CAJ | 학술논문

针对频率约束的结构材料优化问题，基于结构拓扑优化思想，提出变频率区间约束的结构材料优化方法。借鉴均匀化及 ICM（独立、连续、映射）方法，以微观单元拓扑变量倒数为设计变量，导出宏观单元等效质量矩阵及导数，进而获得频率一阶近似展开式。结合变频率区间约束思想，获得以结构质量为目标函数、频率为约束条件的连续体微结构拓扑优化近似模型；采用对偶方法求解。通过算例验证该方法的有效性及可行性，表明考虑质量矩阵变化影响所得优化结果更合理。
침대빈솔약속적결구재료우화문제，기우결구탁복우화사상，제출변빈솔구간약속적결구재료우화방법。차감균균화급 ICM（독립、련속、영사）방법，이미관단원탁복변량도수위설계변량，도출굉관단원등효질량구진급도수，진이획득빈솔일계근사전개식。결합변빈솔구간약속사상，획득이결구질량위목표함수、빈솔위약속조건적련속체미결구탁복우화근사모형；채용대우방법구해。통과산례험증해방법적유효성급가행성，표명고필질량구진변화영향소득우화결과경합리。
Based on the idea of structural topology optimization,a structural material optimization method considering varying frequency interval constraints was proposed.By use of homogenization and ICM (Independence, Continuity and Mapping)method,the effective mass matrix and its derivatives were established by taking the reciprocal topological variables of micro structural elements as design variables,and the first order approximate explicit functions of frequency interval constraints were constructed.Integrating with the idea of varying frequency interval constraints,a topological optimization model of micro structures was formed by taking the structural mass as objective function and the frequency as constraint function.Here,a dual solving method was adopted.The results of two examples show that the proposed method is feasible and effective,and the optimal result obtained by the proposed method,where the variation of mass matrix is considered,is more reasonable.