基于二阶锥规划理论的有限元强度折减法及应用

针对岩土体稳定性问题,常用的方法有极限平衡法和有限元强度折减法等。传统的有限元强度折减法通常需设置很大的最大允许非线性迭代次数(如200或500),计算耗时严重,此外,采用的平衡迭代和应力积分算法可能导致岩土体塑性区计算不够准确,进而影响稳定性分析结果。提出一种二阶锥规划有限元强度折减法,该方法基于Hellinger–Reissner混合变分原理和有限元法,将岩土体弹塑性问题构造成基于有限元框架的二阶锥规划问题,结合强度折减技术来分析岩土体稳定性。将该新方法应用于平面应变岩土体稳定性分析,结果表明:与传统的有限元强度折减法相比,新方法结果可靠,但其计算效率更高,所获得的塑性区更加平滑。

Shear strength reduction finite element method based on second-order cone programming theory and its application

For geotechnical stability problems, the limit equilibrium method (LEM) and shear strength reduction finite element method (SSRFEM) have been commonly used. In the traditional elasto-plastic finite element method, a large maximum allowable number of nonlinear iterations (such as 200 or 500) are often set in the SSRFEM, so that the calculation is generally time-consuming; besides, the equilibrium iteration and stress integration algorithm may probably lead to inaccurate calculation of plastic zone and stability. Based on the Hellinger-Reissner mixed variational principle and finite element method, a new shear strength reduction finite element method is proposed based on the finite element method of second-order cone programming (FEM-SOCP). In the mathematical programming finite element framework, the elasto-plastic finite element problem can be cast into a form of second-order cone programming (SOCP), and when being utilized in conjunction with the strength reduction technique, the resultant approach named SSRFEM-SOCP can be applied to geotechnical stability analysis. When being applied to plane strain problems, it is observed that SSRFEM-SOCP is reliable and efficient, and particularly the plastic zone attained by the SSRFEM-SOCP is generally smoother than that by the conventional SSRFEM method.