A new neural network enhanced Finite Element approach

在工程力学中，结构的变形是通过基于连续介质力学模型的有限元模拟来确定的。根据这些边值问题的复杂程度，模拟时间，例如在碰撞测试中，即使使用高性能计算机也可能需要数小时或数天。由于所用结构和材料的几何和物理非线性，每个时间增量中所有状态变量和切线刚度矩阵的更新是必不可少的，并且占用了大部分计算时间。在该方法中，提出了一种用人工神经网络代替有限元模拟中的整体刚度矩阵和材料定律的新方法。新的效率和效果将通过显著减少计算时间和在增强的有限元模拟中不需要连续介质力学模型来实现。在文献中，关于神经网络增强材料模型、代理模型和运动方程的神经网络解的研究是可用的。然而，到目前为止，还没有一种方法可以用广义位移和力之间的完全相关性来代替物理和几何非线性结构行为。在此，与经典有限元方法相比，本研究具有两个优点。首先，在增强的有限元模拟过程中，除了在训练过程中之外，不再需要底层的连续介质力学模型。其次，与经典的有限元模拟相比，模拟的速度大大加快，从而减少了计算时间。拟议中的方法已经注册为德国专利。

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.