积分背景网格对自适应EFG法拓扑优化的影响研究

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日标的拓扑优化模型。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。

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

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 background 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 criteria of adding node within a region,the scheme of adaptive regular inserting node is created,and continuous structural topology optimization is investigated.It can effectively reduce the number of design variables 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 variables,but also can improve the smoothness of the topology optimization results,and the computational efficiency and accuracy can be improved.