基于混合常应力-光滑应变单元的极限分析方法

Limit analysis method based on mixed constant stress-smoothed strain element

极限分析是岩土工程稳定性评价的重要方法之一。传统的有限元极限分析方法,采用低阶三角形单元时需要引入速度间断面并采用特殊网格布局,或者采用高阶三角形单元等措施来克服体积锁定问题和提高数值精度。在光滑有限元法(smoothed finite element method,简称SFEM)的基础上,提出了一种基于新型混合常应力-光滑应变单元的极限分析方法(mixed constant stress-smoothed strain element limit analysis,简称MCSE-LA方法)。在服从关联流动法则和Mohr-Coulomb屈服准则的基础上,MCSE-LA方法最终将数值极限分析转化为以应力和极限荷载乘子为基本未知量的二阶锥规划(second orderconeprogramming,简称SOCP)问题。MCSE-LA方法具有形式简单、优化变量相对较少和无需显式的写出塑性内能耗散函数的优点,并且根据凸锥优化的对偶理论,可以从对偶问题中获得速度场和塑性乘子等信息。此外,还采用基于最大塑性剪应变率的网格自适应加密算法,该算法在塑性区细化网格,显著提高了新数值极限分析方法的计算效率和精度。最后通过边坡稳定分析的结果对比,验证了MCSE-LA方法的计算精度和效率均高于传统的有限元极限分析方法。

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.