Shear post buckling analysis of FGM annular sector plates based on three dimensional elasticity for different boundary conditions

2018 ◽  
Vol 207 ◽  
pp. 132-147 ◽  
Author(s):  
K. Asemi ◽  
M. Salehi
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Buckling Analysis ◽  
Different Boundary Conditions ◽  
Post Buckling ◽  
Annular Sector ◽  
Three Dimensional Elasticity

On Shear Correction Factor in Vibration of Annular Sector Plates

2010 ◽  
Author(s):  
F. Hejripour ◽  
A. R. Saidi ◽  
S. H. Mirtalaie
Keyword(s):  
Boundary Conditions ◽  
Elasticity Theory ◽  
Correction Factor ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Correction Factors ◽  
Asymmetric Mode ◽  
Shear Correction Factor ◽  
Annular Sector ◽  
Three Dimensional Elasticity

In the present study, the shear correction factors are obtained for annular sector plates using Differential Quadrature (DQ) Method. Based on the three-dimensional elasticity theory, the governing equations of motion for an annular sector plate are obtained. These equations together with the boundary conditions are discretized by employing DQ method. Following DQ procedure an eigenvalue problem is obtained that represents the natural frequencies and mode shapes of the plate. This procedure is also investigated for the analysis of the annular sector plates based on FSDT. The frequency of the first asymmetric mode of thickness direction for various shear correction factors are compared with the results of the three-dimensional elasticity theory. Therefore, the appropriate shear correction factor can be found. Some shear correction factors are obtained for various boundary conditions. It is shown that the value of the shear correction factor depends on the plate geometry and the boundary conditions.

scholarly journals Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huimin Liu ◽  
Fanming Liu ◽  
Xin Jing ◽  
Zhenpeng Wang ◽  
Linlin Xia
Keyword(s):  
Boundary Conditions ◽  
Admissible Function ◽  
Three Dimensional ◽  
Future Research ◽  
Pasternak Foundation ◽  
Arbitrary Boundary ◽  
Thick Plates ◽  
Arbitrary Boundary Conditions ◽  
Ritz Procedure ◽  
Three Dimensional Elasticity

This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

scholarly journals Basic Solutions of Three Dimensional Elasticity

2021 ◽  
Vol 236 ◽  
pp. 05039
Author(s):  
Wx Zhang
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Practical Calculation ◽  
Basic Solution ◽  
Final Solution ◽  
Theoretical Derivation ◽  
Basic Solutions ◽  
Special Solutions ◽  
Basic Equations ◽  
Three Dimensional Elasticity

Elastic calculation method is an important research content of computational mechanics. The problems of elasticity include basic equations and boundary conditions. Therefore, the final solution consists of the general solutions of the basic equations and the special solutions satisfying the boundary conditions. Numerical method is often used in practical calculation, but the analytical solution is also an important subject for researchers. In this paper, the basic solution of three-dimensional elastic materials is given by theoretical derivation.

Buckling analysis of functionally graded annular sector plates resting on elastic foundations

2010 ◽  
Vol 225 (2) ◽  
pp. 312-325 ◽  
Author(s):  
A Naderi ◽  
A R Saidi
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Elastic Foundations ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

In this study, an analytical solution for the buckling of a functionally graded annular sector plate resting on an elastic foundation is presented. The buckling analysis of the functionally graded annular sector plate is investigated for two typical, Winkler and Pasternak, elastic foundations. The equilibrium and stability equations are derived according to the Kirchhoff's plate theory using the energy method. In order to decouple the highly coupled stability equations, two new functions are introduced. The decoupled equations are solved analytically for a plate having simply supported boundary conditions on two radial edges. Satisfying the boundary conditions on the circular edges of the plate yields an eigenvalue problem for finding the critical buckling load. Extensive results pertaining to critical buckling load are presented and the effects of boundary conditions, volume fraction, annularity, plate thickness, and elastic foundation are studied.

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