimized are converted into multiple unit working conditions; the initial working condition i is set to 1, and the finite element software is used to analyze the stress conditions of the mechanism to be optimized under the initial working condition, and the stress field and displacement field of the key components of the mechanism to be optimized under the initial working condition are obtained. The maximum stress value S1 and displacement value D1 corresponding to the N1 working condition (i=1) are recorded; Judge the working condition number, if i=N max , then skip this step and proceed to subsequent calculations. If i is not equal to N max , update the working condition number i=i+1, analyze the finite element under this working condition number, and when reaching the critical stress time domain, merge all the unit working conditions in this time domain, and use the merged working condition as the research object for finite element analysis, where N max is the total number of unit operating conditions; According to the material properties of the key components of the mechanism to be optimized, all equivalent working conditions are equivalently processed from three dimensions: stress, displacement and time domain; According to the material properties of the key components of the mechanism to be optimized, the stress threshold S is set max and displacement threshold D max , for all equivalent working conditions, from the stress S i , displacement D i Time domain T i Equivalence processing is performed in three dimensions. According to the needs of equivalent analysis, all parameters are first unified: Stress parameter L si =S i / S max Displacement parameter L di =D i / D max Time domain parameters The weights of different force-bearing sections in the full working condition of the mechanism to be optimized are controlled to meet actual requirements, and the system equivalent coefficient is calculated. The larger the system equivalent coefficient, the more important the equivalent working condition is in the continuous dynamic working condition of the mechanism to be optimized. The relative density of each unit of the nonlinear finite element model of the key components of the mechanism to be optimized is used as the design variable, and the variable density method is used to perform topological optimization on the finite element analysis results of each equivalent working condition; Set a penalty factor. Set an appropriate value for the penalty factor to control the unit density of the mechanism to be optimized to be as close to 0 or 1 as possible, thereby converting the originally discrete nonlinear finite element model into an easy-to-solve continuous optimization model for calculation; Combined with the system equivalent coefficient Q i , the continuous dynamic working conditions of the optimized mechanism are transformed into equivalent static conditions, and then the structural topology optimization is performed to generate the optimization results.

2. The method according to claim 1, wherein: In the process of converting complex continuous dynamic working conditions into equivalent static conditions, different unit working conditions at different times correspond to different weight coefficients, and the equivalent coefficient is calculated in the following way: L si represents the stress parameter, L di represents the displacement parameter, L ti represents the time domain parameter, V i It represents the volume of the tetrahedron surrounded by stress parameters, displacement parameters, time domain parameters and three coordinate axes under working condition i.

3. The method according to claim 1, wherein: Through the established comprehensive objective function, the structural topology optimization of the continuous dynamic working conditions of the optimized mechanism is carried out to obtain the optimization results, where the comprehensive objective function is as follows: Where F(ρ) is the structural synthesis objective function, C i (ρ) is the structural flexibility value under the i-th working condition, C max and C min Represent the maximum and minimum flexibility of the structure, F i is the resultant force vector of the structure under the i-th working condition, K i is the stiffness matrix of the structure under the i-th working condition, U i is the displacement array of the structure under the i-th working condition, V0 is the initial volume of the structural design area, V is the volume after structural optimization, f is the structural volume fraction constraint parameter, ρ min is the minimum relative density of the unit.

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