摘要
针对关于结构动响应拓扑优化问题的研究较少、有限元分析软件的拓扑优化模块无法实现的问题,采用变密度法研究连续体结构在基础简谐激励下的动响应拓扑优化.将基础简谐激励下的响应控制问题归结为结构在体积约束下目标点响应幅值最小化的优化模型;推导有阻尼结构在基础简谐激励下目标点响应幅值的灵敏度公式;采用变密度法求解该优化问题.采用多项式惩罚模型解决带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP)模型带来的附属效应现象;采用灰度过滤方法改善经典变密度法在优化过程中灰度单元收敛过慢的问题,从而减少变密度法优化的迭代步数并且使优化结果更清晰.以平面悬臂板模型为例,验证该优化方法对目标点响应幅值的优化以及灰度过滤函数对优化迭代的改善.
As to the facts that there are few studies on structural dynamic response topology optimization and it can not be achieved by the topology optimization modules of finite element analysis software,the dynamic response topology optimization of continuum structure under basic harmonic excitation is studied by variable density method.To control the response under basic harmonic excitation,an optimization model is established with an aim for minimization response amplitude of concern points under volume constraint;the response amplitude sensitivity equation of certain points is derived for structure with damp under basic harmonic excitation;then the optimization problem is solved by variable density method.The affiliated effect of SIMP(Solid Isotropic Microstructure with Penalization) model is solved by polynomial penalty model;a gray filtration method is used to solve the low convergence rate of gray elements in the optimization using classical variable density method,and the optimization iteration steps of variable density method are decreased and the optimization result becomes clearer.a plane cantilever plate is optimized,and the result indicates that the method can improve the optimization on the response amplitude of concern points and the gray filtration function can decrease optimization steps.
出处
《计算机辅助工程》
2012年第1期70-73,86,共5页
Computer Aided Engineering
关键词
基础简谐激励
动响应
拓扑优化
变密度法
附属效应
灰度过滤
basic harmonic excitation
dynamic response
topology optimization
variable density method
affiliated effect
gray filtration
