Large Deformation Hermitian Finite Element Coupled Thermoelasticity Analysis of Wave Propagation and Reflection in a Finite Domain

Abstract

In the present paper, a finite element nonlinear coupled thermoelasticity formulation is presented for analysis of the wave propagation, reflection, and mixing phenomena in the finite length isotropic solids. The governing equations are derived based on the second Piola-Kirchhoff stress and the full form of Green’s strain-displacement tensors to account for the large deformations and finite strains. In contrast to the available researches, the assumption of very small temperature changes compared to the reference temperature is released in the present research. Galerkin’s method, a weak formulation, and cubic elements are employed to obtain the time-dependent non-linear finite element governing equations. The proposed solution procedure to the resulting highly nonlinear and time-dependent governing equations employs an updating algorithm and Newmark’s numerical time integration method. The wave propagation and reflection phenomena are investigated for both the mechanical and thermal shocks and time variations of distributions of the resulting displacements, temperature rises, and stresses are illustrated graphically and discussed comprehensively. Furthermore, the effects of the non-linear terms are discussed comprehensively. Results reveal that in the non-linear analysis, no fixed speed of wave propagation can be defined.