A new neural network enhanced Finite Element approach

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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.