Analysis for The Order of Stress Singularity, Displacement and Stress Fields at A Vertex of Three-Dimensional Joints in Electric Devices.

Abstract

We have been so far analyzed several three-dimensional joints using BEM and FEM. However, many unsolved problems in three-dimensional joints exist untill now. In this study, on the basis of FEM using an interpolation function considering a stress singularity field near the vertex of three-dimensional joints, an eigen equation was derived for determining the order of stress singularity. Four typical models of joints are analyzed in our calculations. Model 1 is a typical joint of three-dimensional joints which is composed of two blocks with different properties. Model 2 is a joint which a 1/8 elastic material bonds to a 1/4 elastic material so that a free surface in the 1/8 material coincides with a free surface in the 1/8 elastic material. Model 3 and model 4 are joints which a block of material 1 is embedded into material 2. In model 4, an interface in three interfaces for material 1 surrounding a vertex disbonds from material 2. An accuracy of calculation is examined by varying the mesh size and the number of gaussian integration points in model 1. Contour map of the order of stress singularity is mapped on Dundurs' parameter plane in model 2, model 3 and model 4. The distributions of displacement and stress near a vertex were precisely investigated determining the eigen vector of the eigen equation in model 3 and model 4. The characteristics of displacement and stress can be expressed by a sum of series of the product of the λth power of distance from the vertex and the distribution functions of intensity.