一种椭球凸集参数域结构的高效减基优化方法  

An Efficient Reduced Basis Optimization Method for Structures with Ellipsoidal Convex Parameter Domains

作　　者：张正[1] 毕仁贵[1] 严灿[1] ZHANG Zheng;BI Rengui;YAN Can(College of Physics and Mechanical & Electrical Engineering,Jishou University,Jishou,Hunan,416000)

机构地区：[1]吉首大学物理与机电工程学院

出　　处：《中国机械工程》2019年第17期2039-2043,共5页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(11402096,11662004);吉首大学校级科研项目(jsdxrcyjkyxm201209)

摘　　要：基于减基法提出了一种针对椭球凸集参数域结构的高效优化方法。将椭球凸集参数域作变基处理并找到将其包裹的矩形凸集边界,进而形成标准的矩形凸集参数域以及低维减基空间。在结构的椭球凸集参数域上进行减基列式的快速模拟和计算,并用减基方程代替结构优化模型中的有限元方程,进而将结构的优化模型转变成结构的减基优化模型。研究结果表明:由于将常规的优化模型进行了实质上的减缩和变换,故在不改变通用优化算法的条件下,所提方法能够获得较高的求解效率。结构算例分析验证了所提方法的工程有效性。An efficient optimization method for the structures with ellipsoidal convex parameter domain structures was presented based on the reduced basis method. The ellipsoidal convex parameter domains were processed by changing basis and the rectangular convex boundaries were found for packaging the processed ellipsoidal convex parameter domains, by which the standard rectangular parameter domains and the reduced basis spaces of low dimension were formed. The fast simulation and calculation were conducted on the ellipsoidal convex parameter domains, and the reduced basis equation was used to replace the finite element equation in the structure optimization model, which would change the structure optimization model into an optimization model with reduced basis. The research results show that due to the actual reductions and transformations of the conventional optimization model, the proposed method may obtain higher solution efficiency without changing the general optimization algorithm. The analysis of the structure example herein verifies the engineering effectiveness of the proposed method.

关 键 词：减基法 工程结构 凸集参数域 优化方法 求解效率 

分 类 号：TB121[理学—工程力学] O302[理学—力学]