基于连续统敏度的结构动态形状优化方法

为实现连续体结构动态形状优化设计,运用连续统敏度分析方法,得到了结构体积、固有频率的物质导数. 在此基础上,采用控制点的虚拟位移为设计变量,运用一阶泰勒展开建立优化模型,设置设计变量的运动极限保证了优化迭代的稳健性. 数值算例表明,该方法的实现不必修改有限元源程序,敏度计算所需的有限元分析次数少,适用于各类优化模型.

Dynamic Shape Optimization Based on Continuum Derivatives

Material derivatives of structural volume and natural frequencies are obtained based on continuum derivatives.In order to carry out dynamic shape optimization for continuum structure,virtual displacements of control point are selected as the design variables,approximate model is constructed by Taylor series expansion,move limit of design variables are adopted to ensure algorithmic reliability.The method can be implemented not by modifying source program of finite element method and by less finite element analysis.Numerical examples are shown to demonstrate the efficiency and generality of the method,the method is fit for some kinds of dynamic shape optimization problem.