Analysis of porous micro-plates reinforced with FG-GNPs based on Reddy plate theory

2020 ◽  
Vol 247 ◽  
pp. 112391 ◽  
Author(s):  
Mohammad Arefi ◽  
Saeed Firouzeh ◽  
Elyas Mohammad-Rezaei Bidgoli ◽  
Ömer Civalek
Keyword(s):  
Plate Theory ◽  
Micro Plates

Exact solution for bending analysis of functionally graded micro-plates based on strain gradient theory

2018 ◽  
Vol 25 (3) ◽  
pp. 439-451
Author(s):  
Meisam Mohammadi ◽  
Afshin Iranmanesh ◽  
Seyed Sadegh Naseralavi ◽  
Hamed Farahmand
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Governing Equations ◽  
Micro Plates ◽  
Micro Structures

Abstract In the present article, static analysis of thin functionally graded micro-plates, based on Kirchhoff plate theory, is investigated. Utilizing the strain gradient theory and principle of minimum total potential energy, governing equations of rectangular micro-plates, subjected to distributed load, are explored. In accordance with functionally graded distribution of material properties through the thickness, higher-order governing equations are coupled in terms of displacement fields. Introducing a novel methodology, governing equations are decoupled, with special privilege of solving analytically. These new equations are solved for micro-plates with Levy boundary conditions. It is shown that neutral plane in functionally graded micro-plate is moved from midplane to a new coordinate in thickness direction. It is shown that considering micro-structures effects affects the governing equations and boundary conditions. Finally, the effects of material properties, micro-structures, boundary conditions and dimensions are expounded on the static response of micro-plate. Results show that increasing the length scale parameter and FGM index increases the rigidity of micro-plate. In addition, it is concluded that using classical theories for study of micro-structures leads to inaccurate results.

A NOVEL APPLICATION OF HIGHER CONTINUITY FINITE ELEMENT IN VIBRATION ANALYSIS OF MICRO-PLATES

2013 ◽  
Vol 13 (04) ◽  
pp. 1250080 ◽  
Author(s):  
HAMED FARAHMAND ◽  
ALIREZA AHMADI ◽  
SAID ARABNEJAD
Keyword(s):  
Finite Element ◽  
Vibration Analysis ◽  
Scale Effects ◽  
Plate Theory ◽  
Gradient Elasticity ◽  
Computational Procedure ◽  
Classical Plate Theory ◽  
Vibrational Characteristics ◽  
Gradient Elasticity Theory ◽  
Micro Plates

In this paper, higher continuity p-version finite element, in particular two-dimensional C2 elements are utilized in studying vibrational characteristics of rectangular Flexural Micro-Plates based on the "gradient elasticity theory". In order to verify the computational procedure, results obtained from the finite element framework are compared to the classical plate theory results and to those of the micro-plate and classical plate investigations that are available in literature. Results indicate that the proposed framework, yields highly accurate results. Moreover, it is concluded that, under certain boundary conditions and length scale effects, the differences in predictions are so gross that the validity of classical theory in predicting micro-plates vibrational characteristics can be ruled out completely.

scholarly journals Bending, Free Vibration, and Buckling Analysis of Functionally Graded Porous Micro-Plates Using a General Third-Order Plate Theory

2019 ◽  
Vol 3 (1) ◽  
pp. 15 ◽  
Author(s):  
Semsi Coskun ◽  
Jinseok Kim ◽  
Houssam Toutanji
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Length Scale ◽  
Thickness Direction ◽  
Third Order ◽  
Micro Plates ◽  
Material Length Scale ◽  
Material Length

Static bending, free vibration and buckling of functionally graded porous micro-plates are investigated using a general third order plate theory. In addition, analytical solutions are obtained using the Navier method. The effect of the material length scale factor and the variation of material property through the thickness direction of plates are considered as well as porosity effects. Three different porosity distributions are considered and the effects of porosity variations are examined in the framework of a general third order plate theory. Numerical results show that the effect of each distribution of porosity is distinguished due to coupling between the heterogeneity of the material properties and the variation of porosity.

Refined plate theory and its variants

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 137-146 ◽  
Author(s):  
R. P. Shimpi
Keyword(s):  
Plate Theory ◽  
Refined Plate Theory

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

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