Error analysis of fixed grid formulation for boundary based structural optimisation
Error analysis of fixed grid formulation for boundary based structural optimisation
复制标题
基于边界的结构优化的固定网格公式的误差分析
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
G. Mullineux
中科院分区：
文献类型：
--
作者：
Peter D. Dunning;H. Kim;G. Mullineux
固定网格有限元逼近因其在更新刚度矩阵方面的简单性和快速性而成为基于边界的拓扑优化方法中的一种流行方法。然而，由于双材料单元的均匀化，最大误差出现在边界上。这对于基于边界的优化特别重要，因为沿边界的灵敏度分析经常驱动优化。到目前为止，对固定网格误差的研究有限，主要集中在数值例子上。固定网格刚度矩阵近似中的误差被认为是先前研究中观察到的误差的可能来源。通过与经典有限元计算结果的比较，分析了固定网格刚度矩阵近似的误差。分析表明，一般情况下，误差随着面积比的减小而增大，并且与形状有关。用一个简单的例子研究了固定网格近似的整体效应。
The fixed grid finite element approximation has become popular with boundary based topology optimization methods, due to its simplicity and speed in updating stiffness matrices. However, maximum errors occur on the boundary due to the homogenization of bi-material elements. This is of particular significance to boundary based optimization as sensitivity analysis along the boundary often drives the optimization. To date only a limited study of fixed grid errors exists, focusing on numerical examples. Errors in the fixed grid stiffness matrix approximation were identified as a possible source of errors observed in previous studies. This paper analytically investigates the errors in the fixed grid stiffness matrix approximation compared to classic finite element results. The analysis shows that generally errors increase as area ratio decreases and they are shape dependent. A simple example is used to investigate the global effect of the fixed grid approximation.