Abstract
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.
Highlights
The finite element method (FEM) has been rapidly developed since the 1950s when it was first introduced and successfully commercialized
We devise a new type of finite element called “self-updated finite element” (SUFE) and a method that considerably increases the accuracy of FE solutions through iterative analysis without mesh refinement
The optimal bending direction angle is approximated through the trained neural network, and the angle is employed to update the stiffness matrix of SUFE
Summary
The finite element method (FEM) has been rapidly developed since the 1950s when it was first introduced and successfully commercialized. The convergence of finite element (FE) solutions should only depend on the mesh density. The effectiveness of these methods rapidly diminishes as the element meshes become more distorted. We devise a new type of finite element called “self-updated finite element” (SUFE) and a method that considerably increases the accuracy of FE solutions through iterative analysis without mesh refinement. Computational Mechanics initial analysis; the improved stiffness matrix reflecting this deformation is calculated. The objective is to improve the solutions by minimizing the shear locking effect on the four-node element through iterative analysis. For a given element geometry, material properties, and element deformation, the optimal bending directions are determined such that the element strain energy is minimized. The mode-based finite element formulation used for the SUFE is introduced in Sect.
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