摘要
作为有限元线法(FEMOL)求解非线性问题的系列工作之二,本文将该法应用于形状优化问题,对扭转杆的截面优化这一模型问题作了分析求解。文中首先对双连域截面的扭转问题作了FEMOL推导,然后允许结线的长度改变以描述不同的截面形状,再利用若干变换技巧将形状变量及优化条件引入常微分方程(ODE)体系中,从而将问题转换成标准的非线性ODE问题,并由ODE求解器进行求解。文中算例显示了本法对形状优化问题的求解具有方法简洁、实施方便、效率显著等优点。
As the second paper in this series of nonlinear applications of the finite element method of lines (FEMOL), the present paper applies this method to shape optimization problems by presenting a FEMOL analysis
of the optimization of elastic bars in torsion. Firstly,with the domain boundaries fixed, a set of ordinary differential equations (ODEs) for pure torsion is derived by means of the variational method. Next the changes of nodal lines at end-points on the free boundaries are taken as shape variables
which arc incorporated into the ODE system by using the trivial ODE technique with the supplementary BCs provided by the optimality conditions. As a result, the free boundary problem in ODEs is transformed in to a standard nonlinear ODE problem and solved by standard ODE solvers. Numerical examples are given to show the great convenience, efficiency and accuracy of the present approach.
出处
《工程力学》
EI
CSCD
1993年第2期8-16,共9页
Engineering Mechanics
基金
国家自然科学基金资助项目
关键词
有限元线法
非线性
形状优化
einite element method of lines nohlinearity, shape optimization
