Self-similar elastodynamic solutions for the plane wedge

Abstract

Wave propagation in a two-dimensional elastic wedge is fundamental to a large class of problems in elastodynamic theory, however until now analytical solutions to all but certain degenerate cases were unknown. In this thesis a general elastodynamic solution is derived for the wedge in a state of plane strain. Surface tractions are, restricted to uniform normal and shear loads spreading from the wedge vertex at constant velocity. The geometry and loading then allow self-similar solutions of the governing differential equations and boundary conditions in hyperbolic and elliptic domains. Hyperbolic solutions are found in terms of the elliptic solutions by the method of characteristics, while elliptic solutions are reduced using analytic function theory to two independent Fredholm integral equations of the second kind in one dimension. Although numerical solutions are beyond the scope of the investigation, the integral equations are solvable by standard techniques. Such solutions can be used to solve a number of plane elastodynamic problems involving an edge.