应用类桁架模型的连续体拓扑优化方法

Continuum Topology Optimization Based on Truss-Like Model

为了避免棋盘格、单元铰接等数值不稳定现象,研究了基于类桁架模型的连续体拓扑优化方法.将单元节点处材料密度的大小和方向作为设计变量,采用满应力优化准则对材料密度大小进行优化.为了形成带孔洞的匀质连续体,对设计变量增加了上下限约束,剔除密度低于一定下限的节点,限制节点密度.算例结果表明:不需要进一步处理,就能从类桁架连续体中获得清晰的带孔板.

In order to apply the truss-like model in the topology optimization of continuum and to avoid some numerical instability phenomenon like checkerboard and elements hinge, the topology optimization method of continuum based on truss-like model was investigated. The densities and orientations of material at nodes were taken as design variables. The densities of material were optimized by fully-stressed criteria. In order to form homogenous continuum with holes, the material with densities below the given critical value was removed, densities above upper limit are limited. Numerical ex- amples show that plate with distinct holes can be obtained from the truss-like continua without further process.