一种改进的结构拓扑优化水平集方法

AN IMPROVED LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION

针对有限的结构设计区域,界面力的大小和作用的位置以及部分给定位移的结构边界始终保持不变的要求,为了解决基于水平集方法的结构边界演化停滞等问题,导出了基于水平集演化的结构拓扑优化所需的法向速度场．研究了由该法向速度场导出的序列解的收敛特性,并建立了一套新的结构柔顺度为目标函数,体积为约束条件的水平集演化算法,给出的算例验证了该方法的正确性和有效性．

In practice, a continuum structure is usually designed with tractions applied to a part of its boundary and prescribed displacements imposed on other part of the boundary. The design domains of practical structures are often limited and significantly affect the final optimal design of the structures. Structural boundaries under tractions and prescribed displacements should be treated as a subset of zero level set in the level set methods. However, structural optimization methods based on level set movements do not consider these realistic requirements. To overcome the limitations of current level set methods and the stopping issue of structural boundary movements, this paper constructs new normal speeds required by level set movements. And the convergence characteristics of structural topology optimization series solutions obtained by the proposed normal speeds are studied. Then, we implement the algorithm of the objective function for a problem with the strain energy as the objective function and with material volume as a constraint by use of several robust and efficient numerical techniques of level set methods. The benefits and advantages of the proposed method are illustrated through two 2D examples.