A three-dimensional self-similar problem of supersonic wedging of an elastic body (Q1060615)

A method based on the dynamic theory of elasticity is proposed for solving the three-dimensional problem of supersonic wedging a body by a thin arrow-shaped blade. Using appropriate scale transformation and passing to limit (''the microscope principle''), the problem of the thin blade is reduced to that of the mathematical slit. A solution in closed form is obtained in the case of dependence of displacements, or of some differential transform of these, on two self-similar variables. The input problem is reduced by a change of coordinates to the determination of analytic functions of two complex variables which, after some transformations, reduces to the Dirichlet boundary value problem in a single complex variable, which is solvable by conventional methods.