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Explicit solutions of boundary value problems of elasticity for circle with a double-voids structure

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Abstract

The present paper is devoted to the explicit solutions of the equilibrium boundary value problems (BVPs) for an elastic circle and for full plane with circular hole with a double-voids structure. The regular solution of the system of equations for an isotropic material with a double-voids structure is constructed by means of the elementary (harmonic, bi-harmonic and meta-harmonic) functions. The Dirichlet-type BVPs for a circle and for a plane with a circular hole are solved explicitly. The obtained solutions are presented as absolutely and uniformly convergent series.

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Authors and Affiliations

  1. I. Vekua Institute of Applied Mathematics of Iv. Javakhishvili, Tbilisi State University, 2 University St., 0186, Tbilisi, Georgia

    Lamara Bitsadze

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  1. Lamara Bitsadze
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Correspondence to Lamara Bitsadze.

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Appendix

Appendix

From the point of view of applications, it is interesting to investigate and construct explicit solutions of boundary value problems of elasticity theory for concrete domains (circle, plane with circular hole, sphere, half-space half-plane, ellipse, etc.). In practice, such BVPs are quite common in many areas of science. The motivations to undertake the present problem are to find applications in the treatment of the mechanics of granular materials and manufactured porous bodies. For a circle (half-plane with a circular hole), numerical example can be immediately obtained since the considered BVP has one regular solution in the form as absolutely and uniformly convergent series, useful for the engineering practice.

The potential users of the obtained results will be the scientists and engineers working on the problems of solid mechanics, micro- and nanomechanics, mechanics of materials, engineering mechanics, engineering medicine, biomechanics, engineering geology, geomechanics, hydro-engineering, applied and computing mechanics.

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Bitsadze, L. Explicit solutions of boundary value problems of elasticity for circle with a double-voids structure. J Braz. Soc. Mech. Sci. Eng. 41, 383 (2019). https://doi.org/10.1007/s40430-019-1888-3

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