Artificial neural network assisted numerical quadrature in finite element analysis in mechanics

Abstract

Finite element analysis (FEA) is a numerical tool that is broadly implemented in solving engineering problems. The Gaussian quadrature rule is commonly used to integrate elemental quantities like stiffness matrices over arbitrarily shaped elements in FEA. The Gaussian quadrature rule is a numerical technique in which the accuracy of numerical integration depends on the number of Gauss quadrature points. A higher number of quadrature points in the Gaussian quadrature rule implies higher accuracy but at the cost of higher computations. Thus, the number of Gauss points directly affects the computational cost and accuracy of the FE results. The main objective of the paper is to develop a deep learning model to predict the optimum number of Gauss points required in three-dimensional FEA utilizing hexahedral elements. In recent times some works have been proposed using deep learning in this direction. The present work further explores new possibilities in the area. In this paper, instead of the coordinates of the hexahedral element, its length and angle between two sides are taken as the input to the model, and the optimum number of Gauss quadrature points are predicted. The performance of the model is evaluated by the accuracy and confusion matrix. The present results are compared and are found to be better than the results available in the literature.