Application of the ‘FE-Meshfree’ QUAD4 with continuous nodal stress using radial-polynomial basis functions for vibration and geometric nonlinear analyses

2017 ◽  
Vol 78 ◽  
pp. 31-48 ◽  
Author(s):  
Yongtao Yang ◽  
Guanhua Sun ◽  
Hong Zheng
Keyword(s):  
Basis Functions ◽  
Polynomial Basis ◽  
Nonlinear Analyses ◽  
Geometric Nonlinear

Extension of unsymmetric finite elements US‐QUAD8 and US‐HEXA20 for geometric nonlinear analyses

2007 ◽  
Vol 24 (4) ◽  
pp. 407-431 ◽  
Author(s):  
Ean Tat Ooi ◽  
Sellakkutti Rajendran ◽  
Joon Hock Yeo
Keyword(s):  
Finite Elements ◽  
Nonlinear Analyses ◽  
Geometric Nonlinear

Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation

2011 ◽  
Vol 38 (8) ◽  
pp. 553-559 ◽  
Author(s):  
Carlos A. Almeida ◽  
Juan C.R. Albino ◽  
Ivan F.M. Menezes ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded ◽  
Lagrangian Formulation ◽  
Nonlinear Analyses ◽  
Geometric Nonlinear

Ghost point method using RBFs and polynomial basis functions

2021 ◽  
Vol 111 ◽  
pp. 106618
Author(s):  
Zhiying Ma ◽  
Xinxiang Li ◽  
C.S. Chen
Keyword(s):  
Basis Functions ◽  
Point Method ◽  
Polynomial Basis

Multiscale Element–Free Galerkin Method with Penalty for 2D Burgers’ Equation

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Siaw Ching Liew ◽  
Su Hoe Yeak
Keyword(s):  
Meshless Method ◽  
Burgers Equation ◽  
Basis Functions ◽  
Polynomial Basis ◽  
The Finite Element Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Kronecker Delta ◽  
Local Enrichment ◽  
Element Free

In this paper, a new numerical method which is based on the coupling between multiscale method and meshless method with penalty is developed for 2D Burgers’ equation. The advantage of meshless method over the finite element method (FEM) is that remeshing process is not required. This is because the meshless method approximation is constructed entirely in terms of a set of nodes. Since the moving least squares (MLS) shape function does not satisfy the Kronecker delta property, so penalty method is adopted to enforce the essential boundary conditions in this paper. In order to obtain the fine scale approximation, the local enrichment basis is applied. The local enrichment basis may adopt the polynomial basis functions or any other analytical basis functions. Here, the polynomial basis functions are chosen as local enrichment basis. This multiscale meshless method with penalty will provide a more accurate result especially in the critical region which requires higher accuracy. It is believed that this proposed method is an attractive approach for solving more general problems which involve large deformation.

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