• Structural Engineering and Mechanics
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• 제90권1호
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• pp.1-18
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• 2024

The present study conducts a thorough analysis of thermal vibrations in functionally graded porous nanocomposite beams within a thermal setting. Investigating the temperature-dependent material properties of these beams, which continuously vary across their thickness in accordance with a power-law function, a finite element approach is developed. This approach utilizes a nonlocal strain gradient theory and accounts for a linear temperature rise. The analysis employs four different patterns of porosity distribution to characterize the functionally graded porous materials. A novel two-variable shear deformation beam nonlocal strain gradient theory, based on trigonometric functions, is introduced to examine the combined effects of nonlocal stress and strain gradient on these beams. The derived governing equations are solved through a 3-nodes beam element. A comprehensive parametric study delves into the influence of structural parameters, such as thicknessratio, beam length, nonlocal scale parameter, and strain gradient parameter. Furthermore, the study explores the impact of thermal effects, porosity distribution forms, and material distribution profiles on the free vibration of temperature-dependent FG nanobeams. The results reveal the substantial influence of these effects on the vibration behavior of functionally graded nanobeams under thermal conditions. This research presents a finite element approach to examine the thermo-mechanical behavior of nonlocal temperature-dependent FG nanobeams, filling the gap where analytical results are unavailable.

• Structural Engineering and Mechanics
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• 제64권6권
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• pp.683-693
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• 2017

According to a generalized nonlocal strain gradient theory (NSGT), dynamic modeling and free vibrational analysis of nanoporous inhomogeneous nanoplates is presented. The present model incorporates two scale coefficients to examine vibration behavior of nanoplates much accurately. Porosity-dependent material properties of the nanoplate are defined via a modified power-law function. The nanoplate is resting on a viscoelastic substrate and is subjected to hygro-thermal environment and in-plane linearly varying mechanical loads. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. Obtained results show the importance of hygro-thermal loading, viscoelastic medium, in-plane bending load, gradient index, nonlocal parameter, strain gradient parameter and porosities on vibrational characteristics of size-dependent FG nanoplates.

• Advances in aircraft and spacecraft science
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• 제7권2호
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• pp.169-186
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• 2020

Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton's principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.

• Steel and Composite Structures
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• 제50권1호
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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.

• Advances in nano research
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• 제10권1호
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• pp.15-24
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• 2021

Microtubules (MTs) are the main part of the cytoskeleton in living eukaryotic cells. In this article, a mechanical model of MT buckling, considering the modified strain gradient theory, is analytically examined. The MT is assumed as a cylindrical beam and a new single variable trigonometric beam theory is developed in conjunction with a modified strain gradient model. The main benefit of the present formulation is shown in its new kinematic where we found only one unknown as the Euler-Bernoulli beam model, which is even less than the Timoshenko beam model. The governing equations are deduced by considering virtual work principle. The effectiveness of the present method is checked by comparing the obtained results with those reported by other higher shear deformation beam theory involving a higher number of unknowns. It is shown that microstructure-dependent response is more important when material length scale parameters are closer to the outer diameter of MTs. Also, it can be confirmed that influences of shear deformation become more considerable for smaller shear modulus and aspect ratios.

• Structural Engineering and Mechanics
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• 제60권4호
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• pp.707-727
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• 2016

In this paper, thermal vibration of a nonlocal functionally graded (FG) plates with arbitrary boundary conditions under linear and non-linear temperature fields is explored by developing a refined shear deformation plate theory with an inverse cotangential function in which shear deformation effect was involved without the need for shear correction factors. The material properties of FG nanoplate are considered to be temperature-dependent and graded in the thickness direction according to the Mori-Tanaka model. On the basis of non-classical higher order plate model and Eringen's nonlocal elasticity theory, the small size influence was captured. Numerical examples show the importance of non-uniform thermal loadings, boundary conditions, gradient index, nonlocal parameter and aspect and side-to-thickness ratio on vibrational responses of size-dependent FG nanoplates.

• Advances in nano research
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• 제5권4호
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• pp.393-414
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• 2017

Forced vibration behavior of porous metal foam nanoplates on elastic medium is studied via a 4-variable plate theory. Different porosity distributions called uniform, symmetric and asymmetric are considered. Nonlocal strain gradient theory (NSGT) containing two scale parameters is employed for size-dependent modeling of porous nanoplates. The present plate theory satisfies the shear deformation effect and it has lower field variables compared with first order plate theory. Hamilton's principle is employed to derive the governing equations. Obtained results from Galerkin's method are verified with those provided in the literature. The effects of nonlocal parameter, strain gradient, foundation parameters, dynamic loading, porosity distributions and porosity coefficient on dynamic deflection and resonance frequencies of metal foam nanoscale plates are examined.

• Steel and Composite Structures
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• 제28권1호
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• pp.13-24
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• 2018

A size-dependent novel hyperbolic shear deformation theory of simply supported functionally graded beams is presented in the frame work of the non-local strain gradient theory, in which the stress accounts for only the nonlocal strain gradients stress field. The thickness stretching effect (${\varepsilon}_z{\neq}0$) is also considered here. Elastic coefficients and length scale parameter are assumed to vary in the thickness direction of functionally graded beams according to power-law form. The governing equations are derived using the Hamilton principle. The closed-form solutions for exact critical buckling loads of nonlocal strain gradient functionally graded beams are obtained using Navier's method. The derived results are compared with those of strain gradient theory.

• Structural Engineering and Mechanics
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• 제65권6호
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• pp.645-656
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• 2018

Importance of procuring adequate knowledge about the mechanical behavior of double-layered graphene sheets (DLGSs) incensed the authors to investigate wave propagation responses of mentioned element while rested on a visco-Pasternak medium under hygro-thermal loading. A nonlocal strain gradient theory (NSGT) is exploited to present a more reliable size-dependent mechanical analysis by capturing both softening and hardening effects of small scale. Furthermore, in the framework of a classical plate theory the kinematic relations are developed. Incorporating kinematic relations with the definition of Hamilton's principle, the Euler-Lagrange equations of each of the layers are derived separately. Afterwards, combining Euler-Lagrange equations with those of the NSGT the nonlocal governing equations are written in terms of displacement fields. Interaction of the each of the graphene sheets with another one is regarded by the means of vdW model. Then, a widespread analytical solution is employed to solve the derived equations and obtain wave frequency values. Subsequently, influence of each participant variable containing nonlocal parameter, length scale parameter, foundation parameters, temperature gradient and moisture concentration is studied by plotting various figures.

• 한국전산유체공학회지
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• 제11권1호
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• pp.8-15
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• 2006

The existing approximations of diffusion flux in unstructured cell-centered finite volume methods are examined in detail with each other and clarified to have indefinite expressions in several respects. A new numerical approximation of diffusion flux at cell face center is then proposed, which is second-order accurate even on irregular grids and may be easily implemented in CFD code using cell-centered finite volume method with unstructured grids composed of arbitrary convex polyhedral shape.