结构形状优化响应面方法的改进与应用  

Improvement and Application on Response Surface Methodology in Shape Optimization

作　　者：隋允康[1] 张轩[1] 宇慧平[1] 

机构地区：[1]北京工业大学机械工程与应用电子技术学院工程数值模拟中心,北京100022

出　　处：《北京工业大学学报》2008年第1期31-36,64,共7页Journal of Beijing University of Technology

基　　金：国家自然科学基金(10472003);北京市自然科学基金(3042002)

摘　　要：为了克服了二维连续体形状优化过程中解析敏度求解困难的问题,利用响应面方法将目标函数和约束函数近似显式化,并建立了位移应力约束下的形状优化序列二次规划模型;为了克服响应面方法不够准确的缺点,将响应面方法进行改造,使其在设计点上取精确值;提出了改良的试验设计方法,达到了以较少的结构分析代价构造约束响应面的目的;通过建立二次评价函数,确定了具有自适应能力的运动极限,形成了具有较少计算量和较高逼近精度的优化策略.算例说明这种策略是有效而稳定的.Based on Response Surface Methodology（RSM）, the objective function and constraint conditions are approximately explicit to overcome difficulty of sensitivity analysis, the Sequential Quadratic Programming （SQP） model was formed to find optimal shape under displacement and stress constraints. An improved response surface with exact value on the design point is constructed, which eliminates the intrinsic inaccuracy of response surface. The constraint response surface, combined with improved experiment design method, was constructed through few times structure analysis. A second-order evaluation function was set up for each constraint condition. Rational move limits for each design variable were calculated in terms of the relative errors between constraint response surfaces and evaluation functions. The optimization strategy formed with less computation and higher precision. Examples are given to show the efficiency and stability of this optimization strategy.

关 键 词：形状优化 响应面方法 敏度分析 

分 类 号：TP31[自动化与计算机技术—计算机软件与理论]