基于自适应有限元和B样条曲线的结构优化算法

Evolutionary Structural Shape Optimization Based on Adaptive FEM and Boundary Representation of B-spline

基于渐进结构优化算法(ESO)是结合单元误差估计和自适应有限元的结构形状优化算法.采用B样条曲线描述设计域的边界形状,B样条曲线由作为设计变量的主节点来控制,设计边界的最优形状通过根据节点的应力水平逐步移动和更新主节点的位置来实现.采用应力恢复和自适应FEM的方法解决FEM边界节点应力计算精度低的问题,提出一种边界主节点更新算法,将本算法的精度和效率与解析解进行了对比和讨论.

A structural shape optimization algorithm based on the evolutionary structural optimization（ESO） method in conjunction with element error estimate and adaptive FEM is presented.B-splines are used to describe the boundary of the design domain;the shape of these B-splines is governed by a set of master nodes which can be taken as the design variables.The optimal shape of the design boundary with constant stress is achieved iteratively by the movement and update of the position of the master nodes based on nodal stress leveling.The result quality,in terms of accuracy and efficiency,is tested and discussed with an analytical solution.