**On the solution of a problem of extended thermoelasticity theory (ETE) by using a complete finite element approach**

Shivay Om Namha *, Mukhopadhyay Santwana

Department of Mathematical Sciences

Indian Institute of Technology (BHU)

Varanasi-221005, India

*E-mail: onsj79@gmail.com

### Received:

Received: 08 December 2018; revised: 04 May 2019; accepted: 06 May 2019; published online: 12 June 2019

### DOI: 10.12921/cmst.2018.0000062

### Abstract:

This paper attempts to apply a complete finite element approach for the solution of problems on coupled dynamical thermoelasticity theory. Presently, we employ the extended thermoelasticity theory proposed by Lord and Shulman (1969) and consider a problem of linear thermoelasticity for the hollow disk with a thermal shock applied on its inner boundary. The thermoelastic equations have been solved using the complete finite element approach, where we have used discretization in the time domain as well as space domain and applied the Galerkin’s approach of the finite element for both time and space domain. We implement our scheme for a particular case and carry out computational work to obtain the numerical solution of the problem. Further, we compare the present results with the solutions obtained by FEM with Newmark time integration method and the solutions obtained by a trans-FEM method in which Laplace transform technique is used for the time domain. We show that, there is a perfect match in solutions of complete finite element approach with trans-finite element method and Newmark method. The efficiency of the method with respect to computation time is also compared with other two methods.

### Key words:

coupled thermoelasticity, extended thermoelasticity theory, finite element method, Newmark method, trans-FEM

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