• Steel and Composite Structures
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• v.26 no.5
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• pp.557-572
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• 2018

In this paper, a refined higher-order shear deformation theory including the stretching effect is developed for the analysis of bending analysis of the simply supported functionally graded (FG) sandwich plates resting on elastic foundation. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The theory presented is variationally consistent, without the shear correction factor. The present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Wind and Structures
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• v.35 no.2
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• pp.109-120
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• 2022

The force coefficients of rotating plates in the acceleration stage will vary with rotation rate from 0 to stable rotation rate w₀, which are important for quasi-steady theory of plate-like windborne debris to simulate the trajectory. In this paper, a wind tunnel experiment is carried out to study the effects of geometry and the Reynolds number on the variations of mean force coefficients of rotating plates. The rotational lift coefficients are sensitive to both geometry effect and Reynolds number effect, while the rotational drag and moment coefficients are only sensitive to geometry effect. In addition, new empirical formulas for the rotational lift coefficient and moment coefficients are proposed. Its accuracy is verified by comparing the predicted results with existing test data. Based on the experimental data of rotating plates, a new rotational force model for quasi-steady theory, which can be applied to a wider scope, is proposed to calculate the trajectory of plate-like windborne debris. The results show that the new model provides a better match with the tested trajectories than previous quasi-steady theories.

• Computers and Concrete
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• v.25 no.1
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• pp.37-57
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• 2020

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

• Earthquakes and Structures
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• v.14 no.2
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• pp.117-128
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• 2018

In this research work, free vibrations of simply supported functionally graded plate resting on a Winkler-Pasternak elastic foundation are investigated by a new shear deformation theory. The influence of alternative micromechanical models on the macroscopic behavior of a functionally graded plate based on shear-deformation plate theories is examined. Several micromechanical models are tested to obtain the effective material properties of a two-phase particle composite as a function of the volume fraction of particles which continuously varies through the thickness of a functionally graded plate. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The energy functional of the system is obtained using Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models on natural fundamental frequencies.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.2
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• pp.324-345
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• 2015

A new procedure for determining properties of thick plate finite elements, based on the modified Mindlin theory for moderately thick plate, is presented. Bending deflection is used as a potential function for the definition of total (bending and shear) deflection and angles of cross-section rotations. As a result of the introduced interdependence among displacements, the shear locking problem, present and solved in known finite element formulations, is avoided. Natural vibration analysis of rectangular plate, utilizing the proposed four-node quadrilateral finite element, shows higher accuracy than the sophisticated finite elements incorporated in some commercial software. In addition, the relation between thick and thin finite element properties is established, and compared with those in relevant literature.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.369-383
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• 2018

In this work, a novel hyperbolic shear deformation theory is developed for free vibration analysis of the simply supported functionally graded plates in thermal environment and the FGM having temperature dependent material properties. This theory has only four unknowns, which is even less than the other shear deformation theories. The theory presented is variationally consistent, without the shear correction factor. The present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical model are performed to demonstrate the efficacy of the model.

• Structural Engineering and Mechanics
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• v.62 no.5
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• pp.607-618
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• 2017

In this paper, an analytical procedure based on the perturbation technique is presented to study the free vibrations of annular viscoelastic plates by considering the first order shear deformation theory as the displacement field. The viscoelastic properties obey the standard linear solid model. The equations of motion are extracted for small deflection assumption using the Hamilton's principle. These equations which are a system of partial differential equations with variable coefficients are solved analytically with the perturbation technique. By using a new variable change, the governing equations are converted to equations with constant coefficients which have the analytical solution and they are appropriate especially to study the sensitivity analysis. Also the natural frequencies are calculated using the classical plate theory and finite elements method. A parametric study is performed and the effects of geometry, material and boundary conditions are investigated on the vibrational behavior of the plate. The results show that the first order shear deformation theory results is more closer than to the finite elements with respect to the classical plate theory for viscoelastic plate. The more results are summarized in conclusion section.

• Structural Engineering and Mechanics
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• v.55 no.5
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• pp.1001-1014
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• 2015

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.

• Geomechanics and Engineering
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• v.33 no.5
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• pp.427-437
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• 2023

The objective of this work is to study the wave propagation of an FGM plate via a new integral inverse shear model with temperature-dependent material properties. In this contribution, a new model based on a high-order theory field of displacement is included by introducing indeterminate integral variables and inverse co-tangential functions for the presentation of shear stress. The temperature-dependent properties of the FGM plate are assumed mixture of metal and ceramic, and its properties change by the power functions of the thickness of the plate. By applying Hamilton's principle, general formulas of wave propagation were obtained to plot the phase velocity curves and wave modes of the FGM plate with simply supported edges. The effects of the temperature and volume fraction by distributions on wave propagation of the FGM plate are investigated in detail. The results of the dispersion and the phase velocity curves of the propagation wave in the functionally graded plate are compared with previous research.

• Steel and Composite Structures
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• v.24 no.5
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• pp.569-578
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• 2017

In this research work, a simple and accurate hyperbolic plate theory for the buckling analysis of functionally graded sandwich plates is presented. The main interest of this theory is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\not=}0$), the displacement field is composed only of 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 like in the well-known "higher order shear and normal deformation theories". Thus, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Governing equations are obtained by employing the principle of minimum total potential energy. Comparison studies are performed to verify the validity of present results. A numerical investigation has been conducted considering and neglecting the thickness stretching effects on the buckling of sandwich plates with functionally graded skins. It can be concluded that the present theory is not only accurate but also simple in predicting the buckling response of sandwich plates with functionally graded skins.