基于响应面方法的桁架截面敏度分析和优化

把响应面方法引入桁架截面优化中,将应力和位移约束近似表达为桁架截面倒变量的线性函数。为拟合响应面,基于中心复合和单纯形试验设计方法开发了中心对称和拟单纯形试验设计两种方法,既可保证约束近似精度,又降低了结构分析计算量。对于桁架结构重量目标函数,直接推出倒变量的二阶形式,以桁架重量最小为目标的优化问题构造为标准的二次规划模型。将响应面方法计算的位移对设计变量的敏度与莫尔积分方法的近似显式进行了对比。以MSC.Patran为平台的数值算例表明:结合响应面方法,应用序列二次规划对问题进行寻优,其收敛精度及稳定性都可获得保障。

Sensitivity Analysis and Cross Sectional Optimization of Truss Structure Using Response Surface Methodology

Response surface methodology was introduced into the cross sectional optimization of truss,in which the stress and displacement constraints were expressed as linear functions dependent on the reciprocals of cross sections.For fitting response surfaces,the central symmetric design and quasi-simplex design were developed based on the central composite design and simplex design,respectively.Both methods can achieve good accuracy and cut down computational effort simultaneously.The objective function of minimizing truss mass was expressed in two order form,the optimal problem was formulated as a standard quadratic programming model.The sensitivity of displacement with respect to design variables was compared to the approximate explicit form given by Mohr integration.The numerical example based on MSC.Patran illustrates the effectiveness and efficiency of integrating RSM into the sequential quadratic programming.