平面膜结构拓扑优化的有无复合体方法

将作者对桁架在应力约束下结构拓扑优化的有无复合体模型发展到平面膜结构在应力、位移约束下结构拓扑优化的建模与求解。同时提出了该模型的有效解法,获得了令人满意的数值结果。本文工作表明独立连续拓扑变量的提出对于结构拓扑优化的研究是有意义的。

THE EXIST-NULL COMBINATION METHOD FOR THE TOPOLOGICAL OPTIMIZATION OF PLANE MEMBRANE STRUCTURE

The exist-null combined model introduced in the reference 5] for the truss structural topological optimization with stress constraints is developed to the topological optimization of plane membrane structure with stress and displacement constraints. According to the idea of independent and continuous topological variables, an exist-null combined model of the membrane element for the topological optimization is constructed to implement the transformation between continuous and discrete topological variables without using the filter function. It is proved that the thickness of membrane, the weight and the stiffness matrix are all the linear combinations of the corresponding quantities of the "exist element" and the "null element". Then this linear relation is extended to the allowable stress. In line with the zero order approximation of the stress constraint function and the first order approximation of the displacement constrains function, a model of the topological optimization with continuous variables is established to minimize the structural weight. The model is transformed to an approximate quadratic programming of the dual programming. Finally, a self-adaptive algorithm gives the transformation of the continuous topological variable to discrete variable according to a doorsill. It can get satisfactory computational results with rapid and stable convergence. Research work shows: 1) The exist-null combined model is satisfactory to be used in the topological optimization of plane membrane structure with stress and displacement constraints; 2) This method has very high efficiency; 3) The displacement constraint can change the topological form of the stress constraint; 4) The proposition of independent and continuous topological variable is successful for the structural topology optimization.