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中文摘要：
出现在基于有限元形状优化过程中的网格畸变与扭曲问题，可通过引入无网格方法得到解决。本文首先建立了结构形状优化的数学模型，利用无网格Galerkin（EFG）法对形状优化的设计域进行了离散，采用罚函数法来施加边界条件，借助于直接微分法建立了一种离散型基于无网格Galerkin法的设计灵敏度分析算法，然后用1个具有解析解的实例对其进行了验证，所得结果显示两者是一致的。最后利用对所建立的算法完成了1个工程实例的形状优化设计，并对所得到的优化结果结合工程应用进行了讨论。
英文摘要：
The mesh distortion and twist that appear in shape optimization based on FEM can be eliminated by integrating the meshless element-free Galerkin （EFG） method and the shape optimization technique. The paper, first of all, established the mathematical model for structural shape optimization and discretized the shape optimization design field using the meshless EFG method, on which boundary conditions were imposed using the penalty function method. The discrete design sensitivity analysis algorithm based on the EFG method was established through using direct differential method. Then the paper verified the algorithm using an instance with analytical solution. The verification results are consistent with the algorithm. Finally the algorithm was used to accomplish the shape optimization design of an engineering instance, which was discussed in association with engineering application.
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