Self-updated four-node finite element using deep learning
Self-updated four-node finite element using deep learning
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DOI：
10.1007/s00466-021-02081-7
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发表时间：
2021-08
影响因子：
4.1
通讯作者：
Jaeho Jung;Hyungmin Jun;Phill-Seung Lee
中科院分区：
文献类型：
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作者：
Jaeho Jung;Hyungmin Jun;Phill-Seung Lee
本文提出了自更新有限元的概念。通过迭代过程激活有限元（FE），以提高解的精度，而无需网格细化。针对四节点有限元设计了基于模式的有限元列式，并对弯曲模式采用假设的模式应变。通过对给定元件变形的深度学习来实现最佳弯曲方向的搜索过程，以最大限度地减少剪切锁定。建议的元素被称为一个自更新的四节点有限元，迭代求解程序开发。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，有限元解变得越来越精确，从而通过几次迭代得到非常精确的解。SUFE的概念是非常有效的，特别是当网格粗糙和严重扭曲。通过各种数值例子证明了它的优良性能。
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.