求解桁架结构极值响应的提升投影方法

The lift-and-project methods for the extreme structural response analysis

求解结构的真实极值响应是结构鲁棒优化设计问题的难点,本文提出了求解桁架结构极值响应的新方法。求解结构极值响应的优化模型通常是非凸规划,只有全局最优值才能满足设计要求。然而对于这类非凸规划,求解其全局最优解和最优值是NP困难的问题。在不确定参数为桁架结构的外荷载向量的情况下,本文提出了提升投影方法将原始的非凸规划放松为非线性非光滑的凸规划问题。求解这个凸规划问题的全局最优值就可以得到结构精确极值响应的上界,从而满足了设计要求。数值算例验证了提升投影方法的可行性和高效性。

A new method is proposed for the extreme structural response for truss structures. The key point for the structural robust design and optimization is to calculate the extreme structural response. Mathematically,however, the problem is often a non-convex programming for calculating the extreme structural response, which is NP-hard to obtain the global optimality. A so called ＂Lift-and-Project＂ method is proposed by means of relaxing the original non-convex lower-level problem into a non-linear non-smooth but CONVEX programming, which can be solved globally and efficiently. The design requirements can be fully assured. Numerical examples show the effectiveness of this proposed method.