A quasi-3D higher-order plate theory for bending of FG plates resting on elastic foundations under hygro-thermo-mechanical loads with porosity

2020 ◽  
Vol 82 ◽  
pp. 103985 ◽  
Author(s):  
Daoud S. Mashat ◽  
Ashraf M. Zenkour ◽  
Ahmed F. Radwan
Keyword(s):  
Plate Theory ◽  
Higher Order ◽  
Mechanical Loads ◽  
Elastic Foundations ◽  
Fg Plates

scholarly journals Thermomechanical postbuckling of thick FGM plates resting on elastic foundations with tangential edge constraints

2016 ◽  
Vol 38 (1) ◽  
pp. 63-79
Author(s):  
Hoang Van Tung
Keyword(s):  
Material Properties ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Approximate Solutions ◽  
Higher Order ◽  
Iteration Algorithm ◽  
Rectangular Plates ◽  
Power Law Distribution ◽  
Postbuckling Behavior ◽  
Elastic Foundations

This paper investigates the effects of tangential edge  constraints and elastic foundations on the buckling and postbuckling  behavior of thick FGM rectangular plates resting on elastic foundations and  subjected to thermal and thermomechanical loading conditions. Material  properties are assumed to be temperature dependent, and graded in the  thickness direction according to a simple power law distribution in terms of  the volume fractions of constituents. Governing equations are based on the higher order shear deformation plate theory incorporating the von Karman  geometrical nonlinearity, initial geometrical imperfection, tangential edge  constraints and Pasternak type elastic foundations. Approximate solutions  are assumed to satisfy simply supported boundary conditions and Galerkin  procedure is applied to derive expressions of buckling loads and  load-deflection relations. In thermal postbuckling analysis, an iteration  algorithm is employed to determine critical buckling temperatures and  postbuckling temperature-deflection equilibrium paths. The separate and  simultaneous effects of tangential edge restraints, elastic foundations and  temperature dependence of material properties on the buckling and  postbuckling responses of higher order shear deformable FGM plates are  analyzed and discussed.

scholarly journals Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates

2021 ◽  
Vol 5 (11) ◽  
pp. 305
Author(s):  
Slimane Merdaci ◽  
Hadj Mostefa Adda ◽  
Belghoul Hakima ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Vibration Response ◽  
Governing Equations ◽  
First Order ◽  
Fg Plates ◽  
Free Vibration Response

The present work analyzes the free vibration response of functionally graded (FG) plates made of Aluminum (Al) and Alumina (Al2O3) with different porosity distributions, as usually induced by a manufacturing process. The problem is tackled theoretically based on a higher-order shear deformation plate theory, while proposing a Navier-type approximation to solve the governing equations for simply-supported plates with different porosity distributions in the thickness direction. The reliability of the proposed theory is checked successfully by comparing the present results with predictions available from literature based on further first-order or higher-order theories. A large parametric study is performed systematically to evaluate the effect of different mechanical properties, such as the material indexes, porosity volume fractions, porosity distributions, and length-to-thickness ratios, on the free vibration response of FG plates, as useful for the design purposes of most engineered materials and composite applications.

Study on application of higher order lamination plate theory over various applications of natural fiber cross-ply composites

2021 ◽  
Author(s):  
S. Ramaswamy ◽  
Zahoor Ahmed Shariff ◽  
A. Abdul Munaf ◽  
I. Jerin Leno ◽  
S. Joe Patrick Gnanaraj ◽  
...  
Keyword(s):  
Natural Fiber ◽  
Plate Theory ◽  
Higher Order

A Simple Method for Elastic Analysis of Grillages

1968 ◽  
Vol 12 (02) ◽  
pp. 153-159
Author(s):  
Pin-Yu Chang
Keyword(s):  
Finite Element ◽  
Plate Theory ◽  
Computer Time ◽  
Design Tool ◽  
Matrix Transformations ◽  
Simple Method ◽  
Elastic Foundations ◽  
Beam Analysis ◽  
Order Of Magnitude ◽  
Desk Calculator

The theory of beams supported by elastic foundations has been shown to be particularly well-suited to the analysis of grillage beams [1, 2, 3[.2 This theory leads to a far more general formulation regarding the types of structures amenable to analysis than that offered by the orthotropic plate theory. As compared to the methods of finite element theory, the theory of beams supported by elastic foundations decreases the computer time by an order of magnitude, thus making the analysis particularly valuable as a design tool. This paper shows that the measurement of the grillage beam analysis based upon the elastic foundation concept can be further simplified by certain matrix transformations that uncouple the deflection equations. The problem has, in fact, been simplified to such an extent that many large grillages can be analyzed with the aid of a desk calculator. Whenever comparison with results obtained from finite element methods has been possible, it has been found that, for all practical purposes, complete correlation exists.

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