强迫谐振动下连续体结构拓扑优化  

TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURE WITH FREQUENCY RESPONSE CONSTRAINTS

作　　者：彭细荣[1] 隋允康[2] 

机构地区：[1]哈尔滨工业大学深圳研究生院,深圳518055 [2]北京工业大学数值模拟中心,北京100022

出　　处：《固体力学学报》2008年第2期157-162,共6页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10272006,30470439);北京市中青年骨干教师培养计划专项资助

摘　　要：应用结构拓扑优化ICM(独立连续映射)方法,对强迫谐振动下结构拓扑优化问题建立了以重量极小为目标,位移幅值为约束的优化模型.位移幅值采用一阶泰勒展式近似,由于拓扑优化中设计变量数目通常很多,对强迫谐振动位移幅值的敏度分析推导了伴随法公式,使得一次敏度分析可以计算出对所有设计变量的偏导数,克服了采用直接法敏度分析中一次只能计算出对一个设计变量的偏导数的不足.算例表明用伴随法分析敏度在结构拓扑优化中可以大幅提高计算效率,ICM方法采用独立于截面及形状参数的拓扑优化设计变量更清晰地反映了拓扑优化的本质.Based on ICM（Independent Continuous Mapping） method of structural topology optimiza tion, a model with weight minimum objective and displacement amplitude constraints is established for the topology optimization problem of continuum structure. The displacement amplitude is close expressed by the first order Taylor expression. With a view to that there are always many design variables in the topolo- gy optimization, and the partial derivatives with respect to one design variable can be obtained from a sen sitivity analysis in the direct method, an adjoint method of sensitivity analysis of displacement amplitude with frequency response is developed and the partial derivatives with respect to all design variables can be obtained from a sensitivity analysis. Numeric examples reveal that the computational efficiency can be improved dramatically if sensitivities are analyzed by the adjoint method. Adopting the topology variables which independent of size and shape parameters of structure in ICM method reflects the essence of topology optimization more clearly.

关 键 词：强迫谐振动 敏度分析 伴随法 拓扑优化 

分 类 号：O321[理学—一般力学与力学基础]