Some Variational Principles for Coupled Thermoelasticity

Variational Principles for Some Nonlinear Wave Equations

Generally speaking, there exist two basic ways to describe a physical problem [1]: (1) by differential equations (DE) with boundary or initial conditions; (2) by variational principles (VP). The VP model has many advantages over its DE partner: simple and compact in form while comprehensive in content, encompassing implicitly almost all information characterizing the problem under consideration...

The quasi-adiabatic approximation for coupled thermoelasticity

The equations of coupled thermoelasticity are considered in the case of stationary vibrations. The dimensional and order-of-magnitude analysis of the parameters occurring within these equations prompts the introduction of the new non-dimensionalisation scheme, highlighting the nearly-adiabatic nature of the resulting motions. The departure from the purely adiabatic regime is characterised by a ...

Some Variational Problems for Field Equations Coupled with Maxwell Equations

Coupled Thermoelasticity in a Composite Half-Space

The problem of fully coupled thermoelasticity in a composite half-space is considered where the composite has variations in its physical properties in one direction only. The resulting one dimensional problem thus depends on the so called microscale of the composite. Homogenization of the fully coupled theory provides the leading order system of coupled equations (independent of the microscale)...

Steklov's Operator Technique in Coupled Dynamic Thermoelasticity

In this paper we study non-smooth solutions of coupled non-stationary problems in thermoelasticity. Since the classical tools based on the Tay-lor's expansion of unknown functions may not be appropriate in obtaining a measure of quality for numerical methods, we apply the averaging Steklov operators and the technique based on the Bramble-Hilbert lemma in order to establish the convergence resul...