On the complete solution of the three-dimensional solid space problems based on a novel curvilinear elasticity representation
Artikel i vetenskaplig tidskrift, 2023

A solution scheme is presented for the three-dimensional elasticity theory in the curvilinear cylindrical coordinate, without introducing any new physically dubious potential function. Exact analytical solutions for the essential 3-D solid full- and half-space problems are developed based on the introduced elasticity approach. The Kelvin's classical problem of concentrated force acting in the interior of an infinite solid space, as well as the Boussinesq's half-space problem of concentrated force normal to the free surface of a semi-infinite 3-D solid are treated. Furthermore, the three-dimensional non-axisymmetric problem of semi-infinite solid space under concentrated tangential force on its surface (the so-called Cerruti's problem) is revisited. It is demonstrated that unlike most of the conventional solutions in the literature for the aforementioned problems, the present approach is capable of obtaining the complete solution without needing to combine with other approaches. Evidently, the completeness issue associated with any new method of potentials is not present for the established direct elasticity approach. At the end, an extension of the approach to a nonhomogeneous elastic media is presented and, as an application, the Boussinesq's problem for a nonhomogeneous half-space is solved analytically. The developed representation may serve as an efficient replacement of the original three-dimensional Navier's elasticity equations for solving different 3-D elastic problems in the future.

Displacement-based representation

Solid space problems

Three-dimensional elasticity

New solution scheme

Författare

Rasoul Atashipour

Chalmers, Arkitektur och samhällsbyggnadsteknik, Konstruktionsteknik

Kettering University

Peter Folkow

Chalmers, Mekanik och maritima vetenskaper, Dynamik

European Journal of Mechanics, A/Solids

0997-7538 (ISSN)

Vol. 97 104860

Ämneskategorier

Beräkningsmatematik

Annan matematik

Matematisk analys

DOI

10.1016/j.euromechsol.2022.104860

Mer information

Senast uppdaterat

2023-01-24