• Steel and Composite Structures
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• v.22 no.3
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• pp.691-712
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• 2016

In this editorial, buckling analytical investigation of the nanocomposite plate with square cut out reinforced by carbon nanotubes (CNTs) surrounded by Pasternak foundation is considered. The plate is presumed has square cut out in center and resting on Pasternak foundation. CNTs are used as amplifier in plate for diverse distribution, such as uniform distribution (UD) and three patterns of functionally graded (FG) distribution types of CNTs (FG-X, FG-A and FG-O). Moreover, the effective mechanical properties of nanocomposite plate are calculated from the rule of mixture. Domain decomposition method and orthogonal polynomials are applied in order to define the shape function of nanocomposite plate with square cut out. Finally, Rayleigh-Ritz energy method is used to obtain critical buckling load of system. A detailed parametric study is conducted to explicit the effects of the dimensions of plate, length of square cut out, different distribution of CNTs, elastic medium and volume fraction of CNTs. It is found from results that increase the dimensions of plate and length of square cut out have negative impact on buckling behavior of system but considering CNTs in plate has positive influence.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.819-822
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• 2006

This paper has the objects of deciding dynamic instability regions of thick plates on inhomogeneous Pasternak foundation by finite element method and providing kinematic design data for mats and slabs of building structures. In this paper, dynamic stability analysis of tapered opening thick plate is done by use of Serendipity finite element with 8 nodes considering shearing strain of plate. To verify this finite element method, buckling stress and natural frequencies of thick pate with or without in-plane stress are compared with existing solutions. The results are as follow that this finite element solutions with $4{\times}4$ meshes are shown the error of maximum 0.56% about existing solutions, and the larger foundation parameters, the farther dynamic instability regions are from vertical axis of graph presented relation of ${\beta}\;and\;\overline{\omega}/\omega$.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.681-688
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• 2006

This paper has the object of investigating natural frequencies of tapered thick plate on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. In order to analysis plate which is supported on pasternak foundation. the Winkler parameter is varied with 10, $10^2,\;10^3$ and the shear foundation parameter is 5, 10. This paper is analyzed varying thickness by taper ratio. The taper ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0 respectively.

• Coupled systems mechanics
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• v.10 no.1
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• pp.61-77
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• 2021

The porosity of functionally graded materials (FGM) can affect the static and dynamic behavior of plates, which is important to take this aspect into account when analyzing such structures. The present work aims to study the effect of the distribution shape of porosity on the free vibration response of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is expanded to study the influence of the distribution shape of porosity on the free vibration behavior of FG plates. The findings showed that the distribution shape of porosity significantly influences the free vibration behavior of thick rectangular FG plates for small values of Winkler-Pasternak elastic foundation parameters.

• Structural Engineering and Mechanics
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• v.44 no.2
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• pp.139-161
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• 2012

In this paper, the static behavior of bi-directional functionally graded (FG) non-uniform thickness circular plate resting on quadratically gradient elastic foundations (Winkler-Pasternak type) subjected to axisymmetric transverse and in-plane shear loads is carried out by using state-space and differential quadrature methods. The governing state equations are derived based on 3D theory of elasticity, and assuming the material properties of the plate except the Poisson's ratio varies continuously throughout the thickness and radius directions in accordance with the exponential and power law distributions. The stresses and displacements distribution are obtained by solving state equations. The effects of foundation stiffnesses, material heterogeneity indices, geometric parameters and loads ratio on the deformation and stress distributions of the FG circular plate are investigated in numerical examples. The results are reported for the first time and the new results can be used as a benchmark solution for future researches.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.73-79
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• 1997

It is one of classical problems in the elastic theory to analyze contact stresses between elastic bodies. Concrete pavements under traffic wheel loads can be considered as one of these typical Problems. In the paper, Mindlin plate theory is used to consider the transverse shear effect, 8-node isoparametric plate bending element is adopted in this study, and an elastic plate resting on tensionless elastic half-space is analyzed by finite element method. The Boussineq's solution of elastic half-space is used to evaluate the flexibility of foundation. To obtain the boundary of contact area, the flexibility matrix of foundation is modified after each cycle of analysis iteratively. A Numerical example is presented by using these method.

• Interaction and multiscale mechanics
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• v.5 no.2
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• pp.105-114
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• 2012

The study of rigid roadway pavement under dynamic traffic loads with variable velocity is investigated in this paper. Rigid roadway pavement is modeled as a rectangular damped orthotropic plate supported by elastic Pasternak foundation. The boundary supports of the plate are the steel dowels and tie bars which provide elastic vertical support and rotational restraint. The natural frequencies of the system and the mode shapes are solved using two transcendental equations, obtained from the solution of two auxiliary Levy's type problems, known as the Modified Bolotin Method. The dynamic moving traffic load is expressed as a concentrated load of harmonically varying magnitude, moving straight along the plate with a variable velocity. The dynamic response of the plate is obtained on the basis of orthogonality properties of eigenfunctions. Numerical example results show that the velocity and the angular frequency of the loads affected the maximum dynamic deflection of the rigid roadway pavement. It is also shown that a critical speed of the load exists. If the moving traffic load travels at critical speed, the rectangular plate becomes infinite in amplitude.

• Coupled systems mechanics
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• v.9 no.6
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• pp.575-597
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• 2020

Equilibrium equations of a porous FG plate resting on Winkler-Pasternak foundations with various boundary conditions are derived using a new refined shear deformation theory. Different types of porosity distribution rate are considered. Governing equations are obtained including the plate-foundation interaction. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The novel rule of mixture is proposed to describe and approximate material properties of the FG plates with different distribution case of porosity. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature. Effects of variation of porosity distribution rate, boundary conditions, foundation parameter, power law index, plate aspect ratio, side-to-thickness ratio on the deflections and stresses are all discussed.

• Smart Structures and Systems
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• v.18 no.4
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• pp.755-786
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• 2016

The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.

• Advances in nano research
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• v.7 no.5
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• pp.293-310
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• 2019

In this paper, thermal-buckling behavior of the functionally graded (FG) nanocomposite plates reinforced with graphene oxide powder (GOP) is studied under three types of thermal loading once the plate is supposed to be rested on a two-parameter elastic foundation. The effective material properties of the nanocomposite plate are considered to be graded continuously through the thickness according to the Halpin-Tsai micromechanical scheme. Four types of GOPs' distribution namely uniform (U), X, V and O, are considered in a comparative way in order to find out the most efficient model of GOPs' distribution for the purpose of improving the stability limit of the structure. The governing equations of the plate have been derived based on a refined higher-order shear deformation plate theory incorporated with Hamilton's principle and solved analytically via Navier's solution for a simply supported GOP reinforced (GOPR) nanocomposite plate. Some new results are obtained by applying different thermal loadings to the plate according to the GOPs' negative coefficient of thermal expansion and considering both Winkler-type and Pasternak-type foundation models. Besides, detailed parametric studies have been carried out to reveal the influences of the different types of thermal loading, weight fraction of GOP, aspect and length-to-thickness ratios, distribution type, elastic foundation constants and so on, on the critical buckling load of nanocomposite plates. Moreover, the effects of thermal loadings with various types of temperature rise are investigated comparatively according to the graphical results. It is explicitly shown that the buckling behavior of an FG nanocomposite plate is significantly influenced by these effects.