关键词: 极限分析, 上限有限元, 线性规划, 二阶锥, 线性化, 摩尔-库仑屈服准则

Abstract: For solving stability problems of soil-mass under plane strain condition, finite element upper bound solution based on linear programming needs to linearize second-order cone constraint, forming by Mohr-Coulomb (M-C) yield criterion. The commonly used method is to replace the circular region projected from cone by external polygon. In order to improve accuracy of linearization, the direct way is to increase external polygon edges. This will result in the decision variables of linear programming model containing a large number of plastic multiplier variables, and leading to increase difficulties or even infeasible of calculating process. In order to solve the problem, a second-order cone linearizing method proposed by Ben-Tal and Nemirovsky is introduced and has been embedded into the coded finite element upper bound program. It is found that the results obtained by Ben-Tal method and results obtained from external linear polygon method are confirming each other after case study. Moreover, Ben-Tal method can improve the accuracy of linearization of M-C yield criterion effectively by appropriately increasing the number of decision variables and equality constraints. Simultaneously, it has proved that the formation of linear programming is small-scale. It is expected to be applied commonly to finite element upper bound solution based on linear programming model.

Key words: limit analysis, finite element upper bound solution, linear programming, second-order cone, linearization, Mohr- Coulomb yield criterion