• Computers and Concrete
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• v.32 no.1
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• pp.61-74
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• 2023

This article investigates the wave propagation analysis of the imperfect functionally graded (FG) sandwich plates based on a novel simple four-variable integral quasi-3D higher-order shear deformation theory (HSDT). The thickness stretching effect is considered in the transverse displacement component. The presented formulation ensures a parabolic variation of the transverse shear stresses with zero-stresses at the top and the bottom surfaces without requiring any shear correction factors. The studied sandwich plates can be used in several sectors as areas of aircraft, construction, naval/marine, aerospace and wind energy systems, the sandwich structure is composed from three layers (two FG face sheets and isotropic core). The material properties in the FG faces sheet are computed according to a modified power law function with considering the porosity which may appear during the manufacturing process in the form of micro-voids in the layer body. The Hamilton principle is utilized to determine the four governing differential equations for wave propagation in FG plates which is reduced in terms of computation time and cost compared to the other conventional quasi-3D models. An eigenvalue equation is formulated for the analytical solution using a generalized displacements' solution form for wave propagation. The effects of porosity, temperature, moisture concentration, core thickness, and the material exponent on the plates' dispersion relations are examined by considering the thickness stretching influence.

• Smart Structures and Systems
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• v.21 no.1
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• pp.75-97
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• 2018

In this paper, a novel higher-order shear deformation theory (HSDT) is proposed for the analysis of the hygro-thermo-mechanical behavior of functionally graded (FG) plates resting on elastic foundations. The developed model uses a novel kinematic by considering undetermined integral terms and only four variables are used in this model. The governing equations are deduced based on the principle of virtual work and the number of unknown functions involved is reduced to only four, which is less than the first shear deformation theory (FSDT) and others HSDTs. The Navier-type exact solutions for static analysis of simply supported FG plates subjected to hygro-thermo-mechanical loads are presented. The accuracy and efficiency of the present model is validated by comparing it with various available solutions in the literature. The influences of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratios and elastic coefficients parameters on deflections and stresses of FG plates are also investigated.

• Computers and Concrete
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• v.32 no.1
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• pp.87-97
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• 2023

The bending of a porous FG plate is discussed in this study using a novel higher quasi-3D hyperbolic shear deformation theory with four unknowns. The proposed theory takes into consideration the normal and transverse shear deformation effect and ensures the parabolic distribution of the transverse stresses through the thickness direction with zero-traction at the top and the bottom surfaces of the structure. Innovative porous functionally graded materials (FGM) have through-thickness porosity as a unique attribute that gradually varies with their qualities. An analytical solution of the static response of the perfect and imperfect FG plate was derived based on the virtual work principle and solved using Navier's procedure. The validity and the efficiency of the current model is confirmed by comparing the results with those obtained by others solutions. The comparisons showed that the present model is very efficient and simple in terms of computation time and exactness. The impact of the porosity parameter, aspect ratio, and thickness ratio on the bending of porous FG plate is shown through a discussion of several numerical results.

• Advances in concrete construction
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• v.14 no.3
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• pp.169-183
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• 2022

In this article, vibrational behavior and wave propagation characteristics in (FG) functionally graded plates resting on Kerr foundation with three parameters is studied using a 2D dimensional (HSDT) higher shear deformation theory. The new 2D higher shear deformation theory has only four variables in field's displacement, which means has few numbers of unknowns compared with others theories. The shape function used in this theory satisfies the nullity conditions of the shear stresses on the two surfaces of the FG plate without using shear correction factors. The FG plates are considered to rest on the Kerr layer, which is interconnected with a Pasternak-Kerr shear layer. The FG plate is materially inhomogeneous. The material properties are supposed to vary smoothly according to the thickness of the plate by a Voigt's power mixing law of the volume fraction. The equations of motion due to the dynamics of the plate resting on a three-parameter foundation are derived using the principle of minimization of energies; which are then solved analytically by the Navier technique to find the vibratory characteristics of a simply supported plate, and the wave propagation results are derived by using the dispersion relations. Perceivable numerical results are fulfilled to evaluate the vibratory and the wave propagation characteristics in functionally graded plates and some parameters such wave number, thickness ratio, power index and foundation parameters are discussed in detail.

• Steel and Composite Structures
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• v.32 no.3
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• pp.389-410
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• 2019

In this article, a simple quasi-3D shear deformation theory is employed for thermo-mechanical bending analysis of functionally graded material (FGM) sandwich plates. The displacement field is defined using only 5 variables as the first order shear deformation theory (FSDT). Unlike the other high order shear deformation theories (HSDTs), the present formulation considers a new kinematic which includes undetermined integral variables. The governing equations are determined based on the principle of virtual work and then they are solved via Navier method. Analytical solutions are proposed to provide the deflections and stresses of simply supported FGM sandwich structures. Comparative examples are presented to demonstrate the accuracy of the present theory. The effects of gradient index, geometrical parameters and thermal load on thermo-mechanical bending response of the FG sandwich plates are examined.

• Earthquakes and Structures
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• v.16 no.5
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• pp.547-561
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• 2019

In this work, a new analytical approach using a theory of a high order hyperbolic shear deformation theory (HSDT) has been developed to study the free vibration of plates of functionally graduated material (FGM). This theory takes into account the effect of stretching the thickness. In contrast to other conventional shear deformation theories, the present work includes a new displacement field that introduces indeterminate integral variables. During the manufacturing process of these plates defects can appear as porosity. The latter can question and modify the global behavior of such plates. The materials constituting the plate are assumed to be gradually variable in the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The motion equations are derived by the Hamilton principle. Analytical solutions for free vibration analysis are obtained for simply supported plates. The effects of stretching, the porosity parameter, the power law index and the length / thickness ratio on the fundamental frequencies of the FGM plates are studied in detail.

• Steel and Composite Structures
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• v.43 no.5
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• pp.581-601
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• 2022

The main objective of this research work is to investigate the free vibration behavior of annular sandwich plates resting on the Kerr foundation at thermal conditions. This sandwich configuration is composed of two FGM face sheets as coating layer and a porous GPLRC (GPL reinforced composite) core. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the core thickness direction. To model closed-cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme is used, while the Poisson's ratio and density are computed by the rule of mixtures. Besides, the material properties of two FGM face sheets change continuously through the thickness according to the power-law distribution. To capture fundamental frequencies of the annular sandwich plate resting on the Kerr foundation in a thermal environment, the analysis procedure is with the aid of Reddy's shear-deformation plate theory based high-order shear deformation plate theory (HSDT) to derive and solve the equations of motion and boundary conditions. The governing equations together with related boundary conditions are discretized using the generalized differential quadrature (GDQ) method in the spatial domain. Numerical results are compared with those published in the literature to examine the accuracy and validity of the present approach. A parametric solution for temperature variation across the thickness of the sandwich plate is employed taking into account the thermal conductivity, the inhomogeneity parameter, and the sandwich schemes. The numerical results indicate the influence of volume fraction index, GPLs volume fraction, porosity coefficient, three independent coefficients of Kerr elastic foundation, and temperature difference on the free vibration behavior of annular sandwich plate. This study provides essential information to engineers seeking innovative ways to promote composite structures in a practical way.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.661-679
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• 2015

In this article, nonlinear finite element solutions of bending responses of functionally graded spherical panels are presented. The material properties of functionally graded material are graded in thickness direction according to a power-law distribution of volume fractions. A general nonlinear mathematical shallow shell model has been developed based on higher order shear deformation theory by taking the geometric nonlinearity in Green-Lagrange sense. The model is discretised using finite element steps and the governing equations are obtained through variational principle. The nonlinear responses are evaluated through a direct iterative method. The model is validated by comparing the responses with the available published literatures. The efficacy of present model has also been established by demonstrating a simulation based nonlinear model developed in ANSYS environment. The effects of power-law indices, support conditions and different geometrical parameters on bending behaviour of functionally graded shells are obtained and discussed in detail.

• Advances in materials Research
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• v.5 no.4
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• pp.205-221
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• 2016

In this article, the buckling responses of functionally graded curved (spherical, cylindrical, hyperbolic and elliptical) shell panels under elevated temperature load are investigated numerically using finite element steps. The effective material properties of the functionally graded shell panel are evaluated using Voigt's micromechanical model through the power-law distribution with and without temperature dependent properties. The mathematical model is developed using the higher-order shear deformation theory in conjunction with Green-Lagrange type nonlinear strain to consider large geometrical distortion under thermal load. The efficacy of the proposed model has been checked and the effects of various geometrical and material parameters on the buckling load are analysed in details.

• Steel and Composite Structures
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• v.18 no.3
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• pp.693-709
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• 2015

In this article, nonlinear free vibration behaviour of functionally graded spherical panel is analysed. A nonlinear mathematical model is developed based on higher order shear deformation theory for shallow shell by taking Green-Lagrange type of nonlinear kinematics. The material properties of functionally graded material are assumed to be varying continuously in transverse direction and evaluated using Voigt micromechanical model in conjunction with power-law distribution. The governing equation of the shell panel is obtained using Hamilton's principle and discretised with the help of nonlinear finite element method. The desired responses are evaluated through a direct iterative method. The present model has been validated by comparing the frequency ratio (nonlinear frequency to linear frequency) with those available published literatures. Finally, the effect of geometrical parameters (curvature ratio, thickness ratio, aspect ratio and support condition), power law indices and amplitude of vibration on the frequency ratios of spherical panel have been discussed through numerical experimentations.