Delamination Effects in Circular Sandwich Plates With Laminated Faces of General Layup and a “Soft” Core

2001 ◽  
Author(s):  
Oded Rabinovitch ◽  
Yeoshua Frostig
Keyword(s):  
Sandwich Plate ◽  
Virtual Work ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Solution Procedure ◽  
Theory Of Elasticity ◽  
Soft Core ◽  
Sandwich Plates ◽  
Field Equations ◽  
Circular Sandwich Plates

Abstract The present study is concerned with the behavior of delaminated circular sandwich plates with a compressible “soft” core and composite laminated face sheets of general layup. The analysis follows the concepts of the High-Order Sandwich Plate Theory and employs the variational principle of virtual work for the derivation of the field equations of the fully bonded and delaminated regions. In the penny shaped disbonded region, the delaminated faces can slip horizontally with respect one to another, yet they may be in contact and resist vertical normal compressive stresses. The compressible core is considered using the 3D theory of elasticity and the lamination theory is employed for the modeling of the composite laminated face sheets. The formulation yields coordinate-dependent constitutive relations and governing equations and the solution procedure adopts the Galerkin method in the circumferential direction and the multiple-points shooting method in the radial direction. Numerical results regarding a typical delaminated sandwich plate are presented in terms of deformations and stresses. The results reveal the effect of the anisotropic laminated face sheets on the response of the structure and the influence of the delamination on the overall and, especially, the localized behavior of the plate.

Geometrically Nonlinear Deformation of Circular Sandwich Plates under Transversely Non-Uniform Temperature Rise

2007 ◽  
Vol 353-358 ◽  
pp. 1161-1164 ◽  
Author(s):  
Jing Ning Yang ◽  
Yong Gang Zhao ◽  
Ping Qiu ◽  
Cai Xue Liu
Keyword(s):  
Boundary Conditions ◽  
Temperature Rise ◽  
Sandwich Plate ◽  
Numerical Solutions ◽  
Plate Theory ◽  
Sandwich Plates ◽  
Geometrically Nonlinear ◽  
Uniform Temperature ◽  
Nonlinear Bending ◽  
Circular Sandwich Plates

Geometrically nonlinear bending and buckling of circular sandwich plates subjected to transversely non-uniform temperature rise is investigated in this paper. On the basis of sandwich plate theory, nonlinear equations governing the large thermal axis-symmetric deformations of circular sandwich plate in terms of the middle plane’s displacements are derived. Numerical solutions of the nonlinear boundary value problem are obtained by using the shooting method. Equilibrium paths and configurations for different boundary conditions and different values of materials and geometry parameters are illustrated. Numerical results show that the boundary conditions and the stiffness greatly effect critical buckling loads.

Free vibration analysis of multilayered composite and soft core sandwich plates resting on Winkler–Pasternak foundations

2016 ◽  
Vol 20 (2) ◽  
pp. 169-190 ◽  
Author(s):  
AM Zenkour ◽  
AF Radwan
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Plate Thickness ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Present Theory ◽  
Soft Core ◽  
Sandwich Plates

Free vibration of laminated composite and soft core sandwich plates resting on Winkler–Pasternak foundations using four-variable refined plate theory are presented. The theory accounts for the hyperbolic distribution of the transverse shear strains through the plate thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Equations of motion are derived from the dynamic version of the principle of virtual work. Navier technique is employed to obtain the closed-form solutions of antisymmetric cross-ply, angle-ply, and soft core laminates or soft core sandwich plates resting on elastic foundations. Numerical results obtained using present theory are compared with three-dimensional elasticity solutions and those computed using the first-order and the other higher-order theories. It can be concluded that the proposed theory is not only accurate, but also efficient in predicting the natural frequencies of laminated composite and soft core sandwich plates resting on Winkler–Pasternak foundations.

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.

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.

Stability Analysis of Laminated Soft Core Sandwich Plates Using Higher Order Zig-Zag Plate Theory

2015 ◽  
Vol 22 (11) ◽  
pp. 897-907 ◽  
Author(s):  
H. D. Chalak ◽  
Anupam Chakrabarti ◽  
Abdul Hamid Sheikh ◽  
Mohd. Ashraf Iqbal
Keyword(s):  
Stability Analysis ◽  
Plate Theory ◽  
Higher Order ◽  
Soft Core ◽  
Sandwich Plates

An analytical solution for bending, buckling and vibration responses of FGM sandwich plates

2017 ◽  
Vol 21 (2) ◽  
pp. 727-757 ◽  
Author(s):  
Rafik Meksi ◽  
Samir Benyoucef ◽  
Abdelkader Mahmoudi ◽  
Abdelouahed Tounsi ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Free Vibration ◽  
Transverse Shear ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Numerical Study ◽  
Functionally Graded ◽  
Solution Technique ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Vibration Responses

In this study, a new shear deformation plate theory is introduced to illustrate the bending, buckling and free vibration responses of functionally graded material sandwich plates. A new displacement field containing integrals is proposed which involves only four variables. Based on the suggested theory, the equations of motion are derived from Hamilton’s principle. This theory involves only four unknown functions and accounts for quasi-parabolic distribution of transverse shear stress. In addition, the transverse shear stresses are vanished at the top and bottom surfaces of the sandwich plate. The Navier solution technique is adopted to derive analytical solutions for simply supported rectangular sandwich plates. The accuracy and effectiveness of proposed model are verified by comparison with previous research. A detailed numerical study is carried out to examine the influence of the critical buckling loads, deflections, stresses, natural frequencies and sandwich plate type on the bending, buckling and free vibration responses of functionally graded sandwich plates.

Buckling Analysis of Soft-Core Composite Sandwich Plates Using 3D Finite Element Method

2011 ◽  
Vol 105-107 ◽  
pp. 1768-1772 ◽  
Author(s):  
Mohammad Mahdi Kheirikhah ◽  
Seyyed Mohammad Reza Khalili ◽  
Keramat Malekzadeh Fard
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Sandwich Plate ◽  
Core Layer ◽  
Element Model ◽  
Soft Core ◽  
Geometrical Parameters ◽  
Sandwich Plates ◽  
Fe Model ◽  
3D Finite Element

In the present paper, an accurate 3D finite element model is presented for bucking analysis of soft-core rectangular sandwich plates. The sandwich plate is composed of three layers: top and bottom skins and core layer. Finite element model of the problem has been constructed in the ANSYS 11.0 standard code area. The effect of geometrical parameters of the sandwich plate is studied. Comparison of the present results with those of plate theories confirms the accuracy of the proposed model. The overall buckling loads calculated by FE model are higher than that of the accurate results and the maximum discrepancy is less than 10 percent.

Nonlinear Superharmonic Resonance of Damped Circular Sandwich Plates with Initial Deflection

2011 ◽  
Vol 199-200 ◽  
pp. 1080-1083
Author(s):  
Guo Jun Du ◽  
Xiao Man Liu ◽  
Yu Da Hu ◽  
Chao Yu
Keyword(s):  
Sandwich Plate ◽  
Resonance Phenomenon ◽  
Sandwich Plates ◽  
Necessary And Sufficient Condition ◽  
Third Order ◽  
Circular Sandwich Plate ◽  
Superharmonic Resonance ◽  
Multi Scale ◽  
Circular Sandwich Plates ◽  
Necessary And Sufficient

The nonlinear superharmonic resonance phenomenon of damped circular sandwich plates under uniform load is investigated. From the movement equation of circular sandwich plate showed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. Under the clamped BC. Using multi-scale method, the periodical solutions were obtained which was of nonlinear the third-order superharmonic resonance. The FRF equation of the superharmonic resonance is obtained, and the necessary and sufficient condition on stability of the vibration are obtained synchronously.The infection to the amplitude while the correlative physical and geometric parameters changing were discussed, Drew the trajectories in moving phase planes during the stabilization process, and the stabilities and singularities of the solutions are analyzed.

scholarly journals On a consistent finite-strain plate theory based on three-dimensional energy principle

2014 ◽  
Vol 470 (2171) ◽  
pp. 20140494 ◽  
Author(s):  
Hui-Hui Dai ◽  
Zilong Song
Keyword(s):  
Finite Strain ◽  
Virtual Work ◽  
Plate Theory ◽  
Three Dimensional ◽  
Force Balance ◽  
Two Dimensional ◽  
Field Equations ◽  
Order Error ◽  
Energy Principle ◽  
Balance Structure

This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional potential energy under general loadings with a fourth-order error. Starting from the three-dimensional nonlinear elasticity (with both geometrical and material nonlinearity) and by a series expansion, we deduce a vector plate equation with three unknowns, which exhibits the local force-balance structure. The success relies on using the three-dimensional field equations and bottom traction condition to derive exact recursion relations for the coefficients. Associated weak formulations are considered, leading to a two-dimensional virtual work principle. An alternative approach based on a two-dimensional truncated energy is also provided, which is less consistent than the first plate theory but has the advantage of the existence of a two-dimensional energy function. As an example, we consider the pure bending problem of a hyperelastic block. The comparison between the analytical plate solution and available exact one shows that the plate theory gives second-order correct results. Compared with existing plate theories, it appears that the present one has a number of advantages, including the consistency, order of correctness, generality of loadings, applicability to finite-strain problems and no involvement of non-physical quantities.

Bending analysis of functionally graded sandwich plates using the refined finite strip method

2021 ◽  
pp. 109963622110204
Author(s):  
Mohammad Naghavi ◽  
Saeid Sarrami-Foroushani ◽  
Fatemeh Azhari
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Finite Strip ◽  
Strip Method ◽  
Finite Strip Method

In this study, static analysis of functionally graded (FG) sandwich plates is performed using the finite strip method based on the refined plate theory (RPT). Two types of common FG sandwich plates are considered. The first sandwich plate is composed of two FG material (FGM) face sheets and a homogeneous ceramic or metal core. The second one consists of two homogeneous fully metal and ceramic face sheets at the top and bottom, respectively, and a FGM core. Differential equations of FG sandwich plates are obtained using Hamilton's principle and stiffness and force matrices are formed using the finite strip method. The central deflection and the normal stress values are obtained for a sinusoidal loaded FG sandwich plate and the accuracy of the results are verified against those obtained from other theories such as the classical plate theory (CPT), the first-order shear deformation theory (FSDT), and the higher order shear deformation theory (HSDT). For the first time, this study presents a finite strip formulation in conjunction with the RPT to analyze FG Sandwich plates. While the proposed method is fast and simple, it is capable of modeling a variety of boundary conditions.

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