Abstract 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.

中文翻译：

---

非耦合热弹性的广义卷积正交边界元方法

摘要 机械载荷和温度条件的变化可以在广泛的领域中找到。它们对弹性介质的影响反映在热弹性理论中。对于工程中的典型材料，通常可以使用这种耦合理论的简化，即所谓的非耦合准静态热弹性。其中，变形对温度分布的影响被忽略，机械惯性也被忽略。边界元法用于在三个维度上对这些方程进行数值求解。由于在此边界元素公式中出现卷积积分，因此可以应用卷积正交方法。然而，在热弹性中，解经常显示出快速变化，然后是非常小的变化。因此，具有可变时间步长的时间离散化是可取的。因此，这里应用了所谓的广义卷积正交，它允许非均匀的时间步长。数值结果表明所提出的方法是有效的。正如预期的那样，收敛行为由时间步长方法或空间离散化控制，具体取决于哪个速率较小。此外，它表明对于某些问题，建议使用广义卷积正交是更可取的。取决于哪个速率较小。此外，它表明对于某些问题，建议使用广义卷积正交是更可取的。取决于哪个速率较小。此外，它表明对于某些问题，建议使用广义卷积正交是更可取的。