A Green-Naghdi Model in a 2D Problem of a Mode I Crack in an Isotropic Thermoelastic Plate

I A Abbas,F S Alzahrani

doi:10.1134/s1029959918020017

Abstract

In this article, the generalized thermoelastic theory under Green and Naghdi models are used to study the thermoelastic interaction in an isotropic material containing a finite crack inside the material. The crack boundary is due to a prescribed temperature and stress distribution. Based on the Green-Naghdi type II and type III models, the formulation is applied to generalized thermoelasticity with an appropriate choice of parameters. Numerical solutions of the displacement components, temperature, and stress components are obtained using the finite element method. The results have been verified numerically and are represented graphically. Comparisons were made with expected results from Green and Naghdi model of type III and Green and Naghdi model of type II.

Highlights

Two generalized thermoelasticity theories well-investigated and well-established
Replacing the classical Fourier law by postulating a new thermal conduction law, the theory of generalized thermoelasticity containing one relaxation time has been proposed by Lord and Shulman [1]
Sherief and ElMaghraby [8, 9] studied mode I crack problems using the method of regularization

Summary

Introduction

Two generalized thermoelasticity theories well-investigated and well-established. Replacing the classical Fourier law by postulating a new thermal conduction law, the theory of generalized thermoelasticity containing one relaxation time has been proposed by Lord and Shulman [1]. Green and Lindsay [2] established the generalized of thermoelastic theory containing two relaxation times. Sherief and ElMaghraby [8, 9] studied mode I crack problems using the method of regularization. Prasad et al [10] applied the method of regularization in a two dimensional thermoelastic problem of a mode I crack under Green and Naghdi type III model. Lotfy and Othman [11] studied the effect of magnetic field for a mode I crack on a two-dimensional problem under generalized thermoelastic theory. The solutions of equations resulting from the first and second steps will obtained by the finite element algorithm as in Ref. The present paper investigates a GN model in a two dimensional problem of a mode I crack in a thermoelastic medium using the finite element method.

Basic equation

Formulation of the problem

Application

Finite element solution

Numerical results and discussion

Conclusion