A new neural network enhanced Finite Element approach

一种新的神经网络增强有限元方法

• 批准号: 504279932
• 负责人: Professor Dr.-Ing. Marcus Stoffel
• 金额: --
• 依托单位: Lehrstuhl und Institut für Allgemeine Mechanik
• 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/504279932?language=en
• 关键词: new; neural; network; enhanced; Finite

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.

在工程力学中，结构的变形是通过基于连续体力学模型的有限元模拟来确定的。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。由于所用结构和材料的几何和物理非线性，在每个时间增量中更新所有状态变量和切向刚度矩阵是必不可少的，并且占用了大部分计算时间。本文提出了一种利用人工神经网络在有限元模拟中代替整个刚度矩阵和材料规律的新方法。新的效率和有效性将通过显着降低计算时间和在增强的有限元模拟中不需要连续力学模型来实现。文献中有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。然而，到目前为止，还没有一种方法可以代替广义位移和力之间的完全依赖关系来代替物理和几何非线性结构行为。在此，本文的研究与传统有限元法相比有两个优势。首先，在增强的有限元模拟过程中，除了在训练过程中，不再需要底层的连续力学模型。其次，与传统的有限元模拟相比，仿真速度大大加快，计算时间大大减少。所提出的方法已经注册为德国专利。