Wave Polynomials in Elasticity Problems

The paper demonstrates a new technique of obtaining the approximate solution of the two- and three-dimensional elasticity problems. The system of equations of elasticity can be converted to the system of wave equation. In this case, as solving functions (Trefftz functions), the so-called wave polynomials can be used. The presented method is useful for a finite body of a certain shape. Then the obtained solutions are coupled through initial and boundary conditions. Recurrent formulas for the two- and three-dimensional wave polynomials and their derivatives are obtained. The methodology for solution of systems of partial differential equations with common initial and boundary conditions by means of solving functions is presented. The advantage of using the method of solving functions is that the solution exactly satisfies the given equation (or system of equations). Some examples are included.