Element-Free Galerkin Method for Reinforced Timoshenko Beam on Elastic Foundation

Moving Least Square ◽

Beam On Elastic Foundation ◽

Element Free Galerkin ◽

Mesh Free ◽

System Equations ◽

One of mesh free methods, element free Galerkin method, is presented to analyze the finite beam on elastic foundation. The shape functions are constructed by using the moving least square interpolation based on a set of nodes that are arbitrarily distributed in specified domain. Discrete system equations are derived from the variation form of system equations. Numerical examples of finite beam on elastic foundation are given by establishing Matlab code. The results of this paper demonstrate the effectiveness of the proposed method with small errors compared to analytical solutions. Keywords: mesh free method, element free Galerkin method, moving least square, finite beam, elastic foundation.

Stochastic analysis of thin plates on elastic foundation by combining the generalized polynomial chaos and element free Galerkin method

Journal of Mechanical Science and Technology ◽

10.1007/s12206-017-0329-4 ◽

2017 ◽

Vol 31 (4) ◽

pp. 1813-1824 ◽

Cited By ~ 2

Author(s):

Ehsan Bahmyari ◽

Mohammad Reza Khedmati

Keyword(s):

Galerkin Method ◽

Elastic Foundation ◽

Stochastic Analysis ◽

Polynomial Chaos ◽

Thin Plates ◽

Element Free Galerkin ◽

Generalized Polynomial ◽

Plates On Elastic Foundation ◽

Vibration analysis of nonhomogeneous moderately thick plates with point supports resting on Pasternak elastic foundation using element free Galerkin method

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2013.05.003 ◽

2013 ◽

Vol 37 (10) ◽

pp. 1212-1238 ◽

Cited By ~ 22

Author(s):

Ehsan Bahmyari ◽

Mohammad Reza Khedmati

Keyword(s):

Galerkin Method ◽

Elastic Foundation ◽

Vibration Analysis ◽

Thick Plates ◽

Element Free Galerkin ◽

Pasternak Elastic Foundation ◽

Moderately Thick Plates ◽

Demonstration of a simple method to satisfy homogenous boundary conditions in element-free Galerkin method through the vibration problem of Timoshenko beam

Communications in Numerical Methods in Engineering ◽

10.1002/cnm.578 ◽

2002 ◽

Vol 19 (2) ◽

pp. 155-168 ◽

Cited By ~ 1

Author(s):

Rajeev G. Nair ◽

G. Venkateswara Rao ◽

Gajbir Singh

Keyword(s):

Boundary Conditions ◽

Galerkin Method ◽

Timoshenko Beam ◽

Simple Method ◽

Vibration Problem ◽

Element Free Galerkin ◽

Bending Analysis of Thin Plates with Variable Thickness Resting on Elastic Foundation by Element Free Galerkin Method

Journal of Mechanics ◽

10.1017/jmech.2012.57 ◽

2012 ◽

Vol 28 (3) ◽

pp. 479-488 ◽

Cited By ~ 4

Author(s):

Ahmad Rahbar-Ranji ◽

E. Bahmyari

Keyword(s):

Boundary Conditions ◽

Galerkin Method ◽

Elastic Foundation ◽

Variable Thickness ◽

Thin Plates ◽

Thickness Variation ◽

Element Free Galerkin ◽

Element Free ◽

Foundation Parameters

AbstractElement Free Galerkin method was used to analyze bending of thin plates with variable thickness resting on one parameter elastic foundation. Thickness of plate is considered as linearly varying in one direction. Formulation could be applied to plates of any shape with general boundary conditions and loadings. Convergence of solution was examined for different number of nodes, thickness variation and foundation parameters. It was found that for deflection good results were achieved even with small number of nodes regardless of boundary condition, thickness variation and foundation parameters. Accuracy of method is checked against available results and good agreements were found. Applicability of method is demonstrated by solving numerical examples with different boundary conditions, thickness and foundation parameters, and loadings.

Free vibration analysis of orthotropic plates with variable thickness resting on non-uniform elastic foundation by element free Galerkin method

Journal of Mechanical Science and Technology ◽

10.1007/s12206-012-0713-z ◽

2012 ◽

Vol 26 (9) ◽

pp. 2685-2694 ◽

Cited By ~ 22

Author(s):

Ehsan Bahmyari ◽

Ahmad Rahbar-Ranji

Keyword(s):

Free Vibration ◽

Galerkin Method ◽

Elastic Foundation ◽

Variable Thickness ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Orthotropic Plates ◽

Element Free Galerkin ◽

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

Archives of Hydro-Engineering and Environmental Mechanics ◽

10.2478/heem-2013-0010 ◽

2014 ◽

Vol 60 (1-4) ◽

pp. 87-105 ◽

Cited By ~ 3

Author(s):

Ryszard Staroszczyk

Keyword(s):

Wave Propagation ◽

Galerkin Method ◽

Present Model ◽

Free Surface Elevation ◽

Plane Flow ◽

Element Free Galerkin ◽

Proposed Model ◽

Sloping Bed ◽

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.