结构拓扑优化的一些基本概念和研究方法1)

介绍了结构拓扑优化研究领域的一些基本概念和主要问题。分析了拓扑优化结构的类桁架性质以及离散化性质,给出了几个作为标准 算例的典型解析解答。简述了各种结构拓扑优化数值方法的优化策略和特点。解释了连续体结构拓扑优化数值方法中普遍存在的单元依 赖性、奇异性、棋盘格等数值计算不稳定问题现象。介绍了准则法、序列规划方法和启发式算法等各种数学优化求解方法的基本原理。使 初学者初步建立结构拓扑优化相关基本概念。

SOME FUNDAMENTAL CONCEPTS AND RESEARCH METHOD OF STRUCTURAL TOPOLOGY OPTIMIZATION

Some fundamental concepts and problems in the research field of the structural topology optimization are introduced briefly. The essential characteristics of the truss-like and its discretization are analyzed. The classical analytical solutions as the benchmarks are listed in the references. The optimization strategies and the characteristics of various numerical methods for the structural topology optimization are reviewed. The numerical instabilities, such as the mesh-dependencies, the singular optima, the checkerboards and the local constraints, commonly in the structural topology optimization, are explained. The fundamental principles of the optimality criteria, the sequential programming and the heuristic methods are discussed.