埃特金算法在改进虚功准则法中的应用  

Application of Aitken Algorithm to Improved Virtual Work Criteria

作　　者：徐赐军[1] 韩幸[1] 

机构地区：[1]湖北理工学院机电工程学院,湖北黄石435003

出　　处：《机械设计与制造》2014年第12期255-257,共3页Machinery Design & Manufacture

基　　金：湖北省"机械工程"重点学科;湖北省教育厅科学技术研究计划指导性项目(B20123007);黄石理工学院优秀中青年创新团队计划

摘　　要：针对结构优化设计过程中考虑结构自重和惯性载荷的改进虚功准则方程组,提出高自动化的改进埃特金算法求解策略。通过传统虚功准则方程组的缺陷分析,提出该方程组改进措施,并分析改进埃特金迭代算法在求解结构优化问题中的优势。根据改进虚功准则方程组多元非线性特点,分析改进埃特金迭代算法对其求解的合理性,并证明该算法的加速性及其收敛阶,提出改进虚功准则方程组的埃特金求解方法。通过桁架结构优化算例验证了改进埃特金算法的优越性。A highly automatic solution based on ameliorated Aitken algorithm is presented to solve virtual work criteria equations which include some factors such as dead weight and inertial load of optimized structure. The limitations of traditional virtual work criteria equations are studied and their improvement methods are developed. Then the advantages of ameliorated Aitken algorithm are analyzed, which are applied to solve some problem of structure optimization. According to multivariate nonlinear characteristics of improved criteria equations, an ameliorated A itken algorithm is proved to be suit for solving the equations. Accelerated characteristics and convergence order of the iterative algorithm are studied, and an iterative method based on Aitken algorithm is proposed for solving the equations. The merits of ameliorated Aitken algorithm are demonstrated by an illustrative example showing a structure optimization of five-bar truss.

关 键 词：虚功准则法 结构优化 埃特金算法 收敛阶 

分 类 号：TH16[机械工程—机械制造及自动化]