• Steel and Composite Structures
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• 제23권3호
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• pp.317-330
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• 2017

This paper presents a free vibration analysis of plates made of functionally graded materials and resting on two-layer elastic foundations by proposing a non-polynomial four variable refined plate theory. Undetermined integral terms are introduced in the proposed displacement field and unlike the conventional higher shear deformation theory (HSDT), the present one contains only four unknowns. Equations of motion are derived via the Hamilton's principles and solved using Navier's procedure. Accuracy of the present theory is demonstrated by comparing the results of numerical examples with the ones available in literature.

• Steel and Composite Structures
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• 제11권4호
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• pp.341-358
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• 2011

This paper presents the effects of thermal environment and temperature-dependence of the material properties on axisymmetric bending of functionally graded (FG) circular and annular plates. The material properties are assumed to be temperature-dependent and graded in the thickness direction. In order to accurately evaluate the effect of thermal environment, the initial thermal stresses are obtained by solving the thermoelastic equilibrium equations. Governing equations and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the virtual work principle based on the elasticity theory. The differential quadrature method (DQM) as an efficient and robust numerical tool is used to obtain the initial thermal stresses and response of the plate. Comparison studies with some available results for FG plates are performed. The influences of temperature rise, temperature-dependence of material properties, material graded index and different geometrical parameters are carried out.

• Advances in materials Research
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• 제7권2호
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• pp.83-103
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• 2018

In this paper, the problem of interfacial stresses in damaged reinforced concrete beams strengthened with bonded prestressed functionally graded material plate and subjected to a uniformly distributed load, arbitrarily positioned single point load, or two symmetric point loads is developed using linear elastic theory. The adopted model takes into account the adherend shear deformations by assuming a linear shear stress through the depth of the damaged RC beam. This solution is intended for application to beams made of all kinds of materials bonded with a thin FGM plate. The results show that there exists a high concentration of both shear and normal stress at the ends of the functionally graded material plate, which might result in premature failure of the strengthening scheme at these locations. Finally, numerical comparisons between the existing solutions and the present new solution enable a clear appreciation of the effects of various parameters of the beams on the distributions of the interfacial stresses.

• Coupled systems mechanics
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• 제11권4호
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• pp.357-371
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• 2022

This paper presents a parametric study on the free vibration analysis of a functionally graded material (FGM) circular plate with non-uniform thickness resting on a variable Pasternak elastic foundation. The mechanical properties of the material vary in the transverse direction through the thickness of the plate according to the power-law distribution to represent the constituent components. The equation of motion of the circular plate has been carried out based on the classical plate theory (CPT), and the differential quadrature method (DQM) is employed to solve the governing equations as a semi-analytical method. The grid points are chosen based on Chebyshev-Gauss-Lobatto distribution to achieve acceptable convergence and better accuracy. The influence of geometric parameters, variable elastic foundation, and functionally graded variation for clamped and simply supported boundary conditions on the first three natural frequencies are investigated. Comparisons of results with similar studies in the literature have been presented and two-dimensional mode shapes for particular plates have been plotted to illustrate the effect of variable thickness profile.

• Coupled systems mechanics
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• 제5권3호
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Geomechanics and Engineering
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• 제13권3호
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• pp.385-410
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• 2017

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Steel and Composite Structures
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• 제18권1호
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• pp.187-212
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• 2015

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential 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. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.423-434
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• 2018

In present work, both the hyperbolic shear deformation theory and stress function concept are used to study the mechanical and thermal stability responses of functionally graded (FG) plates resting on elastic foundation. The accuracy of the proposed formulation is checked by comparing the computed results with those predicted by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed formulation can achieve the same accuracy of the existing HSDTs which have more number of governing equations.

• Steel and Composite Structures
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• 제27권6호
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• pp.789-801
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• 2018

A weak-form formulation of finite annular prism methods (FAPM) based on Reissner's mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates with various boundary conditions and under mechanical loads. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of the loaded FG circular plates with both simply-supported and clamped edges are in excellent agreement with the solutions obtained using the 3D analytical approach and two-dimensional advanced plate theories available in the literature.

• Steel and Composite Structures
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• 제25권6호
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• pp.735-745
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• 2017

This work presents a free vibration analysis of functionally graded plates by employing an original high order shear deformation theory (HSDT). This theory use only four unknowns, which is even less than the classical HSDT. The equations of motion for the dynamic analysis are determined via the Hamilton's principle. The original kinematic allows obtaining interesting equations of motion. These equations are solved analytically via Navier procedure. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.