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

非线性结构和弹性动力学中保结构积分的混合方法

• 批准号: 227928419
• 负责人: Professor Dr.-Ing. Peter Betsch
• 金额: --
• 依托单位: Institut für Mechanik (IFM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/227928419?language=en
• 关键词: Mixed; methods; structure; preserving; integration

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.

保持结构的时间步进方案具有较好的数值稳定性和鲁棒性。特别是，能量动量格式的发展是由非线性结构动力学的具体要求指导的。然而，这些发展基本上局限于基于位移的有限元素。另一方面，混合有限元公式在许多应用中是重要的。本项目的目标是开发一种新的方法来设计混合有限元公式的结构保留积分器。为此，将五场变分原理应使用作为空间和时间离散化的新出发点。混合有限元与保结构方案的结合在精度、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大大扩展结构保持积分器的适用性。