二阶锥规划在岩土下限分析中的应用

Application of Second-order Cone Programming in Lower Limit Analysis of Geomechanics

在边坡稳定性分析的下限原理有限元中,一般采用三节点三角形单元来进行网格划分,而且同时要对Mohr-Coulomb屈服准则进行线性化,但是线性逼近会引起一定的误差从而导致其计算精度偏低。针对此类问题,依据下限定理,在满足平衡方程、边界条件、应力间断和屈服条件的基础上,将下限问题的数学模型转化为二阶锥规划(Second-order cone program(SCOP))问题,从而可采用二阶锥规划对该问题进行求解,这样既提高了求解效率,又提高了求解精度。算例分析验证了二阶锥规划方法较线性化方法在精度和效率方面都有很大的优势。

In the finite element of the stability analysis of the slope, three-node triangular elements are used, and the Mohr-Coulomb yield criterion is linearized to formulate the linear programming, which leads to some errors caused by the linear approximation. According to the lower bound theorem, the mathemati cal model of the lower limit theorem is transformed into a second-order cone programming problem satisfy ing the equilibrium equation, boundary condition, stress discontinuity and yield condition, and then the Second-order cone programming（SCOP） is used to solve the problem. SCOP not only improves the effi- ciency of the solution, but also improves the accuracy of the solution. The numerical examples show that the proposed SCOP method has a great advantage in terms of precision and efficiency over linear program-