Evaluation of stress singularity field near vertex on interface of dissimilar material joints based on Akin singular element using three-dimensional order of singularity (Comparison of results in case of tetrahedron and singular elements)

Abstract

This paper presents stress singularity analysis using three-dimensional Akin singular element. In case that Akin singular element is employed, it is necessary to know order of singularity before stress analysis. However, in case of three-dimensional model, it is not easy to obtain order of singularity comparing to 2-dimensional model. Therefore, a finite element eigen analysis is applied to obtain order of singularity in 3-dimensional bonded structure model, and the obtained order of singularity is applied to Akin singular element. This analysis is frequently applied to obtain 3-dimensinal order of singularity. Consequently, it was found that order of singularity obtained by least square approximation is close to that obtained by the finite element eigen analysis comparing to that in case of normal element. Furthermore, it was found that convergence process in conjugate gradient method is almost same between normal and singular elements in case that course mesh is used around singular point. On the other hand, it was found that it takes a lot of iterations in case of use of singular element if fine mesh is employed around singular point.

Keywords

• akin singular element
• stress analysis
• stress singularity
• dissimilar material joints
• order of singularity
• finite element eigen analysis
• conjugate gradient method