Evaluation of Intensity of Singularity for Three-Materials Joints with Power-Logarithmic Singularities using an Enriched Finite Element Method

Abstract

In this study, the enriched finite element method (enriched FEM) is applied to evaluate the intensity of singularity for three-material joints with power-logarithmic singularities. Using this method, the intensity of singularities can be directly evaluated and very refined meshes around the singular point are unnecessary. Analyses for eigenvalue and eigenvector are conducted to calculate the order of stress singularities and the asymptotic displacement fields on the enriched elements. Accuracy of the results for different mesh types (4-node and 8-node elements) and different sizes of the enriched region are compared with the value obtained from extrapolation for stress distribution based on FEM with very fine mesh. Finally, the models with various lengths and thicknesses are investigated to study an influence of geometry on the singular stress field.