关键词: 下限法, 有限单元法, 非线性规划, 可行弧内点算法, Wolfe非精确搜索技术

Abstract: Lower bound finite element method converts the mathematical variation problem of lower bound theorem into an mathematical programming one, which can overcome the difficulty of artificially constructing a statically admissible stress field; thus, it has a broad prospect in engineering practice. The lower bound programming model arising from finite element discretization of stress field contains a large number of optimization variables and constraints; therefore, it is hard to be solved by traditional optimization methods. By analyzing characteristics of the nonlinear lower bound programming model, feasible arc technique and Wolfe’s inaccurate search technique are introduced to enhance the optimization efficiency of this model. Example analysis shows that, based on feasible arc technique and Wolfe’s inaccurate search technique, the convergent speed and step-length searching efficiency of optimization procedure of lower bound finite element method are evidently improved; and numerical stability and good accuracy are acquired. As a result, the new method is more adaptable to engineering practice.

Key words: lower bound method, finite element method, nonlinear programming, feasible arc interior point algorithm, Wolfe’s inaccurate search technique.