A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme

Abstract

This paper presents a novel and efficient solution procedure to improve 3D solid finite element analysis with an enrichment scheme. To this end, we employ finite elements enriched by polynomial cover functions, which can expand their solution space without requiring mesh refinement or additional nodes. To facilitate this solution procedure, an error estimation method and cover function selection scheme for 3D solid finite element analysis are developed. This enables the identification of nodes with suboptimal solution accuracy, allowing for the adaptive application of cover functions in a systematic and efficient manner. Furthermore, a significant advantage of this procedure is its consistency, achieved by excluding arbitrary coefficients from the formulations employed. The effectiveness of the proposed procedure is demonstrated through several numerical examples. In the majority of the examples, it is observed that the stress prediction error is reduced by more than half after applying the proposed procedure.