Mixed methods for the structure-preserving integration in nonlinear structural and elasto-dynamics

结构保持时间步长格式具有优良的数值稳定性和稳健性。特别是，能量动量格式的发展是由非线性结构动力学的特定要求指导的。然而，这些发展基本上局限于基于位移的有限元。另一方面，混合有限元格式在许多应用中都很重要。本项目的目标是开发一种新的方法来设计混合有限元格式的保结构积分器。为此，采用5场变分原理作为时空离散化的新起点。混合有限元和结构保持格式的结合在精度、数值稳定性和稳健性方面具有很大的优势。此外，新提出的时空混合方法有可能极大地扩展保结构积分器的适用性。

Structure-preserving time-stepping schemes are known to exhibit superior numerical stability and robustness. In particular, the development of energy-momentum schemes was guided by the specific demands of nonlinear structural dynamics. However, these developments have essentially been restricted to displacement-based finite elements. On the other hand mixed finite element formulations are important for many applications.The goal of the present project is to develop a new approach to the design of structure-preserving integrators for mixed finite element formulations. For that purpose a 5-field variational principle shall be used as new pointof departure for the discretization in space and time.The combination of mixed finite elements and structure-preserving schemes promises great advantages with regard to accuracy, numerical stability and robustness. In addition to that, the newly proposed mixed method inspace and time has the potential to significantly extend the applicability of structure-preserving integrators.