Nonlinear analysis of quadrilateral composite plates using moving kriging based element free Galerkin method

2017 ◽  
Vol 159 ◽  
pp. 719-727 ◽  
Author(s):  
Gaurav Watts ◽  
S. Pradyumna ◽  
M.K. Singha
Keyword(s):  
Galerkin Method ◽  
Nonlinear Analysis ◽  
Composite Plates ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

scholarly journals The Meshless Element Free Galerkin Method for Buckling Analysis of Simply Supported Laminate Composite Plates

2012 ◽  
Vol 21 (6) ◽  
pp. 096369351202100
Author(s):  
Yeliz Pekbey ◽  
Farshid K. Maleki ◽  
Hasan Yildiz ◽  
Goudarz G. Hesar
Keyword(s):  
Galerkin Method ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Width Ratio ◽  
Laminated Composite Plates ◽  
Element Free Galerkin Method ◽  
Simply Supported ◽  
Element Free Galerkin ◽  
Element Free

A meshless element free Galerkin method (EFG) is presented to analyze the buckling of laminated composite plates using the classical (Kirchhoff's) plate theory (CPT) formulation. In the meshless EFG method, the moving least-squares (MLS) technique which does not satisfies the Kroneckar delta feature is used to set up the shape functions. The accuracy and the efficiency of the meshless EFG method are thus demonstrated by the numerical analysis of laminated composite plates with simply supported boundary conditions. Effects of the number of layers, ply orientations, the length-to-width ratio and modulus ratio on the dimensionless buckling loads are investigated. The results obtained by the EFG method are compared with those obtained by the CPT and the finite-element method (FEM). EFG results have good agreements with the analytical solutions. Comparison of results with the CPT as well as the FEM suggests that the meshless element free Galerkin method (EFG) yields an effective solution method for the analysis of laminated composite plates.

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

2014 ◽  
Vol 60 (1-4) ◽  
pp. 87-105 ◽  
Author(s):  
Ryszard Staroszczyk
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Present Model ◽  
Free Surface Elevation ◽  
Element Free Galerkin Method ◽  
Plane Flow ◽  
Element Free Galerkin ◽  
Proposed Model ◽  
Sloping Bed ◽  
Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

Implementing of Displacement Boundary Conditions of Element-Free Galerkin Method and its Applications Used in Fracture Mechanics

2012 ◽  
Vol 629 ◽  
pp. 606-610
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Dun Fu Zhang
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Transformation Method ◽  
Computational Method ◽  
Reproducing Kernel Particle Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

The main draw back of the Moving Least Squares (MLS) approximate used in element free Galerkin method (EFGM) is its lack the property of the delta function. To alleviate difficulties in the treatment of essential boundary conditions in EFGM, the local transformation method and the boundary singular weight method, which are used in the reproducing kernel particle method, is combined with the element free Galerkin method. The computational method is given to analyze the stress intensity factors and the numerical simulation of crack propagation of two-dimentional problems of the elastic fracture analysis. The application examples reveal the effectiveness and feasibility of the present methods.

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