基于类桁架连续体的结构拓扑优化方法与应用

以各向异性连续体为基结构,采用类桁架连续体材料模型进行结构拓扑优化。以材料在结点位置的密度和方向作为优化设计变量,使材料在设计域内连续分布。并以此建立材料的弹性矩阵和刚度矩阵。优化过程没有抑制中间密度,这从根本上避免了许多拓扑优化方法普遍存在的单元铰接、棋盘格现象以及单元依赖性等数值不稳定问题。采用满应力准则法,借助有限元结构分析,经过少量迭代,建立优化的材料连续分布场,即类桁架连续体结构。由于首先建立的拓扑优化结构是各向异性连续体,从而得到更大优化空间。然后可以结合工程实际需要将其转化为离散的拓扑优化杆系结构。最后,以1个经典Michell桁架和3种形式的拱桥为数值算例,演示了其结构拓扑优化过程。

Topological Optimization Based on Truss-Like Continuum with Applications

This structural topology optimization approach takes anisotropic continuum as ground structure,and the truss-like continuum as material model.The densities and orientations of material fibers at nodes are chosen as optimization design variables to determine the elastic matrix and stiffness matrix.Since intermediate densities are not suppressed in this procedure,the numerical instabilities,such as one-node connected hinges,checkerboard patterns and mesh-dependencies,can be avoided.Combining the fully stressed optimality criterion with finite element analysis,the material distribution is optimized after several iterations.Then this result was transferred to discrete truss structure for some engineering requirements.The topologies of a classical Michell truss and three kinds of arch bridges are optimized as numerical examples.