本文把ICM方法中的过滤函数和变密度方法中的惩罚函数统称为映射函数,研究了该函数的选取问题,探讨了其选取对于结构拓扑优化优化迭代收敛效率的影响.为此,本文提出了高效率收敛的映射函数构造途径,写出了5类常见的具体映射函数形式,提...本文把ICM方法中的过滤函数和变密度方法中的惩罚函数统称为映射函数,研究了该函数的选取问题,探讨了其选取对于结构拓扑优化优化迭代收敛效率的影响.为此,本文提出了高效率收敛的映射函数构造途径,写出了5类常见的具体映射函数形式,提出同高效率收敛映射函数MFHEC(Mapping function with highly efficient convergence)相配套的优化模型和寻优解法,先是自行比较了同类映射函数的过滤函数和准过滤函数寻优中收敛的快慢,然后相互比较了不同形式映射函数的快滤函数寻优收敛的快慢.以ICM方法求解位移约束下结构体积极小的拓扑优化问题为例,通过数值计算比较,印证了MFHEC函数的高效率收敛性.结果表明:同类函数比较中,快滤函数的收敛速度更快;5种不同类型映射函数比较中,幂函数形式的过滤函数收敛速度更快.最后需要强调的是:本文研究的映射函数的结论,包括ICM方法的过滤函数和变密度方法中的惩罚函数,二者都是同样适用的.展开更多
Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable s...Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements： the weak material element method and the tiny section element method. Three criteria （no structural singularity, no violated constraints and no change of structural weight） are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.展开更多
A continuum topology optimization usually produces results similar to a skeleton structure. In addition, the material utilization in the optimized structure is greatly improved compared with the original structure. On...A continuum topology optimization usually produces results similar to a skeleton structure. In addition, the material utilization in the optimized structure is greatly improved compared with the original structure. On the other hand, the redundancy of the structure is greatly reduced due to the removed material. A partial local failure in the optimized structure makes it more difficult for the entire structure to meet the strength/stiffness requirements. By using the independent continuous mapping (ICM) method, with minimal weight as the objective and both stress and displacement as the respective constraints, the continuum topology optimization models can be employed, which also consider damage. A dual-sequence quadratic programming (DSQP) algorithm is used to solve the topology optimization models. Numerical examples confirm the effectiveness and feasibility of the models. The results indicate that both a good load-path and weight reduction can be obtained. In addition, compared with the structure obtained using conventional topology optimization, redundancy is improved greatly, and the strength/stiffness requirements for the structure can be satisfied for each damage scenario. Furthermore, the results indicate that the strength/stiffness of the structure, after topology optimization, is slightly sensitive for local damage.展开更多
This research focuses on the lightweight topology optimization method for structures under the premise of meeting the requirements of stability and vibration characteristics. A new topology optimization model with the...This research focuses on the lightweight topology optimization method for structures under the premise of meeting the requirements of stability and vibration characteristics. A new topology optimization model with the constraints of natural frequencies and critical buckling loads and the objective of minimizing the structural volume is established and solved based on the independent continuous mapping method. The eigenvalue equations and composite exponential filter functions are applied to convert the optimization formulation into a continuous, solvable mathematical programming model. In the process of topology optimization, suitable initial values of the filter functions are chosen to avoid local modes, and the dynamic frequency gap constraints are added in the optimal model to prevent mode switches. Furthermore, for the optimal structures with grey elements obtained by the continuous optimization model, the bisection-inverse iteration is applied to search the optimal discrete structures. Finally, a detailed scheme is given for the buckling and frequency topology optimization problem. Numerical examples illustrate that the modelling method of minimizing the economic index with given performance requirements is practical and feasible for multi-performance topology optimization problems.展开更多
This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the ...This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.展开更多
A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is...A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is obtained based on the geometrically nonlinear finite element analysis.The lightweight topology optimization(TO)model under stress constraints is established to satisfy the strength requirement.Secondly,the distortion energy theory is introduced to transform themodel into structural strain energy constraints in order to solve the implicit relationship between stress constraints and design variables.Thirdly,the sensitivity analysis of the optimization model is derived,and the model is solved by the method of moving asymptotes(MMA).Numerical examples show that temperature has a significant effect on the optimal configuration,and the TO method considering temperature load is closer to engineering design requirements.The proposed method can be extended to the GNTO design with multiple physical field coupling.展开更多
Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the ...Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.展开更多
Hybrid lattice structures consisting of multiple microstructures have drawn much attention due to their excellent performance and extraordinary designability.This work puts forward a novel design scheme of lightweight...Hybrid lattice structures consisting of multiple microstructures have drawn much attention due to their excellent performance and extraordinary designability.This work puts forward a novel design scheme of lightweight hybrid lattice structures based on independent continuous mapping(ICM)method.First,the effective elastic properties of various microstructure configurations serve as a bridge between the macrostructure and the multiple microstructures by the homogenization theory.Second,a concurrent topology optimization model for seeking optimized macroscale topology and the specified microstructures is established and solved by a generalized multi-material interpolation formulation and sensitivity analysis.Third,several numerical examples show that hybrid lattice structures with different anisotropic configurations accomplish a better lightweight effect than those with various orthogonal configurations,which verifies the feasibility of the presented method.Hence,anisotropic configurations are more conducive to the sufficient utilization of constitutive material.The proposed scheme supplies a reference for the design of hybrid lattice structures and extends the application field of the ICM method.展开更多
文摘本文把ICM方法中的过滤函数和变密度方法中的惩罚函数统称为映射函数,研究了该函数的选取问题,探讨了其选取对于结构拓扑优化优化迭代收敛效率的影响.为此,本文提出了高效率收敛的映射函数构造途径,写出了5类常见的具体映射函数形式,提出同高效率收敛映射函数MFHEC(Mapping function with highly efficient convergence)相配套的优化模型和寻优解法,先是自行比较了同类映射函数的过滤函数和准过滤函数寻优中收敛的快慢,然后相互比较了不同形式映射函数的快滤函数寻优收敛的快慢.以ICM方法求解位移约束下结构体积极小的拓扑优化问题为例,通过数值计算比较,印证了MFHEC函数的高效率收敛性.结果表明:同类函数比较中,快滤函数的收敛速度更快;5种不同类型映射函数比较中,幂函数形式的过滤函数收敛速度更快.最后需要强调的是:本文研究的映射函数的结论,包括ICM方法的过滤函数和变密度方法中的惩罚函数,二者都是同样适用的.
基金The project supported by the National Natural Science Foundation of China (10472003)Beijing Natural Science Foundation (3042002)
文摘Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements： the weak material element method and the tiny section element method. Three criteria （no structural singularity, no violated constraints and no change of structural weight） are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.
基金the National Natural Science Foundation of China (Grant 11072009).
文摘A continuum topology optimization usually produces results similar to a skeleton structure. In addition, the material utilization in the optimized structure is greatly improved compared with the original structure. On the other hand, the redundancy of the structure is greatly reduced due to the removed material. A partial local failure in the optimized structure makes it more difficult for the entire structure to meet the strength/stiffness requirements. By using the independent continuous mapping (ICM) method, with minimal weight as the objective and both stress and displacement as the respective constraints, the continuum topology optimization models can be employed, which also consider damage. A dual-sequence quadratic programming (DSQP) algorithm is used to solve the topology optimization models. Numerical examples confirm the effectiveness and feasibility of the models. The results indicate that both a good load-path and weight reduction can be obtained. In addition, compared with the structure obtained using conventional topology optimization, redundancy is improved greatly, and the strength/stiffness requirements for the structure can be satisfied for each damage scenario. Furthermore, the results indicate that the strength/stiffness of the structure, after topology optimization, is slightly sensitive for local damage.
基金the National Natural Science Foundation of China (11872080, 11172013)Natural Science Foundation of Beijing Municipality (3192005)Beijing Education Committee Development Project (SQKM201610005001).
文摘This research focuses on the lightweight topology optimization method for structures under the premise of meeting the requirements of stability and vibration characteristics. A new topology optimization model with the constraints of natural frequencies and critical buckling loads and the objective of minimizing the structural volume is established and solved based on the independent continuous mapping method. The eigenvalue equations and composite exponential filter functions are applied to convert the optimization formulation into a continuous, solvable mathematical programming model. In the process of topology optimization, suitable initial values of the filter functions are chosen to avoid local modes, and the dynamic frequency gap constraints are added in the optimal model to prevent mode switches. Furthermore, for the optimal structures with grey elements obtained by the continuous optimization model, the bisection-inverse iteration is applied to search the optimal discrete structures. Finally, a detailed scheme is given for the buckling and frequency topology optimization problem. Numerical examples illustrate that the modelling method of minimizing the economic index with given performance requirements is practical and feasible for multi-performance topology optimization problems.
基金the National Natural Science Foundation of China(Grant No.11872080)Beijing Natural Science Foundation(Grant No.3192005)Taishan University Youth Teacher Science Foundation(Grant No.QN-01-201901).
文摘This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.
基金provided by the National Natural Science Foundation ofChina(Grant No.11872080)Beijing Natural Science Foundation(Grant No.3192005).
文摘A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is obtained based on the geometrically nonlinear finite element analysis.The lightweight topology optimization(TO)model under stress constraints is established to satisfy the strength requirement.Secondly,the distortion energy theory is introduced to transform themodel into structural strain energy constraints in order to solve the implicit relationship between stress constraints and design variables.Thirdly,the sensitivity analysis of the optimization model is derived,and the model is solved by the method of moving asymptotes(MMA).Numerical examples show that temperature has a significant effect on the optimal configuration,and the TO method considering temperature load is closer to engineering design requirements.The proposed method can be extended to the GNTO design with multiple physical field coupling.
基金This work was supported by the National Natural Science Foundation of China(11872080)Beijing Natural Science Foundation(3192005).
文摘Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.
基金This work was supported by the Beijing Natural Science Foundation(No.3192005)National Natural Science Foundation of China(No.11872080)Taishan University Youth Teacher Science Foundation(No.QN-01-201901).
文摘Hybrid lattice structures consisting of multiple microstructures have drawn much attention due to their excellent performance and extraordinary designability.This work puts forward a novel design scheme of lightweight hybrid lattice structures based on independent continuous mapping(ICM)method.First,the effective elastic properties of various microstructure configurations serve as a bridge between the macrostructure and the multiple microstructures by the homogenization theory.Second,a concurrent topology optimization model for seeking optimized macroscale topology and the specified microstructures is established and solved by a generalized multi-material interpolation formulation and sensitivity analysis.Third,several numerical examples show that hybrid lattice structures with different anisotropic configurations accomplish a better lightweight effect than those with various orthogonal configurations,which verifies the feasibility of the presented method.Hence,anisotropic configurations are more conducive to the sufficient utilization of constitutive material.The proposed scheme supplies a reference for the design of hybrid lattice structures and extends the application field of the ICM method.
