• Advances in nano research
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• 제15권4호
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• pp.339-353
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• 2023

This work aims to present a solution for the buckling behavior of perforated nano/microbeams with deformable boundary conditions using nonlocal strain gradient theory (NLSGT). For the first time, a solution that can provide buckling loads based on the non-local and strain gradient effects of perforated nanostructures on an elastic foundation, while taking into account both deformable and rigid boundary conditions. Stokes' transformation and Fourier series are used to realize this aim and determine the buckling loads under various boundary conditions. We employ the NLSGT to account for size-dependent effects and utilize the Winkler model to formulate the elastic foundation. The buckling behavior of the perforated nano/microbeams restrained with lateral springs at both ends is studied for various parameters such as the number of holes, the length and filling ratio of the perforated beam, the internal length, the nonlocal parameter and the dimensionless foundation parameter. Our results indicate that the number of holes and filling ratio significantly affect the buckling response of perforated nano/microbeams. Increasing the filling ratio increases buckling loads, while increasing the number of holes decreases buckling loads. The effects of the non-local and internal length parameters on the buckling behavior of the perforated nano/microbeams are also discussed. These material length parameters have opposite effects on the variation of buckling loads. This study presents an effective eigenvalue solution based on Stokes' transformation and Fourier series of the restrained nano/microbeams under the effects of elastic medium, perforation parameters, deformable boundaries and nonlocal strain gradient elasticity for the first time.

• Structural Engineering and Mechanics
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• 제61권2호
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• pp.275-282
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• 2017

The Fleck-Hutchinson theory on strain gradient plasticity (SGP), proposed in Adv. Appl Mech 33 (1997) 295, has recently been reformulated by adopting the strategy of decomposing the second order strain presented by Lam et al. in J Mech Pays Solids 51 (2003) 1477. The newly built SGP satisfies the non negativity of plastic dissipation, which is still an outstanding issue in other SGP theories. Furthermore, it explicitly shows how elastic strain gradients and corresponding elastic characteristic length scales come into play in general elastic-plastic loading histories. In this study, the relation between elastic length scales and plastic length scales is investigated by taking wire torsion as an example. It is concluded that the size effects arising when two sets of length scales are of the same order are essentially elastic instead of plastic.

• Advances in Computational Design
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• 제5권4호
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• pp.349-362
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• 2020

Dynamic characteristics of a scale-dependent porous metal foam cylindrical shell under a traveling load have been explored within this article based on a numerical approach. Within the material texture of the metal foams, uniform and non-uniform porosities may be dispersed. Based upon differential quadrature method (DQM) and Laplace transforms, the equations of motion for a shear deformable scale-dependent shell may be solved numerically. Scale-dependent shell modeling has been provided based upon strain gradient elasticity. Solving the equations will give the shell deflection as a function of load speed. Also, it is reported that shell deflection relies on the porosity dispersion and strain gradient influences.

• Advances in materials Research
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• 제8권3호
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• pp.179-196
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• 2019

This paper researches static and dynamic bending behaviors of a crystalline nano-size shell having pores and grains in the framework of strain gradient elasticity. Thus, the nanoshell is made of a multi-phase porous material for which all material properties on dependent on the size of grains. Also, in order to take into account small size effects much accurately, the surface energies related to grains and pores have been considered. In order to take into account all aforementioned factors, a micro-mechanical procedure has been applied for describing material properties of the nanoshell. A numerical trend is implemented to solve the governing equations and derive static and dynamic deflections. It will be proved that the static and dynamic deflections of the crystalline nanoshell rely on pore size, grain size, pore percentage, load location and strain gradient coefficient.

• Advances in nano research
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• 제7권1호
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• pp.1-11
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• 2019

In this article, wave propagation characteristics in magneto-electro-elastic (MEE) nanotube considering shell model is studied in the framework nonlocal theory. To account for the small-scale effects, the Eringen's nonlocal elasticity theory of is applied. Nonlocal governing equations of MEE nanotube have been derived utilizing Hamilton's principle. The results of this investigation have been accredited by comparing them of previous studies. An analytical solution of governing equations is used to obtain phase velocities and wave frequencies. The influences of different parameters, such as different mode, nonlocal parameter, length parameter, geometry, magnetic field and electric field on wave propagation responses of MEE nanotube are expressed in detail.

• Steel and Composite Structures
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• 제28권1호
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• pp.99-110
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• 2018

In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton's principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.

• Smart Structures and Systems
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• 제18권5호
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• pp.839-864
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• 2016

This paper presents an efficient method for updating the structural finite element model. Model updating is performed through minimizing the difference between the recorded acceleration of a real damaged structure and a hypothetical damaged one. This is performed by updating physical parameters (module of elasticity in this study) in each step using iterative process of modified nonlinear conjugate gradient (M-NCG) and modified Broyden-Fletcher-Goldfarb-Shanno algorithm (M-BFGS) separately. These algorithms are based on sensitivity analysis and provide a solution for nonlinear damage detection problem. Three illustrative test examples are considered to assess the performance of the proposed method. Finally, it is demonstrated that the proposed method is satisfactory for detecting the location and ratio of structural damage in presence of noise.

• Advances in nano research
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• 제8권2호
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• pp.157-167
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• 2020

This paper studies forced vibrational behavior of porous nanocrystalline silicon nanoshells under radial dynamic loads using strain gradient theory (SGT). This type of material contains many pores inside it and also there are nano-size grains which define the material character. The formulation for nanocrystalline nanoshell is provided by first order shell theory and a numerical approach is used in order to solve nanoshell equations. SGT gives a scale factor related to stiffness hardening provided by nano-grains. For more accurate description of size effects due to nano-grains or nano-pore, their surface energy influences have been introduced. Surface energy of inclusion exhibit extraordinary influence on dynamic response of the nanoshell. Also, dynamic response of the nanoshell is affected by the scale of nano-grain and nano-pore.

• Steel and Composite Structures
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• 제36권1호
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• pp.63-74
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• 2020

The present research investigates post-buckling behavior of geometrically imperfect tapered curved micro-panels made of graphene oxide powder (GOP) reinforced composite. Micro-scale effects on the panel structure have been included based on strain gradient elasticity. Micro-panel is considered to be tapered based on thickness variation along longitudinal direction. Weight fractions of uniformly and linearly distributed GOPs are included in material properties based on Halpin-Tsai homogenization scheme considering. Post-buckling curves have been determined based on both perfect and imperfect micro-panel assumptions. It is found that post-buckling curves are varying with the changes of GOPs weight fraction, geometric imperfection, GOP distribution type, variable thickness parameters, panel curvature radius and strain gradient.

• 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.