The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through...The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.展开更多
Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers...Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.展开更多
在工业化建造和碳减排的背景下,预制装配化得到了极大关注。以装配式铁路桥梁为对象,首先,考虑4种典型构件类型(箱梁、桥面板、桥墩和盖梁),核算其预制与现浇两种方式在物化阶段的立方单项碳排放和建造成本,并构建以构件预制率为决策变...在工业化建造和碳减排的背景下,预制装配化得到了极大关注。以装配式铁路桥梁为对象,首先,考虑4种典型构件类型(箱梁、桥面板、桥墩和盖梁),核算其预制与现浇两种方式在物化阶段的立方单项碳排放和建造成本,并构建以构件预制率为决策变量的碳排放-成本双目标优化模型,系统优化预制构件的选择与组合;其次,采用非支配排序的鲸鱼优化算法(Non-Dominated Sorting Whale Optimization Algorithm,NSWOA)对构件组合方案进行求解,获得Pareto均衡解集;再次,通过博弈论思想融合主客观权重,并采用优劣解距离法(Technique for Order Preference by Similarity to an Ideal Solution,TOPSIS)对Pareto均衡解集进行科学决策,得到最佳构件组合方案;最后,以某西部装配式铁路桥梁为例开展实证分析。结果显示:优化方案较初始方案碳排放减少了361.66 t,成本减少了213.06万元。此外,预制率情景分析显示,不同的桥梁预制率对应不同的最佳构件组合,且碳排放与成本随预制率变化呈现不同趋势。研究成果可为装配式铁路桥梁低碳施工提供有效的优化策略。展开更多
基金supported by the National Natural Science Foundation of China(Grant 12472113).
文摘The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.
文摘Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.
文摘在工业化建造和碳减排的背景下,预制装配化得到了极大关注。以装配式铁路桥梁为对象,首先,考虑4种典型构件类型(箱梁、桥面板、桥墩和盖梁),核算其预制与现浇两种方式在物化阶段的立方单项碳排放和建造成本,并构建以构件预制率为决策变量的碳排放-成本双目标优化模型,系统优化预制构件的选择与组合;其次,采用非支配排序的鲸鱼优化算法(Non-Dominated Sorting Whale Optimization Algorithm,NSWOA)对构件组合方案进行求解,获得Pareto均衡解集;再次,通过博弈论思想融合主客观权重,并采用优劣解距离法(Technique for Order Preference by Similarity to an Ideal Solution,TOPSIS)对Pareto均衡解集进行科学决策,得到最佳构件组合方案;最后,以某西部装配式铁路桥梁为例开展实证分析。结果显示:优化方案较初始方案碳排放减少了361.66 t,成本减少了213.06万元。此外,预制率情景分析显示,不同的桥梁预制率对应不同的最佳构件组合,且碳排放与成本随预制率变化呈现不同趋势。研究成果可为装配式铁路桥梁低碳施工提供有效的优化策略。
