scholarly journals Structural Imposed Load Analysis of Isotropic Rectangular Plate Carrying a Uniformly Distributed Load Using Refined Shear Plate Theory

2021 ◽  
Vol 6 (4) ◽  
Author(s):  
Festus C. Onyeka ◽  
Chidoebere D. Nwa-David ◽  
Emmanuel E. Arinze
Keyword(s):  
Shear Deformation ◽  
Rectangular Plate ◽  
Plate Theory ◽  
Plate Thickness ◽  
Variational Calculus ◽  
Present Theory ◽  
Numerical Comparison ◽  
Analysis And Design ◽  
Distributed Load ◽  
Uniformly Distributed Load

This presents the static flexural analysis of a three edge simply supported, one support free (SSFS) rectangular plate under uniformly distributed load using a refined shear deformation plate theory. The shear deformation profile used, is in the form of third order. The governing equations were determined by the method of energy variational calculus, to obtain the deflection and shear deformation along the direction of x and y axis. From the formulated expression, the formulars for determination of the critical lateral imposed load of the plate before deflection reaches the specified maximum specified limit  and its corresponding critical lateral imposed load before plate reaches an elastic yield stress  is established. The study showed that the critical lateral imposed load decreased as the plates span increases, the critical lateral imposed load increased as the plate thickness increases, as the specified thickness of the plate increased, the value of critical lateral imposed load increased and increase in the value of the allowable deflection value required for the analysis of the plate reduced the chances of failure of a structural member. This approach overcomes the challenges of the conventional practice in the structural analysis and design which involves checking of deflection and shear after design; the process which is proved unreliable and time consuming. It is concluded that the values of critical lateral load obtained by this theory achieve accepted transverse shear stress to the depth of the plate variation in predicting the flexural characteristics for an isotropic rectangular SSFS plate. Numerical comparison was conducted to verify and demonstrate the efficiency of the present theory, and they agreed with previous studies. This proved that the present theory is reliable for the analysis of a rectangular plate. Keywords— Allowable deflection, critical imposed load, energy method, plate theories, shear deformation, SSFS rectangular plate

A New First-Order Shear Deformation Theory for Free Vibrations of Rectangular Plate

2015 ◽  
Vol 07 (01) ◽  
pp. 1550008 ◽  
Author(s):  
Wei Xiang ◽  
Yufeng Xing
Keyword(s):  
Shear Deformation ◽  
Rectangular Plate ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Present Theory ◽  
Free Vibrations ◽  
Variable Theory ◽  
First Order ◽  
Geometrical Constraints

A new first-order shear deformation theory (FSDT) with pure bending deflection and shearing deflection as two independent variables is presented in this paper for free vibrations of rectangular plate. In this two-variable theory, the shearing deflection is regarded as the only fundamental variable by which the total deflection and bending deflection can be expressed explicitly. In contrast with the conventional three-variable first-order shear plate theory, present variationally consistent theory derived by using Hamiltonian variational principle can uniquely define the bending and the shearing deflections, and give two rotations by the differentiations of bending deflection. Due to more restrictive geometrical constraints on rotations and boundary conditions, the obtained natural frequencies are equal to or higher than those by conventional FSDT for the rectangular plate with at least one pair of opposite edges simply supported. This new theory is of considerable significance in theoretical sense for giving a simple two-variable FSDT which is variational consistent and involve rotary inertia and shear deformation. The relation and differences of present theory with conventional FSDT and other relative formulations are discussed in detail.

ON VIBRATION OF FUNCTIONALLY GRADED PLATES ACCORDING TO A REFINED TRIGONOMETRIC PLATE THEORY

2005 ◽  
Vol 05 (02) ◽  
pp. 279-297 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Shear Deformation ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Series Representation ◽  
Free Vibration Analysis ◽  
Present Theory ◽  
Functionally Graded ◽  
Graded Material

The displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory. This trigonometric shear deformation plate theory is used to perform free-vibration analysis of a simply supported functionally graded thick plate. Lamé's coefficients and density for the material of the plate are assumed to vary in the thickness direction only. Effects of rotatory inertia are considered in the present theory and the vibration natural frequencies are investigated. The results obtained from this theory are compared with those obtained from a 3D elasticity analysis and various equivalent theories that are available. A detailed analysis is carried out to study the various natural frequencies of functionally graded material plates. The influences of the transverse shear deformation, plate aspect ratio, side-to-thickness ratio and volume fraction distributions are investigated.

A NEW TRIANGULAR ELEMENT BASED ON HIGHER ORDER SHEAR DEFORMATION THEORY FOR FLEXURAL VIBRATION OF COMPOSITE PLATES

2002 ◽  
Vol 02 (02) ◽  
pp. 163-184 ◽  
Author(s):  
A. CHAKRABARTI ◽  
A. H. SHEIKH
Keyword(s):  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Higher Order ◽  
Triangular Element

A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis.

scholarly journals Analysis Bending Solutions of Clamped Rectangular Thick Plate

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yang Zhong ◽  
Qian Xu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Shear Deformation ◽  
Thick Plate ◽  
Plate Theory ◽  
Analytic Solutions ◽  
Higher Order ◽  
Numerical Comparison ◽  
Governing Equations ◽  
Partial Differential

The bending solutions of rectangular thick plate with all edges clamped and supported were investigated in this study. The basic governing equations used for analysis are based on Mindlin’s higher-order shear deformation plate theory. Using a new function, the three coupled governing equations have been modified to independent partial differential equations that can be solved separately. These equations are coded in terms of deflection of the plate and the mentioned functions. By solving these decoupled equations, the analytic solutions of rectangular thick plate with all edges clamped and supported have been derived. The proposed method eliminates the complicated derivation for calculating coefficients and addresses the solution to problems directly. Moreover, numerical comparison shows the correctness and accuracy of the results.

Studies Regarding the Shear Correction Factor in the Mindlin Plate Theory for Sandwich Plates

2017 ◽  
Vol 21 ◽  
pp. 301-308 ◽  
Author(s):  
Mihai Vrabie ◽  
Radu Chiriac ◽  
Sergiu Andrei Băetu
Keyword(s):  
Shear Deformation ◽  
Correction Factor ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Stiffness ◽  
Laminated Plates ◽  
Mindlin Plate ◽  
Sandwich Plates ◽  
Shear Correction Factor ◽  
Mindlin Plate Theory

The displacement field from the first-order shear deformation plate theory (FSDT) extents the cinematic aspect of the classical theory of laminated plates (CLPT), including a transverse shear deformation, considered constant on the plate thickness. In order to correct this aspect, in FSDT (named also the Mindlin plate theory) a coefficient Ks was inserted, named shear correction factor, used as a multiplier in the shear stiffness equation of the plate. In this paper are presented the most popular methods for determination of the shear correction factor, identifying the differences between them. To emphasize the influence of the shear correction factor on the stress response, a numerical parametric study was done on some sandwich plates filled with polyurethane foam. The processing of the obtained results allow drawing some conclusions useful in the designing of this type of sandwich plates.

Buckling of Functionally Graded Circular/Annular Plates Based on the First-Order Shear Deformation Plate Theory

2004 ◽  
Vol 261-263 ◽  
pp. 609-614 ◽  
Author(s):  
L.S. Ma ◽  
Tie Jun Wang
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Outer Radius ◽  
Functionally Graded ◽  
First Order ◽  
Annular Plates

Based on the first-order shear deformation theory of plate, governing equations for the axisymmetric buckling of functionally graded circular/annular plates are derived. The coupled deflections and rotations in the pre-buckling state of the plates are neglected in analysis. The material properties vary continuously through the thickness of the plate, and obey a power law distribution of the volume fraction of the constituents. The resulting differential equations are numerically solved by using a shooting method. The critical buckling loads of circular and annular plates are obtained, which are compared with those obtained from the classical plate theory. Effects of material properties, ratio of inter to outer radius, ratio of plate thickness to outer radius, and boundary conditions on the buckling behavior of FGM plates are discussed.

The Effect of Transverse Shear Deformation on the Bending of Elastic Plates

1945 ◽  
Vol 12 (2) ◽  
pp. A69-A77 ◽  
Author(s):  
Eric Reissner
Keyword(s):  
General Solution ◽  
Rectangular Plate ◽  
Transverse Shear ◽  
Plate Theory ◽  
Infinite Plate ◽  
Present Theory ◽  
System Of Equations ◽  
Elastic Plates ◽  
Classical Plate Theory

Abstract A system of equations is developed for the theory of bending of thin elastic plates which takes into account the transverse shear deformability of the plate. This system of equations is of such nature that three boundary conditions can and must be prescribed along the edge of the plate. The general solution of the system of equations is obtained in terms of two plane harmonic functions and one function which is the general solution of the equation Δψ − (10/h2)ψ = 0. The general results of the paper are applied (a) to the problem of torsion of a rectangular plate, (b) to the problems of plain bending and pure twisting of an infinite plate with a circular hole. In these two problems important differences are noted between the results of the present theory and the results obtained by means of the classical plate theory. It is indicated that the present theory may be applied to other problems where the deviations from the results of classical plate theory are of interest. Among these other problems is the determination of the reactions along the edges of a simply supported rectangular plate, where the classical theory leads to concentrated reactions at the corners of the plate. These concentrated reactions will not occur in the solution of the foregoing problem by means of the theory given in the present paper.

Refined hyperbolic shear deformation plate theory

2014 ◽  
Vol 229 (15) ◽  
pp. 2675-2686 ◽  
Author(s):  
K Nareen ◽  
RP Shimpi
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Dimensional Theory ◽  
Classical Plate Theory ◽  
Shear Deformation Plate Theory ◽  
Elasticity Solutions

The paper presents a novel shear deformation plate theory involving only two variables. Taking a cue from exact three-dimensional theory of elasticity solutions for a plate, hyperbolic functions are used for describing displacement variation across plate thickness. The theory involves only two governing equations, which are uncoupled for statics and are only inertially coupled for dynamics. The shear stress free surface conditions are satisfied. No shear correction factor is required. The theory is variationally consistent, has a strong similarity with classical plate theory, and is simple, yet accurate. Illustrative examples for free vibration and for static flexure demonstrate the effectiveness of the theory.

Experimental Investigation of Nonlinear Vibration of a Thin Rectangular Plate

2019 ◽  
Vol 11 (06) ◽  
pp. 1950059 ◽  
Author(s):  
Sohayb Abdulkerim ◽  
Athanasios Dafnis ◽  
Hans-G Riemerdes
Keyword(s):  
Rectangular Plate ◽  
Plate Theory ◽  
Plate Thickness ◽  
Extraction Procedure ◽  
Time History ◽  
Laser Vibrometer ◽  
Classical Plate Theory ◽  
Thin Rectangular Plate ◽  
Sinusoidal Input ◽  
History Of

In this paper, the geometrical nonlinear vibrations of a rectangular plate have been investigated experimentally and numerically. The experiment was conducted on a thin rectangular plate. The plate was excited close to the first fundamental natural frequency. The time history of velocities of the central point has been measured by using a laser vibrometer. While the numerical investigation has been carried using the Finite Element Method (FEM), the numerical results are validated by analytical and experimental results. In order to develop and test the extraction procedure of the bifurcation plot of a dynamical system, a chaotic pendulum has been analyzed. Then, the same successful code has been used again for the experimental dynamics of the investigated plate. The plate has been forced with a sinusoidal input at a gradually stepped and increased amplitude. For every step, the phase portrait is determined, and then processed to extract the bifurcation map. The resulted map has shown successfully the linear range where the classical plate theory is adequate, and the boundary at which the transition to nonlinearity has occurred. The bifurcation has occurred when the lateral amplitude has reached 50% of the plate thickness.

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