关键词: 极限分析上限法, 泰勒展开, 刚体有限元上限法, 等面积多边形

Abstract: The upper bound limit analysis method has a more rigorous theoretical basis and clearer physics meaning compared to the limit equilibrium method. Based on the series expansion, the velocity field of a triangle element is expanded through center point velocity and its velocity gradients. Hence the upper bound FEM method based on the center point velocity and its velocity gradients are introduced as unknowns. The method not only enriches the upper bound limit analysis method, but also has a simpler flow equation. The proposed method can be considered as the multidimensional extension of rigid FE upper bound limit method, and has a more rigorous theoretical basis than rigid FE upper bound limit method. The requirement that all the point must strictly meet the limit properties is relaxed and the equal-area polygon is adopted to approximate the yield circle. Two case studies show that this method can steadily converge into the true solution, and has the same convergence as the traditional method by Sloan; when equal-area polygon is taken, the method yields a good result by less number of polygon edges, with significantly improved convergence.

Key words: upper bound limit analysis method, Taylor expansion, rigid finite elements upper bound limit analysis, equal-area polygon