Static Analysis of Functionally Graded Plate Using Nonlinear Classical Plate Theory with von Karman Strains: A Complex Solution Analysis

2019 ◽  
pp. 1-20
Author(s):  
Simran Jeet Singh ◽  
Suraj Prakash Harsha
Keyword(s):  
Static Analysis ◽  
Plate Theory ◽  
Functionally Graded ◽  
Complex Solution ◽  
Functionally Graded Plate ◽  
Classical Plate Theory ◽  
Von Karman ◽  
Von Kármán

scholarly journals Static Analysis of Functionally Graded Plate Using Nonlinear Classical Plate Theory with Von-Karman Strains

2018 ◽  
Vol 23 (3) ◽  
pp. 707-726 ◽  
Author(s):  
S.J. Singh ◽  
S.P. Harsha
Keyword(s):  
Plate Theory ◽  
Functionally Graded ◽  
Complex Nature ◽  
Thickness Direction ◽  
Complex Solution ◽  
Functionally Graded Plate ◽  
Classical Plate Theory ◽  
Bending Analysis ◽  
Von Karman ◽  
Non Linear

Abstract The present study is based on the nonlinear bending analysis of an FGM plate with Von-Karman strain based on the non-linear classical plate theory (NLCPT) with in-plane displacement and moderate rotation. Non-linear bending analysis based on stresses and transverse deflections is then carried out for the plate for the complex solution obtained using an analytical method viz. Navier’s method. The equations of motion and boundary conditions are obtained using the Principle of Minimum Potential Energy (PMPE) method and material property is graded in thickness direction according to simple power-law distribution in terms of volume fractions of the constituents. The effect of the span-to-thickness ratio and FGM exponent on the maximum central deflection and stresses are studied. The results show that the response is transitional with respect to ceramic and metal and the complex solution predicts the real behavior of stresses and deflections in the functionally graded plate. The functionally graded plate is found to be more effective for moderately thick and thick plates, which is inferred by a complex nature of the solution. For FGM plates, the transverse deflection is in-between to that of metal and ceramic rich plates. The complex nature of the solution also gives information about the stress distribution in the thickness direction.

NONLINEAR BENDING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER PRESSURE LOADS USING A FOUR VARIABLE REFINED PLATE THEORY

2014 ◽  
Vol 11 (04) ◽  
pp. 1350062 ◽  
Author(s):  
MOHAMED ATIF BENATTA ◽  
ABDELHAKIM KACI ◽  
ABDELOUAHED TOUNSI ◽  
MOHAMMED SID AHMED HOUARI ◽  
KARIMA BAKHTI ◽  
...  
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Refined Plate Theory ◽  
Von Karman ◽  
Von Kármán

The novelty of this paper is the use of four variable refined plate theory for nonlinear analysis of plates made of functionally graded materials. The plates are subjected to pressure loading and their geometric nonlinearity is introduced in the strain–displacement equations based on Von–Karman assumptions. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The fundamental equations for functionally graded plates are obtained using the Von–Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for functionally graded plates are given in dimensionless graphical forms; and the effects of material properties on deflections and stresses are determined. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the CPT, but are almost comparable to those obtained using higher order theories having more number of unknown functions.

On Large Deflection of Symmetric Composite Plates under Static Loading

1986 ◽  
Vol 200 (1) ◽  
pp. 13-19 ◽  
Author(s):  
M Gorji
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Lateral Displacement ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Classical Plate Theory ◽  
Maximum Displacement ◽  
Von Karman ◽  
Non Linear ◽  
Von Kármán

The effect of transverse shear deformation on bending of elastic symmetric laminated composite plates undergoing large deformation (in the Von Karman sense) is considered in the present paper. The non-linear terms of the lateral displacement are considered as an additional set of lateral loads acting on the plate. The solution of a Von Karman type plate is therefore reduced to that of an equivalent plate with small displacements. This method offers an alternative technique for obtaining non-linear solutions to plate problems. The solutions of a number of example problems indicate that the non-linear shear deformation theory results, as expected, in higher values of the lateral displacement than the non-linear solutions from the classical plate theory. The difference in the values of the maximum displacement from both solutions, however, remains essentially constant beyond a certain value of the load. It is also noted that the linear and non-linear solutions deviate at a low value of w/h (w = maximum lateral displacement, h = thickness). Consequently, the extent of w/h within which the small deflection theory is applicable to composite plates is much lower than the value of 0.4 typically used for isotropic plates and depends, in general, upon lamination geometry and the degree of anisotropy.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

On the High-Temperature Free Vibration Analysis of Elastically Supported Functionally Graded Material Plates Under Mechanical In-PlaneForce Via GDQR

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Roshan Lal ◽  
Rahul Saini
Keyword(s):  
Mechanical Properties ◽  
Plate Theory ◽  
Elastic Equilibrium ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Axisymmetric Vibration ◽  
Thickness Direction ◽  
Classical Plate Theory ◽  
Linear Temperature

In this article, the effect of Pasternak foundation on free axisymmetric vibration of functionally graded circular plates subjected to mechanical in-plane force and a nonlinear temperature distribution (NTD) along the thickness direction has been investigated on the basis of classical plate theory. The plate material is graded in thickness direction according to a power-law distribution and its mechanical properties are assumed to be temperature-dependent (TD). At first, the equation for thermo-elastic equilibrium and then equation of motion for such a plate model have been derived by Hamilton's principle. Employing generalized differential quadrature rule (GDQR), the numerical values of thermal displacements and frequencies for clamped and simply supported plates vibrating in the first three modes have been computed. Values of in-plane force parameter for which the plate ceases to vibrate have been reported as critical buckling loads. The effect of temperature difference, material graded index, in-plane force, and foundation parameters on the frequencies has been analyzed. The benchmark results for uniform and linear temperature distributions (LTDs) have been computed. A study for plates made with the material having temperature-independent (TI) mechanical properties has also been performed as a special case. Comparison of results with the published work has been presented.

Exact Relationships between Eigenvalues of FGM Circular Plates Based on RPT and those of Isotropic Homogeneous Circular Plates Based on CPT

2007 ◽  
Vol 353-358 ◽  
pp. 3002-3005
Author(s):  
Lian Sheng Ma ◽  
Lei Wu
Keyword(s):  
Eigenvalue Problem ◽  
Plate Theory ◽  
Functionally Graded ◽  
Classical Solutions ◽  
Transverse Shear Deformation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Third Order ◽  
Classical Plate Theory ◽  
Graded Material

Based on the mathematical similarity of the eigenvalue problem of the Reddy’s third-order plate theory (RPT) and the classical plate theory (CPT), relationships between the solutions of axisymmetric vibration or buckling of functionally graded material (FGM) circular plates based on RPT and those of isotropic homogeneous circular plates based on CPT are presented, from which one can easily obtain the RPT solutions of axisymmetric vibration or buckling of FGM circular plates expressed in terms of the well-known CPT solutions of isotropic circular plates without much tedious mathematics. Effects of rotary inertia are not considered in the present analysis. The relationships obtained from the present analysis may be used to check the validity, convergence and accuracy of numerical results of FGM plates based on RPT, and also show clearly the intrinsic features of the effect of transverse shear deformation on the classical solutions.

Vibration Analysis of Rectangular Functionally Graded Plate Bonded With PZT5 Sensor/Actuator

2010 ◽  
Author(s):  
M. H. Kargarnovin ◽  
N. S. Viliani
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Feedback Gain ◽  
Laminated Plate ◽  
Functionally Graded Plate ◽  
Sensor Actuator

The vibration of FG plate embedded with PZT5 rectangular patches on the top and/or the bottom surface(s) as actuators/sensors is investigated. Based on the classical laminated plate theory, the governing differential equations of motion are derived under a variable electric charge. The equation of motion for PZT5 patch is obtained and solved. The effect of feedback gain and FGM volume fraction exponent on the plate frequency and its deflection are studied. It is noticed that increasing the feedback gain leads to the reduction of frequency and displacement. Moreover, by increasing the value of the FGM volume fraction exponent the resonant frequency decreases.

scholarly journals Nonlinear Donati compatibility conditions for the nonlinear Kirchhoff–von Kármán–Love plate theory

2013 ◽  
Vol 351 (9-10) ◽  
pp. 405-409 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Giuseppe Geymonat ◽  
Françoise Krasucki
Keyword(s):  
Plate Theory ◽  
Compatibility Conditions ◽  
Von Karman ◽  
Von Kármán

Nonlinear Vibration of Rotating Thin Disks

2000 ◽  
Vol 122 (4) ◽  
pp. 376-383 ◽  
Author(s):  
Albert C. J. Luo ◽  
C. D. Mote,
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Nonlinear Effects ◽  
Linear Vibration ◽  
Rotating Disks ◽  
Nodal Diameter ◽  
Von Karman ◽  
Thin Disks ◽  
Von Kármán

The response and natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the new plate theory proposed by Luo in 1999. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish and for the von Karman model when the nonlinear effects are modified. They are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers become larger. The critical speeds of the softening disks decrease with increasing deflection amplitudes. [S0739-3717(00)02004-3]

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