In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are reg...In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are regulated through sensitivity filtering tomitigate numerical instabilities associatedwith stress concentrations.Ap-norm aggregation function is employed to globalize local stress constraints,and a normalization technique linearly weights strain energy and stress,transforming the multi-objective problem into a single-objective formulation.The sensitivity of the objective function with respect to design variables is rigorously derived.Three numerical examples are presented,comparing the optimized structures in terms of strain energy,mass,and stress across five different mathematical models with varying combinations of optimization objectives.The results validate the effectiveness and feasibility of the proposed method for achieving a balanced design between structural stiffness and strength.This approach offers a new perspective for future research on stiffness-strength coordinated structural optimization.展开更多
基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)是一种常用的拓扑优化模型,因其计算效率较高而应用广泛。在工程实际中,采用单一材料的结构往往难以满足较好地综合性能,而功能梯度材料结构能充分发挥...基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)是一种常用的拓扑优化模型,因其计算效率较高而应用广泛。在工程实际中,采用单一材料的结构往往难以满足较好地综合性能,而功能梯度材料结构能充分发挥其组成的各相材料的优点,在满足轻量化、高强度的要求的同时,达到良好的经济效益,在工程上应用广泛。然而,传统的SIMP法由于其预先设定材料属性,对功能梯度材料变刚度的结构体拓扑优化稍显不足,本文提出了一种基于有限元素法,采用功能梯度材料的变刚度改进方法,采用改进的SIMP法进行优化问题的求解,使得变刚度结构经过优化后其强度得到提高的同时,充分发挥功能梯度材料其各相组成材料的特性,合理分配材料使用进而降低成本。最后在MATLAB环境中以悬臂梁结构为算例模型验证了该方法的可行性,具有十分广阔的应用前景。展开更多
基金funded by National Nature Science Foundation of China(92266203)National Nature Science Foundation of China(52205278)+1 种基金Key Projects of Shijiazhuang Basic Research Program(241791077A)Central Guide Local Science and Technology Development Fund Project of Hebei Province(246Z1022G).
文摘In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are regulated through sensitivity filtering tomitigate numerical instabilities associatedwith stress concentrations.Ap-norm aggregation function is employed to globalize local stress constraints,and a normalization technique linearly weights strain energy and stress,transforming the multi-objective problem into a single-objective formulation.The sensitivity of the objective function with respect to design variables is rigorously derived.Three numerical examples are presented,comparing the optimized structures in terms of strain energy,mass,and stress across five different mathematical models with varying combinations of optimization objectives.The results validate the effectiveness and feasibility of the proposed method for achieving a balanced design between structural stiffness and strength.This approach offers a new perspective for future research on stiffness-strength coordinated structural optimization.
文摘基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)是一种常用的拓扑优化模型,因其计算效率较高而应用广泛。在工程实际中,采用单一材料的结构往往难以满足较好地综合性能,而功能梯度材料结构能充分发挥其组成的各相材料的优点,在满足轻量化、高强度的要求的同时,达到良好的经济效益,在工程上应用广泛。然而,传统的SIMP法由于其预先设定材料属性,对功能梯度材料变刚度的结构体拓扑优化稍显不足,本文提出了一种基于有限元素法,采用功能梯度材料的变刚度改进方法,采用改进的SIMP法进行优化问题的求解,使得变刚度结构经过优化后其强度得到提高的同时,充分发挥功能梯度材料其各相组成材料的特性,合理分配材料使用进而降低成本。最后在MATLAB环境中以悬臂梁结构为算例模型验证了该方法的可行性,具有十分广阔的应用前景。
