Abstract
Some new theorems are established for the determination of exact solutions of the two-dimensional singular integral equations, used in the theory of elasticity, plasticity and thermoelasticity. The method is based on some inversion formulas for the single integrals, in which the two-dimensional singular integral equations are analyzed. The exact solutions which are given, are based on three different cases by using some arbitrary polynomials. Finally, the proposed method completes the solution of the two-dimensional singular integral equations, which in the past were solved only by numerical methods, like the Boundary Element Method (BEM) and the Singular Integral Operators Method (SIOM).
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