An Eigenfunction Expansion Method in the Stress Concentration Analysis

Abstract

This paper deals with the traditional stress concentration problems based on the eigenfunction expansion approach. Due to the completeness property of the eigenfunction space obtained by the previous researches, the solution of an arbitrary problem can be expressed by their linear combination. Thus the original problem is transformed into finding the combination of these eigenfuctions satisfying boundary conditions. By applying adjoint symplectic relationships of the ortho-normalization, the combination can be obtained numerically. Numerical results in tensional problems show that stress concentration appears when one of the ends of the solid is clamped. The concentration is seriously confined near the boundary of the fixed, and decrease rapidly with the distance of the boundarys.