基于虚拟材料的T-B梁拓扑优化ESO方法

Study of ESO on Tie-beam problem using virtual material

自从Zhou和Rozvany于2001年以T-B梁(Tie-Beam)问题质疑渐进结构优化方法ESO(Evolutionary Structural Optimization)的算法收敛性以来,结构最优化领域的研究者提出了多种算法以求解决这一问题。T-B梁问题仍是当前结构拓扑优化领域的研究热点,因为现有的各种T-B梁解法或是存有不足或是无法获得满意解答。本文在传统ESO算法中,将虚拟材料引入待删除单元,用以检测结构传力路径是否受到破坏,进而确定单元删除的合理性。算例表明,本文算法可有效防止ESO方法求解T-B梁问题时的失效并获得最优解,且本文算法只需在ESO迭代中附加一次检测,不改变ESO方法的迭代进程和寻优能力。

Since Zhou and Rozvany introduced Tie-beam problem to highlight the failure of Evolutionary Structural Optimization （ESO） in 2001, a lot of solutions have been proposed to solve this hard nut. The problem is unsolved yet because the current solutions contain some shortcomings or fail to obtain optimization. A virtual material method is proposed in this paper in which a checking operation is inserted into original ESO iterations. By evaluating the strain energy change of the selected element to which a virtual material with low Young＇s modulus is introduced, the failure of the structure＇s internal load path can be checked. Thereafter, the removal or of an element can be decided upon. The numerical examples show that the proposed method can prevent the ESO from failing to solve the Tie-beam problem. The proposed method does not change the evolutionary procedure of original ESO method and its ability to achieve optimization because the method adds a checking operation in iterations only.