基于离散变量的双层网壳结构拓扑优化设计

Topological optimum design of double-decker dpatial lattice shell based on discrete variables

以工程造价为目标函数 ,建立了包含截面、节点体积和拓扑三类变量的离散变量双层网壳结构拓扑优化数学模型 ,该模型考虑了截面变量与拓扑变量间的耦合关系 ,反映了拓扑优化问题的组合优化本质。同时采用相对差商法及有限元设计软件ALGOR对基于离散变量的双层空间网壳结构进行拓扑优化 ,并通过算例验证该优化方法的可行性和有效性。

Utilizing the overall cost as the objective function, the discrete topological optimum mathematical model of double-decker spatial lattice shell is founded, including three variables, namely size variables of cross sections, volume variables of nodes and topology variables. This model takes into account the coupling relation between size variables of cross sections and topology variables, which reveals the combinatorial optimum nature of the problem of topology optimization. At the same time,adopting the relative difference quotient method and the finite element analysis software-Algor, the double-decker spatial lattice shell based on discrete variables is topologically optimized. Finally,a numerical example is used to test the feasibility and validity of topology optimization method.