Efficient Iterative Solution of Stochastic Finite Element Equations

2009 ◽  
Author(s):  
D.C. Charmpis
Keyword(s):  
Finite Element ◽  
Iterative Solution ◽  
Stochastic Finite Element

Modal properties of macaw palm fruit-rachilla system: An approach by the stochastic finite element method (SFEM)

2021 ◽  
Vol 184 ◽  
pp. 106099
Author(s):  
Fábio Lúcio Santos ◽  
Francisco Scinocca ◽  
Deisenara de Siqueira Marques ◽  
Nara Silveira Velloso ◽  
Flora Maria de Melo Villar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stochastic Finite Element Method ◽  
Stochastic Finite Element ◽  
Palm Fruit ◽  
Modal Properties ◽  
Macaw Palm ◽  
Element Method

scholarly journals Self-updated four-node finite element using deep learning

2021 ◽  
Author(s):  
Jaeho Jung ◽  
Hyungmin Jun ◽  
Phill-Seung Lee
Keyword(s):  
Finite Element ◽  
Deep Learning ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Element Formulation ◽  
Zero Energy ◽  
Energy Mode ◽  
Bending Modes ◽  
Solution Accuracy ◽  
Iterative Solution Procedure

AbstractThis 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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