基于节点敏感性分析的无网格法节点布置研究

在应用无网格法进行数值计算时,由于节点的布置对于计算结果的精度有直接影响,因此节点布置方案以及节点性态特点是无网格法中的研究重点。把有限元和形状优化设计中的节点敏感性这一概念应用于无网格法,选择势能密度作为响应变量对无网格法中的节点进行敏感性分析,得到了节点布置方案与节点敏感性系数之间的关系。通过悬臂梁的数值算例,说明了该方法能够有效地指导并改进节点布置方案,使计算精度明显提高。

Study of meshless nodes distribution on the basis of nodal sensitivities analysis

In the meshless numerical calculation,nodes distribution directly affects the precision of meshless method.So nodes distribution and characters of nodes are emphasis and difficulty of meshless method.On the basis of nodal sensitivities in finite element method and shape optimization,the sensitivity analysis was used to study nodal arranging scheme in meshless method.By choosing potential energy density as response quantities,calculating nodal sensitivities modulus,the relation between sensitivity modulus and nodal distribution scheme was gotten.The case was given.The results show that the meshless method can guide and improve the nodal distribution scheme effectively.The precision of the calculation was improved.