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.

本文介绍了一种称为自更新有限元 (SUFE) 的新概念。有限元 (FE) 通过迭代程序激活，以提高求解精度，无需网格细化。为四节点有限元设计了基于模式的有限元公式，并为弯曲模式采用了假定的模态应变。通过对给定单元变形的深度学习来实现最佳弯曲方向的搜索程序，以最大限度地减少剪切锁定。所提出的单元称为自更新四节点有限元，为此开发了迭代求解程序。该元件通过了贴片和零能量模式测试。随着迭代次数的增加，有限元解决方案变得越来越准确，通过几次迭代就可以得到非常准确的解决方案。SUFE 概念非常有效，尤其是当网格粗糙且严重扭曲时。其优异的性能通过各种数值例子得到了证明。