Intelligent stiffness computation for plate and beam structures by neural network enhanced finite element analysis

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AbstractIn the present study, new methods are proposed to replace the constitutive law and the entire tangent stiffness matrix in finite element analysis by artificial neural networks (ANNs). By combining the FEM with ANN, so‐called intelligent elements are developed. First, as an extension to recent trends in model‐based material law replacement, we introduce an additional loss term corresponding to the material stiffness. This training procedure is referred to as Sobolev training and ensures that the ANN learns both the function approximating the stress behavior and its first derivative (material stiffness). In a following step, we introduce three methods to replace the entire local stiffness matrix of an element by approximating its generalized force‐displacement relations. These methods also adopt ANNs with Sobolev training procedure to predict the mentioned quantities. Since neural networks (NN) are universal function approximators, they are used to extract the stiffness information for elements undergoing plastic deformation. The focus of this work is to establish a neural network‐based FEM framework (independent of NN topology) to introduce an enhanced‐material law and in a consequent step also approximate stiffness information of truss, beam, and plate elements taking physical non‐linear behavior into account.