Thermal Buckling of Simply Supported FGM Square Plates

2011 ◽  
Vol 61 ◽  
pp. 25-32 ◽  
Author(s):  
M. Bouazza ◽  
A. Tounsi ◽  
E.A. Adda-Bedia ◽  
A. Megueni
Keyword(s):  
Mechanical Properties ◽  
Temperature Rise ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Thermal Buckling ◽  
Uniform Temperature ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
First Order

Thermal buckling behaviour of FGM square plates with simply supported edges has been studied in this note using the classic plate theory (CPT). It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power-law FGM (simply called P-FGM) and sigmoid FGM (S-FGM). The plate is assumed to uniform temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of FGM. The results are compared with the results of the first order shear deformation theory.

scholarly journals Review on Thermal Buckling of Symmetric Cross-Ply Laminated Plate

2020 ◽  
pp. 327-333
Author(s):  
Balram Yadav ◽  
Simant ◽  
Shivendra Kumar Yadav
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Thermal Buckling ◽  
Laminated Plate ◽  
Uniform Temperature ◽  
First Order ◽  
Aspect Ratios

In the present work thermal buckling of symmetric cross-ply composite laminates is investigated. In this study, a square plate element is employed for the thermal buckling analysis of composite laminated plates. The maximum buckling temperature of symmetric cross-ply laminates under various sides to thickness ratios, aspect ratios, stacking sequence and boundary condition are studied in detail. The maximum buckling temperature analysis of square composite eight and four layered plates under uniform temperature rise is investigated using the classical laminated plate theory & first order shear deformation theory and material properties (Stiffnesses, Poisson’s ratio and Coefficient of thermal expansion) are considered to be temperature dependent. The classical laminated plate theory and first order shear deformation theory in conjunction with the Rayleigh-Ritz method is used for the evaluation of the thermal buckling parameters of structures made out of graphite fibers with an epoxy matrix. The post-buckling response of symmetrically cross-ply laminated composite plates subjected to a combination of uniform temperature distribution through the thickness and in-plane compressive edge loading is presented. The maximum buckling temperature is obtained from the solution. The computing is done by using MATLAB.

Comparison of First-Order Shear and Plane Strain Assumptions in Warpage Prediction of Simply Supported Printed Wiring Boards

2000 ◽  
Vol 123 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Yarom Polsky ◽  
I. Charles Ume
Keyword(s):  
Plane Strain ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Transverse Load ◽  
Transverse Shear Strain ◽  
Printed Wiring Board ◽  
Simply Supported ◽  
First Order ◽  
Support Conditions ◽  
Wiring Board

The influence of transverse shear strain in the lamination theory modeling of Printed Wiring Board (PWB) deflection due to support conditions was examined. The in-plane mechanical properties of the core materials of a commercial PWB were measured as a function of temperature. Classical laminated plate theory and first-order shear deformation theory solutions for the out-of-plane deflection of a bare board configuration with two opposite edges simply supported and the remaining edges free were obtained. The weight of the board was approximated as a distributed transverse load. The effect of material property decrease with temperature and FR-4 layer thickness were examined to compare first-order shear and plane strain assumptions for the predicted warpage.

Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates

2005 ◽  
Vol 72 (6) ◽  
pp. 809-817 ◽  
Author(s):  
Jun-Sik Kim ◽  
Maenghyo Cho
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Sandwich Plates ◽  
First Order ◽  
Transverse Shear Strains

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

THERMAL BUCKLING OF CLAMPED CYLINDRICAL PANELS BASED ON FIRST-ORDER SHEAR DEFORMATION THEORY

2004 ◽  
Vol 04 (03) ◽  
pp. 313-336 ◽  
Author(s):  
ABDULLATEEF M. AL-KHALEEFI
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Analytical Approach ◽  
Solution Method ◽  
Shear Deformation Theory ◽  
Cylindrical Panel ◽  
Thermal Buckling ◽  
First Order ◽  
Cylindrical Panels ◽  
Dimensional Parameters

Based on the first-order shear deformation shell theory, an analytical approach is developed to predict the thermal buckling response of an all-edge clamped cylindrical panel. The analytical approach adopts a double Fourier solution method suitable for cylindrical panels. The present solutions are compared with the finite element solutions obtained using ANSYS. The effects of various dimensional parameters are included in the study.

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.

scholarly journals Some Inconsistencies in the Nonlinear Buckling Plate Theories—FSDT, S-FSDT, HSDT

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2154
Author(s):  
Zbigniew Kolakowski ◽  
Jacek Jankowski
Keyword(s):  
Shear Deformation ◽  
Composite Structures ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Nonlinear Problems ◽  
Classical Plate Theory ◽  
Nonlinear Buckling ◽  
First Order ◽  
Membrane Components

Bending and membrane components of transverse forces in a fixed square isotropic plate under simultaneous compression and transverse loading were established within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), and the classical plate theory (CPT). Special attention was drawn to the fact that bending components were accompanied by transverse deformations, whereas membrane components were not, i.e., the plate was transversely perfectly rigid. In the FSDT and the S-FSDT, double assumptions concerning transverse deformations in the plate hold. A new formulation of the differential equation of equilibrium with respect to the transverse direction of the plate, using a variational approach, was proposed. For nonlinear problems in the mechanics of thin-walled plates, a range where membrane components should be considered in total transverse forces was determined. It is of particular significance as far as modern composite structures are concerned.

scholarly journals Vibration and buckling analysis of functionally graded sandwich plates with improved transverse shear stiffness based on the first-order shear deformation theory

2013 ◽  
Vol 228 (12) ◽  
pp. 2110-2131 ◽  
Author(s):  
Trung-Kien Nguyen ◽  
Thuc P Vo ◽  
Huu-Tai Thai
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Shear Stiffness ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Simply Supported ◽  
First Order

An improved transverse shear stiffness for vibration and buckling analysis of functionally graded sandwich plates based on the first-order shear deformation theory is proposed in this paper. The transverse shear stress obtained from the in-plane stress and equilibrium equation allows to analytically derive an improved transverse shear stiffness and associated shear correction factor of the functionally graded sandwich plate. Sandwich plates with functionally graded faces and both homogeneous hardcore and softcore are considered. The material property is assumed to be isotropic at each point and vary through the plate thickness according to a power-law distribution of the volume fraction of the constituents. Equations of motion and boundary conditions are derived from Hamilton’s principle. The Navier-type solutions are obtained for simply supported boundary conditions, and exact formulae are proposed and compared with the existing solutions to verify the validity of the developed model. Numerical results are obtained for simply supported functionally graded sandwich plates made of three sets of material combinations of metal and ceramic, Al/Al2O3, Al/SiC and Al/WC to investigate the effects of the power-law index, thickness ratio of layer, material contrast on the shear correction factors, natural frequencies and critical buckling loads as well as load–frequency curves.

scholarly journals Effect of Membrane Components of Transverse Forces on Magnitudes of Total Transverse Forces in the Nonlinear Stability of Plate Structures

Materials ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5262
Author(s):  
Zbigniew Kołakowski ◽  
Jacek Jankowski
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
The Finite Element Method ◽  
Classical Plate Theory ◽  
Plate Structures ◽  
First Order ◽  
Membrane Components ◽  
Membrane Deformations

For an isotropic square plate subject to unidirectional compression in the postbuckling state, components of transverse forces in bending, membrane transverse components and total components of transverse forces were determined within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), the classical plate theory (CPT) and the finite element method (FEM). Special attention was drawn to membrane components of transverse forces, which are expressed with the same formulas for the first three theories and do not depend on membrane deformations. These components are nonlinearly dependent on the plate deflection. The magnitudes of components of transverse forces for the four theories under consideration were compared.

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