Issue 48

A. Fesenko et alii, Frattura ed Integrità Strutturale, 48 (2019) 768-792; DOI: 10.3221/IGF-ESIS.48.70 768 An uncoupled thermoelasticity problem for a semi-infinite layer with regard to its proper weight A. Fesenko, N. Vaysfel’d Faculty of Mathematics, Physics and Information Technologies, Odessa I. I. Mechnikov National University, Ukraine 81anna81@gmail.com, vaysfeld@onu.edu.ua A BSTRACT . The exact solution of the uncoupled thermoelasticity problem for a semi-infinite elastic layer with regard to its proper weight was constructed. The originality of the proposed paper is based on reducing Lame equations to two jointly and one separately, solvable equations. It allows the application of integral transformations directly to the transformed equations of equilibrium and makes it possible to reduce the initial problem to a one-dimensional vector boundary problem. A special technique is given to calculate multiple integrals containing oscillating functions that appear during the inversion of the transforms. The character of the temperature and proper weight influence on the value of normal stress on the lateral face of the semi-infinite layer, the zone of tensile stress depending on the shapes of the distributed load section and the temperature and Poisson's ratio is established. The parameters of dimensionless mechanical load and temperature, when the separation of the side wall of the semi-infinite layer can be eliminated, were established. A study of the influence of the layer’s proper weight on the stress emerging on the layer’s edge is conducted. The constructed exact solution can be used as a model for solving a similar class of problems by numerical methods. K EYWORDS . Uncoupled Thermoelasticity Problem; Semi-infinite Layer; Proper Weight; Tensile Stress. Citation: Fesenko, A., Vaysfel’d, N. An uncoupled thermoelasticity problem for a semi-infinite layer with regard of its proper weight, Frattura ed Integrità Strutturale, 48 (2019) 768-792. Received: 12.12.2019 Accepted: 14.03.2019 Published: 01.04.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION number of methods of three-dimensional problem studies in elasticity are based on representations of homogeneous Lame equation solutions using harmonic and biharmonic functions. Such representations were given by J. V. Boussinesq, W. Thomson (Lord Kelvin), and P. G. Tait [1] where the possibility of reducing the number of harmonic functions to three was also considered. B. G. Galerkin presented the general solution of homogeneous equilibrium equations for an isotropic body through three biharmonic functions. In the works of P. F. Papkovich [2] and H. Neuber [3] a solution form containing four harmonic functions reducing the Lame equations to a harmonic sequence with unshared boundary conditions was proposed. A