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

结构保持时间步进格式具有良好的上级稳定性和鲁棒性。特别是，能量-动量方案的发展是由非线性结构动力学的具体要求指导的。然而，这些发展基本上仅限于基于位移的有限元。另一方面，混合有限元公式在许多应用中是重要的，本项目的目标是发展一种新的方法来设计混合有限元公式的结构保持积分器。为此，本文采用5-场变分原理作为空间和时间离散的新出发点，将混合有限元和保结构格式相结合，在精度、数值稳定性和鲁棒性方面具有很大的优势。此外，新提出的空间和时间混合方法有可能显着扩展结构保持积分器的适用性。

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.