Engineering Transactions, 55, 2, pp. 129–153, 2007

Wave Polynomials in Elasticity Problems

Department of Mathematics Faculty of Management and Computer Modelling Kielce University of Technology

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.
Keywords: elasticity, Trefftz method, wave equation, wave polynomials
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