A simple and accurate sandwich plate theory accounting for transverse normal strain and interfacial stress continuity

2014 ◽  
Vol 107 ◽  
pp. 620-628 ◽  
Author(s):  
X. Wang ◽  
G. Shi
Keyword(s):  
Sandwich Plate ◽  
Plate Theory ◽  
Interfacial Stress ◽  
Normal Strain ◽  
Transverse Normal Strain

A Composite Plate Theory With Rotatory Inertia, Transverse Shear, and Normal Stress Effects

1991 ◽  
Vol 113 (2) ◽  
pp. 127-132 ◽  
Author(s):  
G. Z. Voyiadjis ◽  
P. D. Panera
Keyword(s):  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Composite Plates ◽  
Offshore Structures ◽  
Refined Theory ◽  
Normal Strain ◽  
Rotatory Inertia ◽  
Stress Effects ◽  
Transverse Normal Strain

A refined theory for the flexural motions of composite plates is presented. The theory incorporates rotatory inertia in addition to the influence of transverse normal strain, transverse normal stress, and transverse shear. This is of primary interest for the analysis of offshore structures as well as piping analysis. The classical wave propagation problem is used to test the proposed theory. The results indicate the influence of the transverse normal strain on the wave speed for large values of h/λ. The shear coefficient obtained from the proposed theory has a constant magnitude as opposed to the undetermined coefficient form in previous flexural motion formulations.

Vibrations of an Incompressible Linearly Elastic Plate Using Discontinuous Finite Element Basis Functions for Pressure

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Lisha Yuan ◽  
Romesh C. Batra
Keyword(s):  
Finite Element ◽  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Plate Theory ◽  
Mass Matrix ◽  
Basis Functions ◽  
Mode Shapes ◽  
Normal Strain ◽  
Simply Supported ◽  
Transverse Normal Strain

Abstract We numerically analyze, with the finite element method, free vibrations of incompressible rectangular plates under different boundary conditions with a third-order shear and normal deformable theory (TSNDT) derived by Batra. The displacements are taken as unknowns at the nodes of a 9-node quadrilateral element and the hydrostatic pressure at four interior nodes. The plate theory satisfies the incompressibility condition, and the basis functions satisfy the Babuska-Brezzi condition. Because of the singular mass matrix, Moler's QZ algorithm (also known as the generalized Schur decomposition) is used to solve the resulting eigenvalue problem. Computed results for simply supported, clamped, and clamped-free rectangular isotropic plates agree well with the corresponding analytical frequencies of simply supported plates and with those found using the commercial software, abaqus, for other edge conditions. In-plane modes of vibrations are clearly discerned from mode shapes of square plates of aspect ratio 1/8 for all three boundary conditions. The magnitude of the transverse normal strain at a point is found to equal the sum of the two axial strains implying that higher-order plate theories that assume null transverse normal strain will very likely not provide good solutions for plates made of rubberlike materials that are generally taken to be incompressible. We have also compared the presently computed through-the-thickness distributions of stresses and the hydrostatic pressure with those found using abaqus.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

A refined sinusoidal model for functionally graded plates subjected to thermomechanical loading

2018 ◽  
Vol 53 (14) ◽  
pp. 1883-1896
Author(s):  
Ren Xiaohui ◽  
Wu Zhen
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Normal Strain ◽  
Sinusoidal Model ◽  
Proposed Model ◽  
Graded Material ◽  
Plane Displacement ◽  
Stress Free Boundary ◽  
Transverse Normal Strain

A refined sinusoidal model considering transverse normal strain has been developed for thermoelastic analysis of functionally graded material plate. Although transverse normal strain has been considered, the additional displacement parameters are not increased as transverse normal strain only includes the thermal expansion coefficient and thermal loading. Moreover, the merit of the previous sinusoidal model satisfying tangential stress-free boundary conditions on the surfaces can be maintained. It is important that the effects of transverse normal thermal deformation are incorporated in the in-plane displacement field, which can actively influence the accuracy of in-plane stresses. To assess the performance of the proposed model, the thermoelastic behaviors of functionally graded material plates with various configurations have been analyzed. Without increase of displacement variables, accuracy of the proposed model can be significantly improved by comparing to the previous sinusoidal model. Agreement between the present results and quasi-dimensional solutions are very good, and the proposed model only includes the five displacement variables which can illustrate the accuracy and effectiveness of the present model. In addition, new results using several models considered in this paper have been presented, which can serve as a reference for future investigations.

A Refined Theory for Laminated Anisotropic, Cylindrical Shells

1974 ◽  
Vol 41 (2) ◽  
pp. 471-476 ◽  
Author(s):  
J. M. Whitney ◽  
C.-T. Sun
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Theory Of Elasticity ◽  
Small Radius ◽  
Refined Theory ◽  
Normal Strain ◽  
Governing Equations ◽  
Transverse Normal Strain ◽  
Anisotropic Cylindrical Shell ◽  
Good Agreement

A set of governing equations and boundary conditions are derived which describe the static deformation of a laminated anisotropic cylindrical shell. The theory includes both transverse shear deformation and transverse normal strain, as well as expansional strains. The validity of the theory is assessed by comparing solutions obtained from the shell theory to results obtained from exact theory of elasticity. Reasonably good agreement is observed and both shear deformation and transverse normal strain are shown to be of importance for shells having a relatively small radius-to-thickness ratio.

Calculation for Elastic Global Buckling of Sandwich Plates with Ribs

2012 ◽  
Vol 188 ◽  
pp. 25-30 ◽  
Author(s):  
Qi Chao Xue ◽  
Guang Ping Zou ◽  
Ye Wu ◽  
Hai Lin Xiong ◽  
Meng Chai
Keyword(s):  
Energy Method ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Sandwich Plates ◽  
Buckling Stress ◽  
Global Buckling ◽  
Simple Support ◽  
Rectangular Sandwich Plate ◽  
Two Sides ◽  
Rectangular Sandwich Plates

Based on Reissner’s sandwich plate theory, the critical globlal buckling equation of sandwich plate with ribs is deduced by energy method under simple support boundary conditions. And the critical buckling solution is obtained and discussed here. Afterwards a rectangular sandwich plate with steel faceplate and polyurthane core is taken as an example. The influence on critical global buckling stress with different inertia moments in rectangular sandwich plates are discussed. simularly the effect of the lengh ratio of two sides and the thickness of rectangular sandwich plate are also studied.

FLUTTER SUPPRESSION OF AN ELASTICALLY SUPPORTED PLATE WITH ELECTRO-RHEOLOGICAL FLUID CORE UNDER YAWED SUPERSONIC FLOWS

2013 ◽  
Vol 13 (01) ◽  
pp. 1250073 ◽  
Author(s):  
SEYYED M. HASHEMINEJAD ◽  
M. NEZAMI ◽  
M. E. ARYAEE PANAH
Keyword(s):  
Elastic Foundation ◽  
Sandwich Plate ◽  
Sliding Mode ◽  
Plate Theory ◽  
System Response ◽  
First Order ◽  
Fluid Core ◽  
Pasternak Elastic Foundation ◽  
Elastically Supported ◽  
Er Fluid

This paper investigates the active control of the supersonic flutter motion of an elastically supported rectangular sandwich plate, which has a tunable electrorheological (ER) fluid core and rests on a Winkler–Pasternak elastic foundation, subjected to an arbitrary flow of various yaw angles. The classical thin plate theory is adopted. The ER fluid core is modeled as a first order Kelvin–Voigt material, and the quasi-steady first order supersonic piston theory is employed for the aerodynamic loading. The generalized Fourier expansions in conjunction with Galerkin method are employed to formulate the governing equations in the state-space domain. The critical dynamic pressures at which unstable panel oscillations occur are obtained for a square sandwich plate, with or without an interacting soft/stiff elastic foundation, for selected applied electric field strengths and flow yaw angles. The Runge–Kutta method is then used to calculate the open-loop aeroelastic response of the system in various basic loading configurations. Subsequently, a sliding mode control (SMC) synthesis is set up to actively suppress the closed loop system response in yawed supersonic flight conditions with imposed excitations. The results demonstrate the performance, effectiveness, and insensitivity with respect to the spillover of the proposed SMC-based control system.

Boundary Integral Equation Methods for a Refined Model of Elastic Plates

2006 ◽  
Vol 11 (6) ◽  
pp. 642-654
Author(s):  
Radu Mitric ◽  
Christian Constanda
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Normal Strain ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Neumann Problems ◽  
Integral Equation Methods ◽  
Transverse Normal Strain ◽  
System Of Equilibrium Equations

A theory of bending of elastic plates is considered, in which the effect of transverse shear deformation and transverse normal strain are taken into account through a specific form of the displacement field. It is shown that the system of equilibrium equations is elliptic and that Betti and Somigliana formulae can be established, which permit the solution of the interior and exterior Dirichlet and Neumann problems by means of boundary integral equation methods.

Natural frequency, damping and forced responses of sandwich plates with viscoelastic core and graphene nanoplatelets reinforced face sheets

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1165-1177 ◽  
Author(s):  
Ali Mohseni ◽  
Meisam Shakouri
Keyword(s):  
Sandwich Plate ◽  
Effective Properties ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Graphene Nanoplatelets ◽  
Complex Eigenvalue ◽  
Viscoelastic Core ◽  
Forced Vibration Analysis ◽  
Forced Responses

The free and forced vibration analysis of a sandwich plate with the viscoelastic core and face layers reinforced functionally with multilayered graphene nanoplatelets is presented. Different graphene nanoplatelet distributions are considered through the thickness, and the effective properties of the graphene reinforced nanocomposite are obtained by the rule of mixture. The equations of motion are extracted using Hamilton’s principle and assuming the classical thin plate theory for face layers and the first-order shear deformation theory for the thick viscoelastic core. Assuming the simply-supported boundary condition for all edges, the displacement components are proposed by Fourier series and the complex eigenvalue problem is solved to obtain the natural frequencies as well as the loss factors. The results are validated with available investigations, and effects of some important parameters on the free and forced responses of the sandwich plate are studied.

BENDING OF FGM PLATES BY A SIMPLIFIED FOUR-UNKNOWN SHEAR AND NORMAL DEFORMATIONS THEORY

2013 ◽  
Vol 05 (02) ◽  
pp. 1350020 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Virtual Work ◽  
Plate Thickness ◽  
Present Theory ◽  
Normal Strain ◽  
Principle Of Virtual Work ◽  
Governing Equations ◽  
Shear Strains ◽  
Transverse Normal Strain ◽  
Transverse Shear Strains ◽  
Bending Response

The bending response of FGM plates is presented based upon a simplified shear and normal deformations theory. The present simplified theory is accounted for an adequate distribution of transverse shear strains through the plate thickness and tangential stress-free on the plate surfaces. The effect of transverse normal strain is also included. The number of unknown functions involved here is only four as against six in case of other shear and normal deformations theories. The principle of virtual work is employed to derive the governing equations. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory. Additional results for all stresses are investigated through-the-thickness of the FGM plate.

Sign in / Sign up

Export Citation Format

Share Document