A combined scheme of edge-based and node-based smoothed finite element methods for Reissner–Mindlin flat shells

In this paper, a combined scheme of edge-based smoothed finite element method (ES-FEM) and node-based smoothed finite element method (NS-FEM) for triangular Reissner–Mindlin flat shells is developed to improve the accuracy of numerical results. The present method, named edge/node-based S-FEM (ENS-FEM), uses a gradient smoothing technique over smoothing domains based on a combination of ES-FEM and NS-FEM. A discrete shear gap technique is incorporated into ENS-FEM to avoid shear-locking phenomenon in Reissner–Mindlin flat shell elements. For all practical purpose, we propose an average combination (aENS-FEM) of ES-FEM and NS-FEM for shell structural problems. We compare numerical results obtained using aENS-FEM with other existing methods in the literature to show the effectiveness of the present method

A mortar method combined with an augmented Lagrangian approach for treatment of mechanical contact problems

peer reviewedThis work presents a mixed penalty-duality formulation from an augmented Lagrangian approach for treating the contact inequality constraints. The augmented Lagrangian approach allows to regularize the non differentiable contact terms and gives a C1 differentiable saddle-point functional. The relative displacement of two contacting bodies is described in the framework of the Finite Element Method (FEM) using the mortar method, which gives a smooth representation of the contact forces across the bodies interface. To study the robustness and performance of the proposed algorithm, validation numerical examples with finite deformations and large slip motion are presented