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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
The main difficulty in solving the structural ultimate load lies in how to handle the unity of calculation accuracy and calculation efficiency. Based on the high precision of Galerkin boundary element method, the calculation limit of structure is established based on the lower bound theorem of limit analysis. At the same time, the self-balance stress field is constructed by using the stress difference of different iteration steps on the same increment step in the Galerkin boundary element elastic-plastic incremental calculation as the basic vector. The limit analysis of the structure is attributed to the nonlinear programming problem and is directly performed by the complex method Solving, the lower limit multiplier of two-dimensional structure under the proportional load is obtained. The numerical results show that the computational accuracy and computational efficiency of the proposed method are satisfactory