Variational-based finite element simulation of fiber-reinforced materials with fiber bending stiffness inmoving thermodynamical systems.

移动热力学系统中具有纤维弯曲刚度的纤维增强材料的基于变分的有限元模拟。

• 批准号: 427519416
• 负责人: Professor Dr.-Ing. Michael Groß
• 金额: --
• 依托单位: Institut für Mechanik und Thermodynamik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/427519416?language=en
• 关键词: Variational; based; finite; element; simulation

In scientific research and material science, computational simulations are more and more used for reducing costly and time consuming experimental investigations. Especially in the case of composite materials, computational simulations provide the possibility to determine appropriate composites numerically first, before these composite materials are produced physically. In this way, many work hours and financial expense can be saved in the sample production, because the number of samples will be reduced. In order to determine appropriate composite materials by using the common finite element method, there is a need for an exact as possible modelling of the appearing stress states in the considered parts. In the case of the often appearing thin-walled composite structures, the exact description of the bending behaviour in a computational simulation is therefore necessary. Especially regarding dynamical loads, bending vibrations have to be predictable, in order to know the right surrounding space and the appropriate support of the composite parts. This requires to avoid locking effects in finite elements and the modelling of each material stiffness. Thus, in the case of fiber-reinforced polymers with a predominant portion of solid fibers, the computational modelling of a fiber bending stiffness is necessary. Especially for parts subject to dynamical loads, the modelling of an inertia influence by means of the fibers contributes to obtain meaningful computational results.The goal of the submitted research project is the modelling of fiber bending or finite fiber diameter, respectively, in the scope of thermodynamics, such that a dynamical simulation of the underlying material model is numerically exact, numerically stable and CPU-time efficient. This is provided by the energy-momentum consistent time integration algorithms to be developed in this research project, which are based on a locking-free space discretization and an automatic time-step size control.

在科学研究和材料科学中，计算模拟越来越多地用于减少昂贵且耗时的实验研究。特别是在复合材料的情况下，计算模拟提供了在物理生产这些复合材料之前首先在数值上确定合适的复合材料的可能性。这样，在样品制作中可以节省很多工时和财务费用，因为样品数量会减少。为了使用常见的有限元方法确定合适的复合材料，需要对所考虑的零件中出现的应力状态进行尽可能精确的建模。因此，在经常出现的薄壁复合结构的情况下，有必要在计算模拟中精确描述弯曲行为。特别是在动态载荷方面，弯曲振动必须是可预测的，以便了解正确的周围空间和复合材料零件的适当支撑。这需要避免有限元中的锁定效应以及每种材料刚度的建模。因此，在纤维增强聚合物以实心纤维为主的情况下，纤维弯曲刚度的计算建模是必要的。特别是对于承受动态载荷的零件，通过纤维对惯性影响进行建模有助于获得有意义的计算结果。提交的研究项目的目标是分别在以下范围内对纤维弯曲或有限纤维直径进行建模热力学，使得底层材料模型的动态模拟在数值上精确、数值稳定且 CPU 时间高效。这是由本研究项目中开发的能量动量一致时间积分算法提供的，该算法基于无锁定空间离散化和自动时间步长控制。