Thermo‐electro‐mechanical coupling problems solved by FE‐formulation

Abstract

Coupled problems are of great interest in the area of technical applications. In the current paper we present the theory of thermo‐electro‐mechanical coupling and provide a discretization by using the method of finite elements. The thermo‐electro‐mechanical effect presents a physical interaction between the fundamental quantities of the sub‐domains elastomechanics, electrostatics and heat balance. Throughout thermodynamic analysis we derive the constitutive equations which describe the above behaviour and relate the main quantities which describe the three fields. From the principal equations of elastomechanics, electrostatics and heat balance separately, we derive the weak formulation of the load equilibrium, the electrostatic equilibrium and the heat balance individually. Furthermore a FE‐formulation leads the weak formulations of the coupled problem to a system of three coupling differential equations. This system is non‐linear with respect to the temperature and we solve it using an incremental solution. The numerical result is to be shown on a one‐dimensional test example.

Citation

Bouranta, K., Malegiannakis, G.A. and Kröplin, B. (1998), "Thermo‐electro‐mechanical coupling problems solved by FE‐formulation", Engineering Computations, Vol. 15 No. 6, pp. 804-828. https://doi.org/10.1108/EUM0000000004538