Response of ramp-type heating in a monoclinic generalized thermoelastic material

Abstract

Purpose

The two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear temperature ramping function is used to more realistically model: thermal loading of the half-space surface. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The comparison for Lord-Shulman (L-S), Green and Lindsay (G–L), Green and Naghdi (G–N) and Chandrasekharaiah and Tzou (CTU) theories have been shown graphically to estimate the effect of ramping parameter of heating for an insulated and temperature gradient boundaries.

Design/methodology/approach

The design of the study is eigenvalue approach

Findings

Homogeneous, thermally conducting monoclinic material has been taken under consideration to study the effect of linear temperature ramping parameter on temperature and normal displacement field. It is observed that magnitude of field quantities is large near the point of application of source for the non-dimensional values of time in all the four models. The numerical values for the field quantities are computed graphically for a wide range of values of finite pulse rise-time in the two situations t₀ < t, t₀ > t for generalized thermoelasticity theories.

Originality/value

(1) Governing equations for homogeneous, t₀ thermally conducting, monoclinic material are described and solved. (2) Eigen value approach is used to solve the problem. (3) The effect of ramping parameter of heating has been studied for various models of the thermoelasticity to show the comparision between them.

Citation

Rani, L. and Shekhar, S. (2020), "Response of ramp-type heating in a monoclinic generalized thermoelastic material", Multidiscipline Modeling in Materials and Structures, Vol. 16 No. 6, pp. 1373-1384. https://doi.org/10.1108/MMMS-12-2019-0214