Abstract
We introduce an asymptotic algorithm that allows us to construct both approximate and exact solutions to a set of equations in the linear elasticity theory. The exact solutions are expressed by polynomials in one of coordinates, while their coefficients include polyharmonic functions that depend on two other coordinates. For the sake of ordering of solutions, one can associate every exact solution with the number of the asymptotic approximation.
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N. G. Ryabenkov and R. F. Faizullina, “The Common Asymptotic Nature of Methods of Solving Problems of the Theory of Elasticity for Plates,” J. Appl. Math. Mech. 70(3), 399–407 (2006).
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Original Russian Text © N.G. Ryabenkov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 7, pp. 45–51.
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Ryabenkov, N.G. Polyharmonic functions in structures of exact solutions in the elasticity theory. Russ Math. 57, 39–44 (2013). https://doi.org/10.3103/S1066369X13070049
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DOI: https://doi.org/10.3103/S1066369X13070049