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 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.

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.

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 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.

Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations

2018 ◽  
Vol 55 ◽  
pp. 42-56 ◽  
Author(s):  
Belkacem Kadari ◽  
Aicha Bessaim ◽  
Abdelouahed Tounsi ◽  
Houari Heireche ◽  
Abdelmoumen Anis Bousahla ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Scale Effects ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Higher Order ◽  
Small Scale ◽  
Classical Plate Theory

This work presents the buckling investigation of embedded orthotropic nanoplates by using a new hyperbolic plate theory and nonlocal small-scale effects. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modeled with only three unknowns and three governing equation as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal differential constitutive relations of Eringen is employed to investigate effects of small scale on buckling of the rectangular nanoplate. The elastic foundation is modeled as two-parameter Pasternak foundation. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns. Keywords: Buckling; orthotropic nanoplates; a simple 3-unknown theory; nonlocal elasticity theory; Pasternak’s foundations. * Corresponding author; [email protected]

Mechanical analysis of shrink-fitted thick FG cylinders based on first order shear deformation theory and FE simulation

2021 ◽  
pp. 095440622110127
Author(s):  
Mohammad Reza Salehi Kolahi ◽  
Hossein Rahmani ◽  
Hossein Moeinkhah
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Fe Simulation ◽  
Shear Deformation Theory ◽  
Mechanical Analysis ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
First Order ◽  
Analytical Functions ◽  
Plane Elasticity Theory

In this paper, the first order shear deformation theory is used to derive an analytical formulation for shrink-fitted thick-walled functionally graded cylinders. It is assumed that the cylinders have constant Poisson’s ratio and the elastic modulus varies radially along the thickness with a power function. Furthermore, a finite element simulation is carried out using COMSOL Multiphysics, which has the advantage of defining material properties as analytical functions. The results from first order shear deformation theory are compared with the findings of both plane elasticity theory and FE simulation. The results of this study could be used to design and manufacture for elastic shrink-fitted FG cylinders.

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