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中文摘要：
建立了结构形状优化的数学模型，根据无网格法的离散策略定义了节点位移的设计速度域；引入Lagrange乘子法和罚函数来施加边界条件，借助直接微分法，分别建立了一种离散型的基于无网格Galerkin法的设计灵敏度分析算法；将建立的优化算法结合曲线描述方式对两个工程应用实例进行了形状优化研究，并与基于有限元优化的结果进行了比较，所得结果能够满足工程实际的需求。
英文摘要：
The mathematics model of shape optimization was presented firstly, and the design velocity field of nodes was built on the basis of the discrete strategy of meshless method. A numerical method for discrete design sensitivity analysis using the meshless Galerkin method was proposed by means of direct differential method, and the essential boundary conditions were imposed by Lagrange multiplier method and penalty function. Finally, the shape optimizations of two examples are finished by combination of the presented optimal algorithm and description of the boundary shape of structure with a known curve function, and optimal results are compared with ones based on finite element method. The results obtained can meet the demands of engineering applications.
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