Nonlinear Bending Analysis of Isotropic Plates Supported on Winkler Foundation Using Element Free Galerkin Method

2015 ◽  
Author(s):  
Gaurav Watts ◽  
◽  
M. K. Singha ◽  
S. Pradyumna
Keyword(s):  
Galerkin Method ◽  
Winkler Foundation ◽  
Element Free Galerkin Method ◽  
Nonlinear Bending ◽  
Bending Analysis ◽  
Element Free Galerkin ◽  
Isotropic Plates ◽  
Element Free

Bending Solution of Plates on Winkler Foundation by Element-Free Galerkin Method Based on Mindlin Plate Theory

2012 ◽  
Vol 166-169 ◽  
pp. 3136-3141
Author(s):  
Min Yan Xu ◽  
Jian Dong Sun ◽  
Shi Qi Cui ◽  
Lei Shi
Keyword(s):  
Weight Function ◽  
Galerkin Method ◽  
Plate Theory ◽  
Positive Definite Matrix ◽  
Mindlin Plate ◽  
Winkler Foundation ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Control Equation ◽  
Element Free

Element-free Galerkin method (EFGM) is successfully applied to solve the bending problem of plates on a Winkler foundation. The shape function which is characteristic of high-time continuity is formulated by means of weight function. A way to incorpor- ate the self-adaptive influential radius in weight function is proposed. Based on variational principle, this paper derives control equation for the bending of plates on a Winkler foundation from Mindlin-Reissner plate theory. Using penalty function mothed, assembled stiffness matrix which is real symmetry positive definite matrix is deduced. This method can solve the bending problem of plates with different boundary conditions on a Winkler foundation. The corresponding computer programs of EFGM and post-process programs are also developed. Numerical examples show that EFGM solving the bending of plates on a Winkler found is reasonable and feasible. This present study provides a newly effective numerical method for the Winkler foundation bending problem and expands the application field of EFGM.

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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