【作者】 张利；

【导师】 郭旭；

【作者基本信息】 大连理工大学 ， 工程力学， 2013， 硕士

【摘要】 传统的的拓扑优化问题通常在确定性的结构框架下提出,并假定问题的结构边界几何形状是确定的。然而由于信息不全、测量误差和制造误差等因素的存在,边界不确定性在实际工程制造中是不可避免的。而且众所周知,优化问题的解对边界摄动极为敏感,这可能导致制造出来的实际结构的性能与最优设计结果差距很大或者不能满足工程设计要求。因此,将边界不确定性的影响考虑到结构拓扑优化中是非常重要。在本文中,我们基于水平集方法提出了一种考虑边界不确定性的结构拓扑优化方法。首先,为了降低最优设计对边界摄动的敏感性,我们选取承受最不利摄动后的结构响应作为目标函数从而保证最优设计解的鲁棒性。其次,通过运用Schwarz不等式,将原来复杂的双层优化问题转化为易于计算求解的单层优化问题。从而将原来的优化问题转化为一个最不利设计问题。最后,用大量数值算例证明本文算法的有效性。更多还原

【Abstract】 Traditionally, topology optimizations are often carried out in a deterministic framework, where it is assumed that the boundary involved in the problem can be determined exactly. However, boundary uncertainties are unavoidable in real-world applications due to incomplete information, observation errors and manufacturing imperfections, etc. Furthermore, it is also well known that solutions to optimization problems may exhibit remarkable sensitivity to boundary perturbations. This may lead to the performance of the actual structure far from optimal or cannot meet the design requirements. Therefore it is of great importance to take the effect of boundary uncertainty into consideration for optimal topology designs of structures.In the present paper, we proposed a approach for structural topology optimization considering the uncertainty of boundary variations via level set approach. First, in order to make the optimal design less sensitive to the possible boundary variations, we choose the response of structure enduring the worst case perturbation as the objective function for ensuring the robustness of the optimal solution. Second, with use of the Schwarz inequality, the original Bi-level optimization problem is transformed to a single-level optimization problem, which can be solved efficiently. Then the corresponding optimization problem formulated as a worst case design problem. Last, numerical examples demonstrate the effectiveness of the proposed approach.更多还原