结构极限分析的Galerkin边界元方法

求解结构极限载荷的主要困难在于如何处理好计算精度和计算效率的统一。利用 Galerkin边界元方法的应力精度高的优势 ,基于极限分析的下限定理建立了结构极限分析的计算格式。同时利用 Galerkin边界元弹塑性增量计算中同一增量步上不同迭代步的应力差作为基矢量构造了自平衡应力场 ,将结构极限分析归结为非线性规划问题 ,并通过复合形法直接进行求解 ,得到了二维结构在比例载荷作用下的下限乘子。数值计算结果表明 ,该文所用方法的计算精度和计算效率都是令人满意的

Limit analysis of structures using the symmetric Galerkin boundary element method

The computational formulation of the lower bound limit analysis was established using the symmetric Galerkin boundary element method based on Melan's theory. The self equilibrium stress field was constructed by a linear combination of several basic vectors that were the stress differences between different iteration steps at the same incremental step using the traditional elastoplastic incremental method. The limit analysis problem was then expressed by nonlinear programming according to Melan's theory. The lower bound load multipler of two dimensional structures with proportional loads was obtained using the complex method to directly solve the nonlinear programming. Computational examples show the efficiency and precision of the present method.