湖北大学学报（自然科学版）
湖北大學學報（自然科學版）
호북대학학보（자연과학판）
2013年
3期
315-319
,共5页
结构设计%拓扑优化%数值稳定性%类桁架材料模型
結構設計%拓撲優化%數值穩定性%類桁架材料模型
결구설계%탁복우화%수치은정성%류항가재료모형
structural design%topology optimization%numerical stabilities%truss-like material model
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。
推導瞭2相正交類桁架材料模型，建立瞭基于類桁架連續體材料模型的單工況和多工況應力約束拓撲優化方法。以桿件在結點位置的密度和方嚮為設計變量，在單工況下，採用滿應力準則法優化桿件密度，將桿件方嚮與主應力方嚮對齊；在多工況下，採用方嚮剛度包絡線擬閤的方法，由各單工況優化結構導齣。通過反複迭代形成類桁架連續體材料優化分佈場，進而形成類桁架結構。通過3箇經典算例，驗證瞭不同有限單元網格密度和形狀下該拓撲優化方法的穩定性，剋服瞭各種拓撲優化普遍存在的單元依賴性。
추도료2상정교류항가재료모형，건립료기우류항가련속체재료모형적단공황화다공황응력약속탁복우화방법。이간건재결점위치적밀도화방향위설계변량，재단공황하，채용만응력준칙법우화간건밀도，장간건방향여주응력방향대제；재다공황하，채용방향강도포락선의합적방법，유각단공황우화결구도출。통과반복질대형성류항가련속체재료우화분포장，진이형성류항가결구。통과3개경전산례，험증료불동유한단원망격밀도화형상하해탁복우화방법적은정성，극복료각충탁복우화보편존재적단원의뢰성。
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 .
