基于类桁架材料模型优化方法计算稳定性研究

推导了2相正交类桁架材料模型,建立了基于类桁架连续体材料模型的单工况和多工况应力约束拓扑优化方法.以杆件在结点位置的密度和方向为设计变量,在单工况下,采用满应力准则法优化杆件密度,将杆件方向与主应力方向对齐;在多工况下,采用方向刚度包络线拟合的方法,由各单工况优化结构导出.通过反复迭代形成类桁架连续体材料优化分布场,进而形成类桁架结构.通过3个经典算例,验证了不同有限单元网格密度和形状下该拓扑优化方法的稳定性,克服了各种拓扑优化普遍存在的单元依赖性.

Study on calculation stability of optimization method based on truss-like material model

The truss-like continuum material model with two families of orthotropic members was derived.The topology optimization method,based on the truss-like continum material model,with stress constraint under singular load case and multiple load cases was established.The densities and orientations of the members at nodes were taken as design variables.Under singular load case,the densities of members were optimized by fully-stressed criteria.The orientations of member were align to orientation of principal stress.Structures under multiple load cases were optimized by fitting envelopes of directional stiffness under singular loads.The distributed field of truss-like continuum material was optimized by iterative approach.Furthermore truss-like structures were obtained.Three numerical examples of classical trusses were analyzed to demonstrate the numerical stability of the topology optimization method by adopting different finite elements densities and shapes.The problems of dependence on elements,which happened frequently in most optimization methods,was overcome.