On a planar exterior problem in linear elasticity

Ramkissoon, H.

doi:10.1090/qam/793521

Author: H. Ramkissoon
Journal: Quart. Appl. Math. 43 (1985), 135-141
MSC: Primary 73C02
DOI: https://doi.org/10.1090/qam/793521
MathSciNet review: 793521
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note a representation is obtained for the solution of the planar Dirichlet boundary-value problem of linear elasticity. It consists of a double-layer potential and a linear combination of three basic functions whose form is determined by the shape of the boundary. This representation is similar to that obtained for the analogous problem in hydrodynamics.

N. K. Korenev, A certain representation of the solution of a linearized stationary problem for the Navier-Stokes equation in the case of two space variables, Trudy Mat. Inst. Steklov. 116 (1971), 95–100, 235 (Russian). Boundary value problems of mathematical physics, 7. MR 0364908
V. D. Kupradze, Potential methods in the theory of elasticity, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., New York, 1965. Translated from the Russian by H. Gutfreund; Translation edited by I. Meroz. MR 0223128

V. D. Kupradze, Dynamical problems in elasticity, Progr. in Solid Mech., 3 (1963)

D. Ieşan, Existence theorems in the theory of micropolar elasticity, Internat. J. Engrg. Sci. 8 (1970), 777–791 (English, with French, German, Italian and Russian summaries). MR 0270603, DOI https://doi.org/10.1016/0020-7225%2870%2990004-2