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Explicit solution of one boundary value problem in the full coupled theory of elasticity for solids with double porosity. (English) Zbl 1329.74035

Summary: Our goal was to consider the two-dimensional version of the full coupled linear equilibrium theory of elasticity for materials with double porosity and to construct explicitly the solutions of BVPs, in the form of absolutely and uniformly convergent series that is useful in engineering practice. In this paper, the Neumann-type BVPs of statics for an elastic circle and for a plane with circular hole are considered. The uniqueness theorems of the considered boundary value problems are proved.

MSC:

74B05 Classical linear elasticity
35Q74 PDEs in connection with mechanics of deformable solids
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35C10 Series solutions to PDEs
74G05 Explicit solutions of equilibrium problems in solid mechanics
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