Method of Initial Functions in Two-Dimensional Elastodynamic Problems

Abstract

The method of initial functions is formulated for the two-dimensional elastodynamic problems both in plane stress and plane strain. Knowing the stresses and displacements on a given layer of an elastic body in a plane state, the stresses and displacements at any other layer or point can be obtained by the method developed in this paper. The method is illustrated in the case of a deep beam subjected to time-dependent transverse loads. A particular solution for a straight-crested wave traveling along an infinite beam is obtained. Exact value of the dynamic shear coefficient for the well-known Timoshenko beam equation is derived. This method is also applied to the dynamic analysis of layered beams.