积分背景网格对自适应EFG法拓扑优化的影响研究  

Study on effects of background integration mesh on topology optimization based on adaptive EFG method

作　　者：伍贤洪[1] 龚曙光[1] 曾兴国[1] 钟勇文[1] 

机构地区：[1]湘潭大学机械工程学院,湘潭411105

出　　处：《计算力学学报》2012年第5期693-698,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50875223);湖南省自然科学基金(09JJ9005)资助项目

摘　　要：采用应力能量范数作为误差指标,探讨了EFG法中积分背景网格对计算精度的影响,得到了合理划分背景网格的建议;建立了以节点密度为设计变量、以最小化柔度为优化目标的拓扑优化模型。采用以节点密度值为加点判据的自适应规则加点方案,开展了连续体结构的拓扑优化研究,该加点方案能有效地减少设计变量的个数,探讨了背景网格对拓扑优化结果的影响。算例结果表明,采用合适的背景网格不仅能进一步减少设计变量的个数,而且能够改善拓扑优化结果的光滑性,使计算效率和精度得到提高。The effect of background integration mesh on calculating accuracy in element-free Galerkin method is discussed by using stress-energy norm as the error indicators. A suitable division of the back- ground mesh is recommended. The topological optimization model is built by selecting nodal density as design variables and flexibility as objective function. While the density value of node is used as the crite- ria of adding node within a region,the scheme of adaptive regular inserting node is created,and continu- ous structural topology optimization is investigated. It can effectively reduce the number of design varia- bles that the program of inserting node is used in the process of topology optimization. The effects of background integration mesh on topology optimization results are discussed. The numerical results obtained show that a suitable background cell can not only further reduce the number of design varia- bles, but also can improve the smoothness of the topology optimization results, and the computational ef- ficiency and accuracy can be improved.

关 键 词：拓扑优化 无网格GALERKIN法 自适应 背景网格 误差估计 

分 类 号：TH123[机械工程—机械设计及理论] O241.82[理学—计算数学]