A new neural network enhanced Finite Element approach

在工程力学中，结构的变形通过基于连续体力学模型的有限元模拟来确定。根据这些边界值问题的复杂性，模拟时间，例如碰撞测试，即使使用高性能计算机也可能需要数小时或数天。由于所使用的结构和材料的几何和物理非线性，在每个时间增量中的所有状态变量和切线刚度矩阵的更新是必不可少的，并且花费了大部分计算时间。在本方法中，提出了一种新的方法，取代整个刚度矩阵和材料的法律，通过人工神经网络有限元模拟。新的效率和有效性将实现显着降低计算时间，并在增强的有限元模拟中不需要连续力学模型。在文献中，研究神经网络增强材料模型，代理模型，运动方程的神经网络解决方案。然而，一种方法来取代物理和几何非线性结构行为的广义位移和力之间的完整的依赖性是目前还没有。在这里，本研究进来，并导致两个优点相比，经典的有限元方法。首先，在增强的有限元模拟过程中，除了在训练过程中，不再需要基础连续体力学模型。其次，模拟速度显著加快，因此计算时间比经典有限元模拟少得多。该方法已被注册为德国专利。

In engineering mechanics, deformations of structures are determined by means of Finite Element simulations based on continuum mechanical models. Depending on the complexity of these boundary value problems, the simulation time, e.g. in crash tests, can take hours or days even with high-performance computers. Due to the geometrical and physical nonlinearity of the used structures and materials, the update of all state variables and tangent stiffness matrices in each time increment is essential and takes the majority of computational time. In the present approach, a new method is proposed for replacing entire stiffness matrices and material laws by means of artificial neural networks in Finite Element simulations. The new efficiency and effectiveness will be achieved by significantly lower computing time and by the lack of need for a continuum mechanical model in the enhanced FE simulations. In literature, studies about neural network enhanced material models, surrogate models, and neural network solutions of equations of motion are available. However, a method for substituting the complete dependency between generalised displacements and forces for physically and geometrically nonlinear structural behaviour is not available so far. Here, the present study comes in and leads to two advantages compared to the classical Finite Element Method. Firstly, during the enhanced Finite Element simulations, an underlying continuum mechanical model is not necessary anymore, except in the training process. Secondly, the simulation is accelerated significantly and leads therefore to much less computational time, than the classical Finite Element simulations. The proposed method was already registered as a german patent.