Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges

2010 ◽  
Vol 14 (3) ◽  
pp. 187-195 ◽  
Author(s):  
Yan Wang ◽  
Zhong-min Wang ◽  
Miao Ruan
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Rectangular Plates ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Elastically Restrained Edges ◽  
Elastically Restrained ◽  
Element Free

Stability Analyses of a Moving Rectangular Plate by the Element Free Galerkin Method

2012 ◽  
Vol 594-597 ◽  
pp. 2651-2654
Author(s):  
Yan Wang ◽  
Zhong Min Wang
Keyword(s):  
Galerkin Method ◽  
Thin Plate ◽  
Thin Plates ◽  
Complex Eigenvalue ◽  
Rectangular Plates ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
The Stability ◽  
Element Free ◽  
Moving Speed

The element-free Galerkin method is proposed to solve the stability of the moving rectangular plates. Utilizing the extended Hamilton’s principle for the elastic dynamics system, the variational expression of the moving thin plate are established. The dimensionless equations of motion of the moving thin plate are obtained by the element-free Galerkin method, and the complex eigenvalue equation is presented. Via numerical calculation, the variation relationship between the first three complex frequencies of the system and the moving speed is obtained. The effects of dimensionless moving speed on the stability and critical load of the thin plates are analyzed.

scholarly journals Free Vibration Analysis of Symmetrically Laminated Folded Plate Structures Using an Element-Free Galerkin Method

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
L. X. Peng
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Laminated Plate ◽  
Element Free Galerkin Method ◽  
Plate Structures ◽  
Element Free Galerkin ◽  
Mass Matrices ◽  
Element Free

An element-free Galerkin method for the solution of free vibration of symmetrically laminated folded plate structures is introduced. Employing the mature meshfree folded plate model proposed by the author, a folded laminated plate is simulated as a composite structure of symmetric laminates that lie in different planes. Based on the first-order shear deformation theory (FSDT) and the moving least-squares (MLS) approximation, the stiffness and mass matrices of the laminates are derived and supposed to obtain the stiffness and mass matrices of the entire folded laminated plate. The equation governing the free vibration behaviors of the folded laminated plate is thus established. Because of the meshfree characteristics of the proposed method, no mesh is involved to determine the stiffness and mass matrices of the laminates. Therefore, the troublesome remeshing can be avoided completely from the study of such problems as the large deformation of folded laminated plates. The calculation of several numerical examples shows that the solutions given by the proposed method are very close to those given by ANSYS, using shell elements, which proves the validity of the proposed method.

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.

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