• Computers and Concrete
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• v.24 no.3
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• pp.185-192
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• 2019

In this paper, the buckling of micro sandwich hollow circular plate is investigated with the consideration of the porous core and piezoelectric layer reinforced by functionally graded (FG)carbon nano-tube. For modeling the displacement field of sandwich hollow circular plate, the high-order shear deformation theory (HSDT) of plate and modified couple stress theory (MCST) are used. The governing differential equations of the system can be derived using the principle of minimum potential energy and Maxwell's equation that for solving these equations, the Ritz method is employed. The results of this research indicate the influence of various parameters such as porous coefficients, small length scale parameter, distribution of carbon nano-tube in piezoelectric layers and temperature on critical buckling load. The purpose of this research is to show the effect of physical parameters on the critical buckling load of micro sandwich plate and then optimize these parameters to design structures with the best efficiency. The results of this research can be used for optimization of micro-structures and manufacturing different structure in aircraft and aerospace.

• Advances in nano research
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• v.7 no.1
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• pp.25-38
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• 2019

This research is aimed at studying the asymmetric thermal buckling of porous functionally graded (FG) annular nanoplates resting on an elastic substrate which are made of two different sets of porous distribution, based on nonlocal elasticity theory. Porosity-dependent properties of inhomogeneous nanoplates are supposed to vary through the thickness direction and are defined via a modified power law function in which the porosities with even and uneven type are approximated. In this model, three types of thermal loading, i.e., uniform temperature rise, linear temperature distribution and heat conduction across the thickness direction are considered. Based on Hamilton's principle and the adjacent equilibrium criterion, the stability equations of nanoporous annular plates on elastic substrate are obtained. Afterwards, an analytical solution procedure is established to achieve the critical buckling temperatures of annular nanoplates with porosities under different loading conditions. Detailed numerical studies are performed to demonstrate the influences of the porosity volume fraction, various thermal loading, material gradation, nonlocal parameter for higher modes, elastic substrate coefficients and geometrical dimensions on the critical buckling temperatures of a nanoporous annular plate. Also, it is discussed that because of present of thermal moment at the boundary conditions, porous nanoplate with simply supported boundary condition doesn't buckle.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.419-432
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• 2023

This paper studies the effects of porosity distributions on buckling and post-buckling behaviors of a functionally graded saturated porous (FGSP) circular plate. The plate is under the uniformly distributed radial loading and simply supported and clamped boundary conditions. Pores are saturated with compressible fluid (e.g., gases) that cannot escape from the porous solid. Elastic modulus is assumed to vary continuously through the thickness according to three different functions corresponding to three different cases of porosity distributions, including monotonous, symmetric, and asymmetric cases. Governing equations are derived utilizing the classical plate theory and Sanders nonlinear strain-displacement relations, and they are solved numerically via shooting method. Results are verified with the known results in the literature. The obtained results for the monotonous and symmetric cases with the asymmetric case presented in the literature are shown in comparative figures. Effects of the poroelastic material parameters, boundary conditions, and thickness change on the post-buckling behavior of the plate are discussed in details. The results reveal that buckling and post-buckling behaviors of the plate in the monotonous and symmetric cases differ from the asymmetric case, especially in small deflections, that asymmetric distribution of elastic moduli can be the cause.

• Advances in nano research
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• v.12 no.6
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• pp.593-603
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• 2022

The critical buckling temperature rise of a newly proposed piezoelectrically active sandwich plate (ASP) has been investigated in this work. This structure includes a porous polymeric layer integrated between two piezoelectric nanocomposite layers. The piezoelectric material is made of a passive polymeric material that is activated by lead-free nanowires (NWs) of zinc oxide (ZnO) embedded inside the matrix. In both nanocomposite layers and porous core, functional graded (FG) patterns have been considered for the distributions of ZnO NWs and voids, respectively. By adopting a higher-order theory of plates, the governing equations of thermal buckling are obtained. This set of equations is then treated using an extended mesh-free solution. The effects of plate dimensions, porosity states, and the nanowire parameters have been investigated on the critical buckling temperature rises of the proposed lightweight ASPs with different boundary conditions. The results disclose that the use of porosities in the core and/or mixing ZnO NWs in the face sheets substantially arise the critical buckling temperatures of the newly proposed active sandwich plates.

• Earthquakes and Structures
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• v.15 no.4
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• pp.369-382
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• 2018

A free vibration analysis and wave propagation of functionally graded porous beams has been presented in this work using a high order hyperbolic shear deformation theory. Unlike other conventional shear deformation theories, a new displacement field that introduces indeterminate integral variables has been used to minimize the number of unknowns. The constituent materials of the beam are assumed gradually variable along the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The variation of the pores in the direction of the thickness influences the mechanical properties. It is therefore necessary to predict the effect of porosity on vibratory behavior and wave velocity of FG beams in this study. A new function of the porosity factor has been developed. Hamilton's principle is used for the development of wave propagation equations in the functionally graded beam. The analytical dispersion relationship of the FG beam is obtained by solving an eigenvalue problem. Illustrative numerical examples are given to show the effects of volume fraction distributions, beam height, wave number, and porosity on free vibration and wave propagation in a functionally graded beam.

• Steel and Composite Structures
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• v.37 no.6
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• pp.711-731
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• 2020

This paper deals with free vibration of FG sandwich annular sector plates on Pasternak elastic foundation with different boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. The influence of carbon nanotubes (CNTs) waviness, aspect ratio, internal pores and graphene platelets (GPLs) on the vibrational behavior of functionally graded nanocomposite sandwich plates is investigated in this research work. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness of upper and bottom layers of the sandwich sectorial plates and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The core of structure is porous and the internal pores and graphene platelets (GPLs) are distributed in the matrix of core either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. A semi-analytic approach composed of 2D-Generalized Differential Quadrature Method (2D-GDQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.

• Advances in nano research
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• v.5 no.2
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• pp.141-169
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• 2017

In this paper, a nanobeam connected to a rotating molecular hub is considered. The vibration behavior of rotating functionally graded nanobeam based on Eringen's nonlocal theory and Euler-Bernoulli beam model is investigated. Furthermore, axial preload and porosity effect is studied. It is supposed that the material attributes of the functionally graded porous nanobeam, varies continuously in the thickness direction according to the power law model considering the even distribution of porosities. Porosity at the nanoscopic length scale can affect on the rotating functionally graded nanobeams dynamics. The equations of motion and the associated boundary conditions are derived through the Hamilton's principle and generalized differential quadrature method (GDQM) is utilized to solve the equations. In this paper, the influences of some parameters such as functionally graded power (FG-index), porosity parameter, axial preload, nonlocal parameter and angular velocity on natural frequencies of rotating nanobeams with pure ceramic, pure metal and functionally graded materials are examined and some comparisons about the influence of various parameters on the natural frequencies corresponding to the simply-simply, simplyclamped, clamped-clamped boundary conditions are carried out.

• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.513-524
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• 2019

The present article deals with thermal buckling of functionally graded plates with porosity and resting on elastic foundation. The basic formulation is based on quasi 3D theory. The present theory contains only four unknowns and also accommodates the thickness stretching effect. Porosity-dependent material coefficients of the plate are compositionally graded throughout the thickness according to a modified micromechanical model. Different patterns of porosity distributions are considered. The thermal loads are assumed to be uniform, linear and non-linear temperature rises through the thickness direction. The plate is assumed to be simply supported on all edges. Various numerical examples are given to check the accuracy and reliability of the present solution, in which both the present results and those reported in the literature are provided. In addition, several numerous new results for thick FG plates with porosity are also presented.

• Steel and Composite Structures
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• v.50 no.1
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• pp.15-24
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• 2024

This research presents dynamical reaction investigation of pore-dependent and nano-thickness beams having functional gradation (FG) constituents exposed to a movable particle. The nano-thickness beam formulation has been appointed with the benefits of refined high orders beam paradigm and nonlocal strain gradient theory (NSGT) comprising two scale moduli entitled nonlocality and strains gradient modulus. The graded pore-dependent constituents have been designed through pore factor based power-law relations comprising pore volumes pursuant to even or uneven pore scattering. Therewith, variable scale modulus has been thought-out until process a more accurate designing of scale effects on graded nano-thickness beams. The motion equations have been appointed to be solved via Ritz method with the benefits of Chebyshev polynomials in cosine form. Also, Laplace transform techniques help Ritz-Chebyshev method to obtain the dynamical response in time domain. All factors such as particle speed, pores and variable scale modulus affect the dynamical response.

• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.443-459
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• 2023

This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.