基于节点密度的自适应EFG法拓扑优化方法研究

针对无网格法拓扑优化中设计变量庞大、计算效率低的问题，提出了基于节点密度的自适应EFG拓扑优化方法。该方法以节点相对密度为设计变量，建立了以结构柔度最小为优化目标的自适应EFG拓扑优化模型，给出了拓扑优化中自适应节点加密准则、节点加密方法和新增节点设计变量更新规则。算例结果表明，采用本文提出的自适应EFG拓扑优化方法进行结构拓扑优化时，可以减少结构分析和优化的设计变量数目，提高优化效率。

STUDY ON TOPOLOGY OPTIMIZATION METHOD OF ADAPTIVE EFG METHOD BASED ON NODAL DENSITY

This study proposed a topology optimization method of adaptive EFG method based on the node density, in response to the problems of huge number of variables and low efficiency in the topology optimization of the meshless method. The adaptive EFG topology optimization model was established with minimizing the compliance of the structure from using nodal density for design variables in the topology optimization. The adaptive node refinement criteria, the node refinement scheme and the added nodes variables updating rule were detailedly described. Numerical examples prove that the proposed method can extremity reduce the number of the design variables, and improve the efficiency of optimization.