• Advances in nano research
• /
• v.9 no.2
• /
• pp.69-82
• /
• 2020

In this paper, a new explicit analytical formula is derived for the critical buckling load of Double Walled Carbon Nanotubes (DWCNTs) embedded in Winkler elastic medium without taking into account the effects of the nonlocal parameter, which indicates the effects of the surrounding elastic matrix combined with the intertube Van der Waals (VdW) forces. Furthermore, we present a model which predicts that the critical axial buckling load embedded in Winkler, Pasternak or Kerr elastic medium under axial compression using the nonlocal Donnell shell theory, this model takes into account the effects of internal small length scale and the VdW interactions between the inner and outer nanotubes. The present model predicts that the critical axial buckling load of embedded DWCNTs is greater than that without medium under identical conditions and parameters. We can conclude that the embedded DWCNTs are less susceptible to axial buckling than those without medium.

• Geomechanics and Engineering
• /
• v.31 no.1
• /
• pp.99-112
• /
• 2022

The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton's principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs.

• Structural Engineering and Mechanics
• /
• v.60 no.4
• /
• pp.615-631
• /
• 2016

In this paper, an analytical method for the Post-buckling response of cylindrical shells with spiral stiffeners surrounded by an elastic medium subjected to external pressure is presented. The proposed model is based on two parameters elastic foundation Winkler and Pasternak. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. According to the Von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method is used to solve the nonlinear problem. To valid the formulations, comparisons are made with the available solutions for nonlinear static buckling of stiffened homogeneous and un-stiffened FGM cylindrical shells. The obtained results show the elastic foundation Winkler on the response of buckling is more effective than the elastic foundation Pasternak. Also the ceramic shells buckling strength higher than the metal shells and minimum critical buckling load is occurred, when both of the stiffeners have angle of thirty degrees.

• Advances in nano research
• /
• v.7 no.4
• /
• pp.265-275
• /
• 2019

In this work, the effect of size on the axial buckling behavior of single-layered graphene sheets embedded in elastic media is studied. We incorporate Eringen's nonlocal elasticity equations into three plate theories of first order shear deformation theory, higher order shear deformation theory, and classical plate theory. The surrounding elastic media are simulated using Pasternak and Winkler foundation models and their differences are evaluated. The results obtained from different nonlocal plate theories include the values of Winkler and Pasternak modulus parameters, mode numbers, nonlocal parameter, and side lengths of square SLGSs. We show here that axial buckling behavior strongly depends on modulus and nonlocal parameters, which have different values for different mode numbers and side lengths. In addition, we show that in different nonlocal plate theories, nonlocality is more influential in first order shear deformation theory, especially in certain range of nonlocal parameters.

• Structural Engineering and Mechanics
• /
• v.82 no.6
• /
• pp.701-711
• /
• 2022

The nonlocal elasticity as well as Mindlin's first-order shear deformation plate theory are proposed to investigate thermal vibrational of a nanoplate placing on a three-factor foundation. The Winkler-Pasternak elastic foundation is connected with the viscous damping to obtain the present three-parameter viscoelastic model. Differential equations of motion are derived and resolved for simply-supported nanoplates to get their natural frequencies. The influences of the nonlocal index, viscous damping index, and temperature changes are investigated. A comparison example is dictated to validate the precision of present results. Effects of other factors such as aspect ratio, mode numbers, and foundation parameters are discussed carefully for the vibration problem. Additional thermal vibration results of nanoplates resting on the viscoelastic foundation are presented for comparisons with future investigations.

• Steel and Composite Structures
• /
• v.23 no.6
• /
• pp.623-631
• /
• 2017

Present paper deals with the temperature-dependent buckling analysis of sandwich nanocomposite plates resting on elastic medium subjected to magnetic field. The lamina layers are reinforced with carbon nanotubes (CNTs) as uniform and functionally graded (FG). The elastic medium is considered as orthotropic Pasternak foundation with considering the effects of thermal loading on the spring and shear constants of medium. Mixture rule is utilized for obtaining the effective material properties of each layer. Adopting the Reddy shear deformation plate theory, the governing equations are derived based on energy method and Hamilton's principle. The buckling load of the structure is calculated with the Navier's method for the simply supported sandwich nanocomposite plates. Parametric study is conducted on the combined effects of the volume percent and distribution types of the CNTs, temperature change, elastic medium, magnetic field and geometrical parameters of the plates on the buckling load of the sandwich structure. The results show that FGX distribution of the CNTs leads to higher stiffness and consequently higher buckling load. In addition, considering the magnetic field increases the buckling load of the sandwich nanocomposite plate.

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

• Structural Engineering and Mechanics
• /
• v.55 no.4
• /
• pp.743-763
• /
• 2015

This work presents a new nonlocal hyperbolic shear deformation beam theory for the static, buckling and vibration of nanoscale-beams embedded in an elastic medium. The present model is able to capture both the nonlocal parameter and the shear deformation effect without employing shear correction factor. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as nanobeams. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale-beam are obtained using Hamilton's principle. The effect of the surrounding elastic medium on the deflections, critical buckling loads and frequencies of the nanobeam is investigated. Both Winkler-type and Pasternak-type foundation models are used to simulate the interaction of the nanobeam with the surrounding elastic medium. Analytical solutions are presented for a simply supported nanoscale-beam, and the obtained results compare well with those predicted by the other nonlocal theories available in literature.

• Advances in nano research
• /
• v.6 no.3
• /
• pp.279-298
• /
• 2018

Present investigation deals with the free vibration characteristics of nanoscale-beams resting on elastic Pasternak's foundation based on nonlocal strain-gradient theory and a higher order hyperbolic beam model which captures shear deformation effect without using any shear correction factor. The nanobeam is lying on two-parameters elastic foundation consist of lower spring layers as well as a shear layer. Nonlocal strain gradient theory takes into account two scale parameters for modeling the small size effects of nanostructures more accurately. Hamilton's principal is utilized to derive the governing equations of embedded strain gradient nanobeam and, after that, analytical solutions are provided for simply supported conditions to solve the governing equations. The obtained results are compared with those predicted by the previous articles available in literature. Finally, the impacts of nonlocal parameter, length scale parameter, slenderness ratio, elastic medium, on vibration frequencies of nanosize beams are all evaluated.

• Smart Structures and Systems
• /
• v.21 no.1
• /
• pp.15-25
• /
• 2018

This work presents the buckling investigation of embedded orthotropic nanoplates such as graphene by employing a new refined plate theory and nonlocal small-scale effects. The elastic foundation is modeled as two-parameter Pasternak foundation. The proposed two-variable refined plate theory takes account of transverse shear influences and parabolic variation of the transverse shear strains within the thickness of the plate by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. Nonlocal governing equations for the single layered graphene sheet are obtained from the principle of virtual displacements. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.