Structure preserving time integration schemes for thermomechanical systems

本研究计画之主题为发展耦合系统接触问题之数值模拟方法。特别是，我们的目标是完全耦合的热力学问题和相应的接触formulations.Variationally一致的方法在空间和时间被认为是所产生的系统的数值处理。因此，Mortar方法的热机械系统的空间离散化和结构保持的时间离散化的积分器被开发。拉格朗日以及NURBS（等几何分析，伊加）为基础的离散化的基本有限元方法被认为是。在第二个资助期的建议，我们专注于发展的结构保持时间积分计划伊加砂浆接触元素。此外，我们的目标是将复杂的和高度非线性的摩擦法精确模拟的热机械摩擦问题。

Topic of this research project is the development of numerical methods for the simulation of contact problem for coupled systems. In particular, we aim at fully coupled thermomechanical problems and the corresponding contact formulations.Variationally consistent methods in space and time are considered for the numerical treatment of the arising system. Therefore, Mortar methods for the spatial discretisation of the thermomechanical system and structure preserving integrators for the temporal discretisation are to be developed. Lagrangian as well as NURBS (Isogeometric analysis, IGA) based discretisation of the underlying finite element methods are considered.In this proposal for the second funding period we focus on the development of structure preserving time integration schemes for IGA Mortar contact elements. Furthermore, we aim at the incorporation of complex and highly non-linear friction laws for a precise simulation of thermomechanical friction problems.