关键词: 数值极限分析, 常应力?光滑应变混合单元, 二阶锥规划, 自适应网格加密

Abstract: Limit analysis approach is one of the classical methods for the stability evaluation of geotechnical infrastructures. Low-order triangular elements with velocity discontinuities and special layout of mesh, or high-order triangular elements are usually used to overcome the volumetric locking problem encountered in the traditional finite-element upper bound limit analysis. However, the accuracy of this method depends heavily on the layout of discontinuities. In this study, a mixed constant stress-smoothed strain element is proposed to discretize the constrained functional of generalized variational principle, and a novel method of mixed constant stress-smoothed strain element limit analysis (MCSE-LA) is established for limit analysis. Following the associated flow rule and Mohr-Coulomb yield criterion, the novel MCSE-LA is finally converted to a second order cone programming (SOCP) that contains only stress variables and limit load multiplier. The MCSE-LA method has a simple representation form, and relatively few optimization variables, and in particular, there is no need for an explicit plastic internal energy dissipation function. Based on the duality of the convex optimization, the optimal velocity field and plastic multiplier can be solved in the dual problem simultaneously. Moreover, an adaptive mesh refinement algorithm is proposed based on the maximum plastic shear strain rate. This algorithm could refine the mesh in the plastic zone and significantly improve the computational efficiency and accuracy of the proposed method. Finally, by a comparative analysis of the slope stability problem, the proposed MCSE-LA method is verified to have higher computational accuracy and efficiency compared with the traditional finite-element limit analysis.

Key words: numerical limit analysis, mixed constant stress-smoothed strain element, second order cone programming, adaptive mesh refinement