• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.867-891
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• 2014

An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

• Advanced Composite Materials
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• v.16 no.1
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• pp.63-81
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• 2007

Based on the Kirchhoff hypothesis of normal-remain-normal, the present work analyses piezoelectric laminated plates, wherein poled piezoelectric laminae are transversely isotropic and function as actuators. A quadric electric field is induced inside a piezoelectric lamina under a given applied voltage and mechanical bending. The governing equations for the piezoelectric laminated plate derived from the principle of virtual work in terms of the electric enthalpy have the same forms as those for a conventional composite laminated plate. We use rectangular sandwich plates of Al/PZT/Al and PZT/Al/PZT with four simply supported edges to demonstrate the prediction of the maximum bending stress in the PZT layer. The analytic solutions are verified by three-dimensional finite element analysis.

• Steel and Composite Structures
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• v.32 no.5
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• pp.633-642
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• 2019

In this work, lightweight sandwich plates consisting of a functionally graded porous (FGP) core and two laminated composite face sheets resting on elastic foundation have been proposed. Three different profiles are considered for the distributions of porosities along core thickness. The main aim of this paper is the investigation of the buckling behavior of the proposed porous sandwich plates (PSPs) by reporting their critical mechanical loads and their corresponding mode shapes. A finite element method (FEM) based on first order shear deformation theories (FSDT) is developed to discretize governing equations for the buckling behavior of the proposed sandwich plates. The effects of porosity dispersion and volume, the numbers and angles of laminated layers, sandwich plate geometrical dimensions, elastic foundation coefficients, loading and boundary conditions are studied. The results show that the use of FGP core can offer a PSP with half weight core and only 5% reduction in critical buckling loads. Moreover, stacking sequences with only ${\pm}45$ orientation fibers offer the highest values of buckling loads.

• Advances in Computational Design
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• v.3 no.3
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• pp.213-232
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• 2018

First time, an exact solution for free vibration of the Levy-type rectangular laminated plate is developed considering the most efficient Zig-Zag theory (ZIGT) and third order theory (TOT). The plate is subjected to hard simply supported boundary condition (Levy-type) along x axis. Using the equilibrium equations and the plate constitutive relations, a set of 12 m first order differential homogenous equations are obtained, containing displacements and stress resultant as primary variables. The natural frequencies of a single-layer isotropic, multi-layer composites and sandwich plates are tabulated for three values of length-to-thickness ratio (S) and five set of boundary conditions and further assessed by comparing with existing literature and recently developed 3D EKM (extended Kantorovich method) solution. It is found that for the symmetric composite plate, TOT produces better results than ZIGT. For antisymmetric and sandwich plates, ZIGT predicts the frequency for different boundary conditions within 3% error with respect to 3D elasticity solution while TOT gives 10% error. But, ZIGT gives better predictions than the TOT concerning the displacement and stress variables.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.763-774
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• 2019

The main aim of this paper is enhancing design of traditional laminated composite plates subjected to static loads. In this regard, this paper suggests embedding a lightweight porous layer in the middle of laminated composite as the core layer of the resulted sandwich plate. The static responses of the suggested structures with uniform, symmetric and non-symmetric porosity distributions are compared to optimize their design. Using the first order shear deformation theories, the static governing equations of the suggested laminated composite plates with a porous layer (LCPPL) rested on two-parameter foundation are obtained. A finite element method is also utilized to solve the governing equations of LCPPLs. Effects of laminated composite and porosity characteristics as well as geometry dimension, edges' boundary conditions and foundation coefficients on the static deflection and stress distribution of the suggested composite plates have been investigated. The results reveal that the use of core between the layers of laminated composites leads to a sharp reduction in the static deflections of LCPPLs. Furthermore, in compare with perfect cores, the use of porous core between the layers of laminated composite plates can offer a considerable reduction in structural weight without a significant difference in their static responses.

• International Journal of Aerospace System Engineering
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• v.3 no.1
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• pp.10-16
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• 2016

A trigonometric Layerwise higher order shear deformation theory (TLHSDT) is developed and implemented for free vibration and buckling analysis of laminated composite and sandwich plates by analytical and finite element formulation. The present model assumes parabolic variation of out-plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag model able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. Hence, botheration of shear correction coefficient is neglected. In the case of analytical method, the governing differential equation and boundary conditions are obtained from the principle of virtual work. For the finite element formulation, an efficient eight noded $C^0$ continuous isoparametric serendipity element is established and employed to examine the dynamic analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches.

• Journal of Korean Society of Steel Construction
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• v.12 no.6
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• pp.749-758
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• 2000

This study presents a governing equations of bending behavior of sandwich plates with thick metal, polymer composite facings. Based on zig-zag models for through thickness deformations, the transverse shear deformation of composite facings is included. All edges of plate are assumed to be simply supported. Results of the bending analysis under lateral loads are presented for the influence of various lay up sequences of antisymmetric angle-ply laminated facings. The accuracy of the approach is ascertained by comparing solutions from the sandwich plates theory with composite facings to the laminated plates theory. Since the present analysis considers the bending stiffness of the core and also the transverse shear deformations of the laminated facings, the proposed method showed higher than that calculated according to the general laminated plates theory. The information presented might be useful to design sandwich plates structure with metal, polymer matrix composite facings.

• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.325-334
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• 2018

The Nonlinear dynamic response of a sandwich plate subjected to the low velocity impact is theoretically and experimentally investigated. The Hertz law between the impactor and the plate is taken into account. Using the Extended High Order Sandwich Panel Theory (EHSAPT) and the Ritz energy method, the governing equations are derived. The skins follow the Third order shear deformation theory (TSDT) that has hitherto not reported in conventional EHSAPT. Besides, the three dimensional elasticity is used for the core. The nonlinear Von Karman relations for strains of skins and the core are adopted. Time domain solution of such equations is extracted by means of the well-known fourth-order Runge-Kutta method. The effects of core-to-skin thickness ratio, initial velocity of the impactor, the impactor mass and position of the impactor are studied in detail. It is found that these parameters play significant role in the impact force and dynamic response of the sandwich plate. Finally, some low velocity impact tests have been carried out by Drop Hammer Testing Machine. The results are compared with experimental data acquired by impact testing on sandwich plates as well as the results of finite element simulation.

• Computers and Concrete
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• v.26 no.2
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• pp.185-201
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• 2020

This research is devoted to investigate the bending and free vibration behaviour of laminated composite/sandwich plates and shells, by applying an analytical model based on a generalized and simple refined higher-order shear deformation theory (RHSDT) with four independent unknown variables. The kinematics of the proposed theoretical model is defined by an undetermined integral component and uses the hyperbolic shape function to include the effects of the transverse shear stresses through the plate/shell thickness; hence a shear correction factor is not required. The governing differential equations and associated boundary conditions are derived by employing the principle of virtual work and solved via Navier-type analytical procedure. To verify the validity and applicability of the present refined theory, some numerical results related to displacements, stresses and fundamental frequencies of simply supported laminated composite/sandwich plates and shells are presented and compared with those obtained by other shear deformation models considered in this paper. From the analysis, it can be concluded that the kinematics based on the undetermined integral component is very efficient, and its use leads to reach higher accuracy than conventional models in the study of laminated plates and shells.

• Steel and Composite Structures
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• v.26 no.5
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.