Generalized convolution quadrature based boundary element method for uncoupled thermoelasticity

Mechanical loads together with changing temperature conditions can be found in a wide variety of fields. Their effects on elastic media are reflected in the theory of thermoelasticity. For typical materials in engineering, very often a simplification of this coupled theory can be used, the so-called uncoupled quasistatic thermoelasticity. Therein, the effects of the deformations onto the temperature distribution is neglected and the mechanical inertia effects as well. The Boundary Element Method is used to solve numerically these equations in three dimensions. Since convolution integrals occur in this boundary element formulation, the Convolution Quadrature Method may be applied. However, very often in thermoelasticity the solution shows rapid changes and later on very small changes. Hence, a time discretisation with a variable time step size is preferable. Therefore, here, the so-called generalised Convolution Quadrature is applied, which allows for non-uniform time steps. Numerical results show that the proposed method works. The convergence behavior is, as expected, governed either by the time stepping method or the spatial discretisation, depending on which rate is smaller. Further, it is shown that for some problems the proposed use of the generalised Convolution Quadrature is the preferable. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

In a wide variety of fields, the effects of mechanical loads and changing temperature conditions on elastic media are reflected in the theory of thermoelasticity. The uncoupled quasistatic thermoelasticity is often used in engineering for typical materials, simplifying the coupled theory by neglecting the effects of deformations onto temperature distribution and mechanical inertia effects. The Boundary Element Method is utilized to solve these equations numerically in three dimensions, and the generalised Convolution Quadrature method is applied for solving problems with non-uniform time steps in thermoelasticity.