基于类桁架材料的Hermite有限元优化方法

Optimization method using Hermite elements based on truss-like material

提出了一种采用高阶单元进行结构拓扑优化的方法。在设计域内优化杆件的C0阶连续分布场以形成类桁架连续体;采用Hermite矩形单元,推导了对应的类桁架材料的刚度矩阵;将结点位置的应变直接作为基本变量,并选择类桁架连续体中的有限杆件,形成了近优化的离散杆系结构;通过弹性模量E=210GPa、允许应力σp=160MPa的悬臂结构、简支结构、多个荷载作用下的悬臂梁等典型数值算例验证了该方法的有效性。结果表明:在有限元自由度和迭代次数相同的条件下,应力约束最大误差由双线性矩形单元的6%减小到0.01%。

A high order finite element method for optimization is presented.The C0-continuous material distribution field in design domain is optimized to form a truss-like continuum.The Hermite rectangular elements are used.The stiffness matrix of truss-like continuum is derived.The strains at nodes are chosen as basic variables in finite element analysis,which avoids finding the derivative of displacement.Then,parts of members,which are formed according to the member distribution field,are chosen to form the nearly optimum discrete structure.Since intermediate densities are not suppressed in the whole procedure,numerical instabilities such as checkerboard and mesh dependencies disappear without any additional technique.Examples are presented to demonstrate the capability of the proposed method.