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.

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 A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

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.

scholarly journals Application of alternative II theory to vibration and stability analysis of thick rectangular plates (Isotropic and orthotropic)

2020 ◽  
Vol 39 (1) ◽  
pp. 52-62
Author(s):  
O.M. Ibearugbulem ◽  
S.I. Ebirim ◽  
U.C. Anya ◽  
L.O. Ettu
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequency ◽  
Deformation Theory ◽  
Thick Plate ◽  
Shape Function ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
First Order ◽  
Fundamental Natural Frequency

This work analysed the free vibration and stability of thick isotropic and orthotropic plates with SSSS and SSFS support conditions by applying the alternative II theory based on polynomial shape function. The total potential energy which was obtained by combining the strain energy and external work was reduced to three governing equations using Ritz method. Polynomial shape function which varies with Poisson’s ratio was substituted into the governing equation to obtain the fundamental natural frequency, linear frequency and critical buckling load. The values of frequencies of the first mode and critical loads obtained were compared with those obtained using first order shear deformation theory. For span depth ratio of 10, the fundamental linear frequency for orthotropic SSFS plate corresponding to modulus of elasticity ratios (E1/E2) of 10, 25 and 40 are 0.00156, 0.00219 and 0.00255Hz. The corresponding values using first order shear deformation theory are 0.00152, 0.00212 and 0.00245Hz. Keywords: Fundamental natural frequency, SSSS plate, SSFS plate, Ritz method, Orthotropic thick plate, Isotropic thick plate, Stability, Free vibration

BUCKLING ANALYSIS OF TAPERED COMPOSITE PLATES USING RITZ METHOD BASED ON FIRST-ORDER SHEAR DEFORMATION THEORY

2012 ◽  
Vol 12 (04) ◽  
pp. 1250030 ◽  
Author(s):  
SHAIKH AKHLAQUE-E-RASUL ◽  
RAJAMOHAN GANESAN
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Turbine Blades ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Width Ratio ◽  
First Order ◽  
Closed Form Analytical Solution

Tapered composite plates have various engineering applications such as helicopter yoke, robot arms and turbine blades in which the structure needs to be stiff at one end and flexible at another end. No closed form analytical solution of tapered composite plates using Ritz method based on first-order shear deformation theory (FSDT) is available at present. In the present paper, the buckling analysis of different types of composite plates with longitudinal-internal-ply-drop-off configuration is investigated using Ritz method. The buckling analysis of these plates is also conducted using ANSYS®. The efficiency and accuracy of the developed formulation are established in comparison with available solutions, where applicable. A detailed parametric study has been conducted on various taper and lay-up configurations, all made of NCT/301 graphite-epoxy, in order to investigate the effects of taper angle, length-to-height ratio, length-to-width ratio, boundary conditions, and taper and lay-up configurations.

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.

Peridynamic Analysis of Laminated Composite Plates Based on First-Order Shear Deformation Theory

2020 ◽  
Vol 12 (03) ◽  
pp. 2050031 ◽  
Author(s):  
Mehmet Dorduncu ◽  
Kadir Kaya ◽  
Omer Faruk Ergin
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations ◽  
First Order ◽  
Aspect Ratios

A nonlocal Peridynamic Differential Operator (PDDO) is presented for static analysis of laminated composite plates based on the First-order Shear Deformation Theory (FSDT). The equilibrium equations and boundary conditions of the FSDT were derived from the principle of virtual work. The local spatial derivatives in these equations were replaced with their nonlocal PD forms. The continuous transverse shear stresses were achieved by integrating the stress equilibrium equations through the thickness of the plate. This approach was validated against an existing analytical solution by considering a simply supported laminated composite plate under uniformly distributed sinusoidal load for different aspect ratios. The performance of this formulation was investigated by comparing through-the-thickness stress variations against the analytical solutions.

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