Mathematics of Element Formulation

2018 ◽  
pp. 187-241
Author(s):  
M. Okereke ◽  
S. Keates
Keyword(s):  
Element Formulation

scholarly journals Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics

2021 ◽  
Vol 383 ◽  
pp. 113917
Author(s):  
Andrea Borio ◽  
François P. Hamon ◽  
Nicola Castelletto ◽  
Joshua A. White ◽  
Randolph R. Settgast
Keyword(s):  
Finite Difference ◽  
Element Formulation ◽  
Virtual Element

scholarly journals Numerical prediction of ice rubble field loads on the Norströmsgrund lighthouse using cohesive element formulation

2021 ◽  
Vol 223 ◽  
pp. 108638
Author(s):  
Aniket Patil ◽  
Bjørnar Sand ◽  
Andrzej Cwirzen ◽  
Lennart Fransson
Keyword(s):  
Numerical Prediction ◽  
Element Formulation ◽  
Cohesive Element

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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