The enriched 2D solid finite elements in geometric nonlinear analysis

Abstract

The primary strength of the enriched finite element method (enriched FEM) is its ability to enhance solution accuracy without mesh refinement. It also allows for the selective determination of cover function degrees based on desired accuracy. Furthermore, there is an adaptive enrichment strategy that applies enriched elements to targeted areas where accuracy may be lacking rather than across the entire domain, demonstrating its powerful use in engineering applications. However, its application to solid and structural problems encounters a linear dependence (LD) issue induced by using polynomial functions as cover functions. Recently, enriched finite elements that address the LD problem in linear analysis have been developed. In light of these advancements, this study is devoted to a robust extension of the enriched FEM to nonlinear analysis. We propose a nonlinear formulation of the enriched FEM, employing 3-node and 4-node 2D solid elements for demonstration. The formulation employs a total Lagrangian approach, allowing for large displacements and rotations. Numerical examples demonstrate that the enriched elements effectively improve solution accuracy and ensure stable convergence in nonlinear analysis. We also present results from adaptive enrichment to highlight its effectiveness.