Finite Elements Using Neural Networks and a Posteriori Error

This paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

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“…The assumed deformed shape of the element domain obtained using Eqs. (20) and ( 21) is shown in Fig. 3b.…”

Section: Assumed Modal Strainmentioning

confidence: 94%

“…Here, the neural network is constructed to determine a suitable bending direction angle, m . Recently, applications of neural networks to the finite element method have been studied [19][20][21].…”

Section: Deep Learning For Estimating the Optimal Bending Directionsmentioning

confidence: 99%