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

2012 ◽  
Vol 26 (9) ◽  
pp. 2685-2694 ◽  
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 Method ◽  
Element Free Galerkin ◽  
Element Free

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.

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

2012 ◽  
Vol 28 (3) ◽  
pp. 479-488 ◽  
Author(s):  
Ahmad Rahbar-Ranji ◽  
E. Bahmyari
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Elastic Foundation ◽  
Variable Thickness ◽  
Thin Plates ◽  
Thickness Variation ◽  
Element Free Galerkin Method ◽  
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.

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