动态优化中的动响应高阶修改及灵敏度分析

 本文通过建立设计变量空间到重分析变量空间的映射关系,然后在重分析变量空间,考虑动响应高阶方向导数及动响应修改量的泰勒级数表达式,利用模态分析技术,推导出一套动响应高阶修改和计算动响应梯度的公式。其工作量完全同于一阶导数修改。公式适合于采用模态截断来限制计算代价的大型飞机结构动态优化设计。算例表明公式具有高精度和高效率。

HIGHER-ORDER UPDATES AND SENSITIVITY ANALYSIS FOR DYNAMIC RESPONSES IN STRUCTURAL OPTIMIZATION DESIGN

A set of formulas calculating higher-order updates and gradient for dynamic responses is derived by setting up the mapping relationship between the design variables space and the re-analysis variables space, hence, higher-order directional derivatives of dynamic response and the Taylor-series representation of dynamic reponse updates considered in the re-analysis variables space. and the technique of modal analysis is utilized. What is significantly noteworthy is that the computational effort needed in obtaining the expression of the convergent series is based entirely on the first-order information. The formulas are suitable to the dynamic response optimal design of large scale structures where the modal truncation can be employed to reduce the computational costs. Numerical examples are provided to illustrate accuracy and efficiency of the proposed procedures.