• Advances in Computational Design
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• v.2 no.3
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• pp.165-194
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• 2017

The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).

• Advances in nano research
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• v.9 no.3
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• pp.183-191
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• 2020

The content of this study focuses on bending of flexoelectric Magneto-Electro-Elastic (MEE) nanobeams inserted within the foundation of Winkler-Pasternak according to nonlocal elasticity theory. Applying Hamilton's principle, the nonlocal nanobeams' governing equations in the framework higher order refined beam theory are attained and resolved through adapting an analytical solution. A parametric research is demonstrated for studying the effects that magneto-electro-mechanical loadings, the nonlocal parameter, flexoelectric, as well as the aspect ratio all have on the deflection properties of nanobeams. A discovery lead to beam geometrical parameters, the boundary conditions, flexoelectricity and nonlocal parameter partake substantial effects on nanoscale beams' dimensionless deflection.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.495-510
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• 2015

Free vibration of non-uniform embedded nanoplates based on classical (Kirchhoff's) plate theory in conjunction with nonlocal elasticity theory has been studied. The nanoplate is assumed to be rested on two-parameter Winkler-Pasternak elastic foundation. Non-uniform material properties of nanoplates have been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinates. Detailed analysis has been reported for all possible casesof such variations. Trial functions denoting transverse deflection of the plate are expressed in simple algebraic polynomial forms. Application of the present method converts the problem into generalised eigen value problem. The study aims to investigate the effects of non-uniform parameter, elastic foundation, nonlocal parameter, boundary condition, aspect ratio and length of nanoplates on the frequency parameters. Three-dimensional mode shapes for some of the boundary conditions have also been illustrated. One may note that present method is easier to handle any sets of boundary conditions at the edges.

• Advances in nano research
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• v.8 no.3
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• pp.203-214
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• 2020

This paper investigated bending of magneto-electro-elastic (MEE) nanobeams under hygro-thermal loading embedded in Winkler-Pasternak foundation based on nonlocal elasticity theory. The governing equations of nonlocal nanobeams in the framework parabolic third order beam theory are obtained using Hamilton's principle and solved implementing an analytical solution. A parametric study is presented to examine the effect of the nonlocal parameter, hygro-thermal-loadings, magneto-electro-mechanical loadings and aspect ratio on the deflection characteristics of nanobeams. It is found that boundary conditions, nonlocal parameter and beam geometrical parameters have significant effects on dimensionless deflection of nanoscale beams.

• 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.

• Smart Structures and Systems
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• v.15 no.6
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• pp.1569-1582
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• 2015

Two hyperbolic displacement models are used for the bending response of simply-supported orthotropic laminated composite plates resting on two-parameter elastic foundations under mechanical loading. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The present theory takes into account not only the transverse shear strains, but also their parabolic variation across the plate thickness and requires no shear correction coefficients in computing the shear stresses. The governing equations are derived and their closed-form solutions are obtained. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other theories models given in the literature. It is found that the theories proposed can predict the bending analysis of cross-ply laminated composite plates resting on elastic foundations rather accurately. The effects of Winkler and Pasternak foundation parameters, transverse shear deformations, plate aspect ratio, and side-to-thickness ratio on deflections and stresses are investigated.

• Computers and Concrete
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• v.26 no.1
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• pp.53-62
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• 2020

Concrete is the most widely used substance in construction industry, so it's been required to improve its quality using new technologies. Nowadays, nanotechnology offers new frontiers for improving construction materials. In this paper, we study the stability analysis of the Single Walled Carbon Nanotubes (SWCNT) reinforced concrete cylindrical shell embedded in elastic foundation using the Donnell cylindrical shell theory. In this regard, we propose a new explicit analytical formula of the critical buckling load which takes into account the distribution of SWCNT reinforcement through the thickness of the concrete shell using the U, X, O and V forms and the elastic foundation using Winkler and Pasternak models. The rule of mixture is used to calculate the effective properties of the reinforced concrete cylindrical shell. The influence of diverse parameters on the stability behavior of the reinforced concrete shell is also discussed.

• Advances in nano research
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• v.5 no.2
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• pp.179-192
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• 2017

The transverse vibration of double walled carbon nanotube (DWCNT) embedded in elastic medium with an initial imperfection is considered. In this paper, Timoshenko beam theory is employed. However the nonlocal theory is used for modeling the nano scale of nanotube. In addition, the governing Equations of motion are obtained utilizing the Hamilton's principle and simply-simply boundary conditions are assumed. Furthermore, the Navier method is used for determining the natural frequencies of DWCNT. Hence, some parameters such as nonlocality, curvature amplitude, Winkler and Pasternak elastic foundations and length of the curved DWCNT are analyzed and discussed. The results show that, the curvature amplitude causes to increase natural frequency. However, nonlocal coefficient and elastic foundations have important role in vibration behavior of DWCNT with imperfection.

• Advances in nano research
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• v.7 no.6
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• pp.391-403
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• 2019

In this article the frequency response analysis of curved magneto-electro-viscoelastic functionally graded (CMEV-FG) nanobeams resting on viscoelastic foundation has been carried out. To this end, the study incorporates the Euler-Bernoulli beam model in association with Eringen's nonlocal theory to incorporate the size effects. The viscoelastic foundation in the current investigation is assumed to be the combination of Winkler-Pasternak layer and viscous layer of infinite parallel dashpots. The equations of motion are derived with the aid of Hamilton's principle and the solution to vibration problem of CMEV-FG nanobeams are obtained analytically. The material gradation is considered to follow Power-law rule. This study thoroughly investigates the influence of prominent parameters such as linear, shear and viscous layers of foundation, structural damping coefficient, opening angle, magneto-electrical field, nonlocal parameter, power-law exponent and slenderness ratio on the frequencies of FG nanobeams.

• Advances in nano research
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• v.6 no.4
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• pp.339-356
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• 2018

In this article, the critical buckling of a single-walled carbon nanotube (SWCNT) embedded in Kerr's medium is studied. Based on the nonlocal continuum theory and the Euler-Bernoulli beam model. The governing equilibrium equations are acquired and solved for CNTs subjected to mechanical loads and embedded in Kerr's medium. Kerr-type model is employed to simulate the interaction of the (SWNT) with a surrounding elastic medium. A first time, a comparison with the available results is made, and another comparison between various models Winkler-type, Pasternak-type and Kerr-type is studied. Effects of nonlocal parameter and aspect ratio of length to diameter of nanobeam, as well as the foundation parameters on buckling of CNT are investigated. These results are important in the mechanical design considerations of nanocomposites based on carbon nanotubes.