• Computers and Concrete
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• 제24권4호
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• pp.347-367
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• 2019

This work investigates the effect of Winkler/Pasternak/Kerr foundation and porosity on dynamic behavior of FG plates using a simple quasi-3D hyperbolic theory. Four different patterns of porosity variations are considered in this study. The used quasi-3D hyperbolic theory is simple and easy to apply because it considers only four-unknown variables to determine the four coupled vibration responses (axial-shear-flexion-stretching). A detailed parametric study is established to evaluate the influences of gradient index, porosity parameter, stiffness of foundation parameters, mode numbers, and geometry on the natural frequencies of imperfect FG plates.

• Steel and Composite Structures
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• 제43권1호
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• pp.1-17
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• 2022

The free and forced nonlinear dynamic behaviors of Porous Functionally Graded Material (PFGM) plates are examined by means of a High-Order Implicit Algorithm (HOIA). The formulation is developed using the Third-order Shear Deformation Theory (TSDT). Unlike previous works, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite, and the distribution of the porosity is assumed to be gradually variable through the thickness of the PFGM plates. Using the Hamilton principle, we establish the governing equations of motion. The Finite Element Method (FEM) is used to compute approximations of the resulting equations; FEM is adopted using a four-node quadrilateral finite element with seven Degrees Of Freedom (DOF) per node. Nonlinear equations are solved by a HOIA. The accuracy and the performance of the proposed approach are verified by presenting comparisons with literature results for vibration natural frequencies and dynamic response of PFGM plates under external loading. The influences of porosity volume fraction, porosity distribution, slenderness ratio and other parameters on the vibrations of PFGM plate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of the PFGM plate.

• Advances in materials Research
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• 제7권1호
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• pp.29-44
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• 2018

In this paper, a closed-form rigorous solution for interfacial shear stress in simply supported beams strengthened with bonded prestressed E-FGM plates and subjected to an arbitrarily positioned single point load, or two symmetric point loads is developed using linear elastic theory. This improved solution is intended for application to beams made of all kinds of materials bonded with a thin plate, while all existing solutions have been developed focusing on the strengthening of reinforced concrete beams, which allowed the omission of certain terms. The theoretical predictions are compared with other existing solutions. Finally, numerical results from the present analysis are presented to study the effects of various parameters of the beams on the distributions of the interfacial shear stresses. The results of this study indicated that the E-FGM plate strengthening systems are effective in enhancing flexural behavior of the strengthened RC beams.

• Steel and Composite Structures
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• 제43권5호
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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.

• Geomechanics and Engineering
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• 제21권5호
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• pp.471-487
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• 2020

In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Applying the principle of virtual displacements, the governing equations and boundary conditions are obtained. To solve the buckling problem for different boundary conditions, Galerkin's approach is utilized for symmetric EGM sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of plate aspect ratio, elastic foundation coefficients, ratio, side-to-thickness ratio and boundary conditions on the buckling response of FGM sandwich plates. A good agreement between the results obtained and the available solutions of existing shear deformation theories that have a greater number of unknowns proves to demonstrate the precision of the proposed theory.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.453-464
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• 2018

In this paper, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinear thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from the principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependent FG plates.

• Structural Engineering and Mechanics
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• 제53권6호
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• pp.1215-1240
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• 2015

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

• Geomechanics and Engineering
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• 제28권1호
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• pp.49-64
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• 2022

In this work, the bending and dynamic behaviors of advanced composite plates resting on variable visco-Pasternak foundations are studied using a simple shear deformation integral plate model. The research is carried out with a view to a three-parameter foundation including the influences of the variable Winkler coefficient, the constant Pasternak coefficient and the damping coefficient of the elastic medium. The present theory uses a displacement field with integral terms instead of derivative terms by including also the shear deformation effect without introducing the shear correction factors. The equations of motion for advanced composite plates are obtained using the Hamilton principle. Analytical solutions for the bending and dynamic analysis are deduced for simply supported plates resting on variable visco-Pasternak foundations. Some numerical results are presented to demonstrate the impact of material index, elastic foundation type, and damping coefficient of the foundation, on the bending and dynamic responses of advanced composite plates.

• Advances in concrete construction
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• 제14권3호
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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.

• Structural Engineering and Mechanics
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• 제68권4호
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• pp.409-421
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• 2018

In the present paper, functionally graded (FG) materials are presented to investigate the bending analysis of simply supported plates. It is assumed that the material properties of the plate vary through their length according to the power-law form. The displacement field of the present model is selected based on quasi-3D hyperbolic shear deformation theory. By splitting the deflection into bending, shear and stretching parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Governing equations are derived from the principle of virtual displacements. Numerical results for deflections and stresses of powerly graded plates under simply supported boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other shear deformation theories and so it becomes more attractive due to smaller number of unknowns. Some numerical results are provided to examine the effects of the material gradation, shear deformation on the static behavior of FG plates with variation of material stiffness through their length.