摘要
对响应面方法中两个最为关键的概念———近似函数及试验设计做了简单描述,选择线性函数作为约束条件的近似函数形式,并对位移和应力约束作不同处理,位移约束不含常数项,而应力约束含常数项。提出了一种适合建立一阶形式响应面并使结构分析次数最少的试验设计方法———中心扩展法。求解响应面时在最小二乘法的基础之上作了改进,提出中心点精确响应面法,使拟合的响应面中心点处的响应值精确等于有限元分析值。最后通过数值算例说明改进后的响应面法对于板壳结构优化的可行性和优越性。
A simple description was made on two of the most key concepts, approximation .function and experimental design, in the response surface method. Choosing linear function as the approximate function form of the constraint condition and different treatments were made on displacement and stress. Displacement constraint doesn＇t include constant item but stress constraint does. A kind of experimental design method, central expansion method, that suits to establish the first order formed response surface and let the number of structure analysis to be the least has been put forward. An improvement was made based on the least squire method while making the solution on response surface. The precise response surface method for central point was put forward to let the response value＇ at the place of central point of response surface being matched to be precisely an equivalent of analytical value of finite element. Finally by means of a numerical computation example explained the feasibility and superiority on the optimization of plate-shell structure made by the response surface method after improvement.
出处
《机械设计》
CSCD
北大核心
2005年第11期10-13,共4页
Journal of Machine Design
基金
国家自然科学基金资助项目(10072005)
北京市自然科学基金资助项目(3042002)
北京市教委资助项目(KM200410005019)
关键词
响应面法
结构优化
近似函数
数值实验
板壳结构
response surface method
structural optimization, approximation function, numerical text
plate-shell structure
