An implicit stabilized node-based smoothed finite element method for ultimate bearing capacity analysis of strip footing

Abstract

The node-based smoothed finite element method (NS-FEM) has gained significant attention over the past decade. Nodal integration in NS-FEM, however, may lead to spurious oscillation of deformations of soil mass. To address the spurious oscillation of deformations associated with nodal integration, some stabilization techniques have been developed, but most of the stabilized NS-FEM have been implemented in the explicit finite element framework. The implicit framework, nonetheless, may offer some advantages including the high efficiency, good numerical accuracy, and suitability for handling large load increments and static problems. In this study, a novel stabilized NS-FEM by referring to the Taylor series expansion and incorporating the secant shear modulus, named sNS-FEM-KF(Gs), is developed in the implicit finite element framework. Based on the ultimate bearing capacity analysis of some strip footings, it is found that sNS-FEM-KF(Gs) may effectively eliminate the spurious oscillations observed in NS-FEM, and may resolve the overly-stiff behaviors of soil mass predicted by sNS-FEM-KF which is a reduced version of sNS-FEM-KF(Gs). Even compared to the standard finite element method with the 6-node triangular (T6) elements (i.e. FEM(T6)), sNS-FEM-KF(Gs) with linear 3-node triangular (T3) elements may outperform FEM(T6) in the investigated strip footing problems, indicating its good applicability in geotechnical analysis.