基于导重法的自重载荷下悬臂梁结构拓扑优化

针对自重载荷悬臂梁结构拓扑优化末端区域材料分布不收敛的问题，提出了一种拓扑优化方法。根据虚功相等原理，利用四节点矩形单元的形函数、单元体积密度和质量的关系建立了载荷等效方法。根据优化模型的Kuhn-Tucker条件推导出了导重准则，以及目标函数的灵敏度公式和考虑自重载荷拓扑优化的迭代算法。针对自重载荷作用下悬臂梁结构拓扑优化存在的末端区域材料分布模糊问题，研究了变密度法和非结构质量相结合的求解策略，揭示了典型因素对拓扑结构的影响规律。结果表明:所提方法能够解决自重载荷下悬臂梁末端区域材料分布模糊问题。 

Topology opti mization of cantilever structure with self-weight load based on guide-weight method

Aiming at the problem of non-convergence of the material distribution at the end of the cantilever beam structure under self-weight load, a topology optimization method for the cantilever beam structure under self-weight load is proposed to solve the problem. According to the principle of virtual work equal, the load equivalent method was established by the relationship among the shape function of the four-node rectangular element, the unit volume density and the mass. According to the Kuhn-Tucker condition of the optimization model, the guide-weight criterion was derived, the sensitivity formula of the objective function was obtained, and the iterative formula considering the topology optimization of the self-weight load was derived. Aimed at the problem of ambiguity of material distribution in the end region of the topological optimization of a cantilever beam structure under self-weight load, a solution strategy combining variable density method and non-structural mass was studied, and the influence of typical factors on the topological structure was revealed. The results show that this method can solve the problem of fuzzy material distribution at the end of a cantilever beam under self-weight.