• Advances in nano research
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• v.12 no.3
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• pp.281-290
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• 2022

In the current research, the thermal buckling characteristics of the bi-directional functionally graded nano-scale tapered beam on the basis of a couple of nonlocal Eringen and classical beam theories are scrutinized. The nonlocal governing equation and associated nonlocal boundary conditions are constructed using the conservation energy principle, and the resulting equations are solved using the generalized differential quadrature method (GDQM). The mechanical characteristics of the produced material are altered along both the beam length and thickness direction, indicating that it is a two-dimensional functionally graded material (2D-FGM). It is thought that the nanostructures are defective because to the presence of porosity voids. Finally, the obtained results are used to design small-scale sensors and make an excellent panorama of developing the production of nanostructures.

• Steel and Composite Structures
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• v.48 no.2
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• pp.235-250
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• 2023

The present paper examines the stability analysis of the buckling differentiae of the small-scale, non-uniform porosity-dependent functionally graded (PD-FG) tube. The high-order beam theory and nonlocal strain gradient theory are operated for the mathematical modeling of nanotubes based on the Hamilton principle. In this paper, the external radius function is non-uniform. In contrast, the internal radius is uniform, and the cross-section changes along the tube length due to these radius functions based on the four types of useful mathematical functions. The PD-FG material distributions are varied in the radial direction and made with ceramics and metals. The governing partial differential equations (PDEs) and associated boundary conditions are solved via a numerical method for different boundary conditions. The received outcomes concerning different presented parameters are valuable to the design and production of small-scale devices and intelligent structures.

• Advances in nano research
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• v.13 no.3
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• pp.297-312
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• 2022

Coughing and breath shortness are common symptoms of nano (small) cell lung cancer. Smoking is main factor in causing such cancers. The cancer cells form on the soft tissues of lung. Deformation behavior and wave vibration of lung affected when cancer cells exist. Therefore, in the current work, phase velocity behavior of the small cell lung cancer as a main part of the body via an exact size-dependent theory is presented. Regarding this problem, displacement fields of small cell lung cancer are obtained using first-order shear deformation theory with five parameters. Besides, the size-dependent small cell lung cancer is modeled via nonlocal stress/strain gradient theory (NSGT). An analytical method is applied for solving the governing equations of the small cell lung cancer structure. The novelty of the current study is the consideration of the five-parameter of displacement for curved panel, and porosity as well as NSGT are employed and solved using the analytical method. For more verification, the outcomes of this reports are compared with the predictions of deep neural network (DNN) with adaptive optimization method. A thorough parametric investigation is conducted on the effect of NSGT parameters, porosity and geometry on the phase velocity behavior of the small cell lung cancer structure.

• Advances in nano research
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• v.7 no.5
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• pp.325-335
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• 2019

In the present study, nonlocal strain gradient theory (NSGT) is developed for wave propagation of functionally graded (FG) nanoscale plate in the thermal environment by considering the porosity effect. $Si_3N_4$ as ceramic phase and SUS304 as metal phase are regarded to be constitutive material of FG nanoplate. The porosity effect is taken into account on the basis of the newly extended method which considers coupling influence between Young's modulus and mass density. The motion relation is derived by applying Hamilton's principle. NSGT is implemented in order to account for small size effect. Wave frequency and phase velocity are obtained by solving the problem via an analytical method. The effects of different parameters such as porosity coefficient, gradient index, wave number, scale factor and temperature change on phase velocity and wave frequency of FG porous nanoplate have been examined and been presented in a group of illustrations.

• Computers and Concrete
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• v.27 no.3
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• pp.269-282
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• 2021

A dynamic analytical solution for a simply supported, rectangular functionally graded plate with a porous middle layer under time-dependent load based on a refined third-order shear deformation theory with a cubic variation of in-plane displacements according to the thickness and linear/quadratic transverse displacement is presented. The solution achieved in the trigonometric series form and rests on the Green's function method. Two porosity types and their influence on material properties, and mechanical behavior are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using the power-law distribution idealization. Numerical calculations have been carried out to demonstrate the accuracy of the kinematic model for the dynamic problem, the effect of porosity, thickness of porous layers, power-law index, and type of loading on the dynamic response of an imperfect functionally graded material plate.

• Advances in materials Research
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• v.12 no.2
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• pp.133-159
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• 2023

In this paper, a size-dependent dynamic investigation of a porous metal foams microbeamsis presented. The novelty of this study is to use a metal foam microbeam that contain porosities based on the refined high order shear deformation beam model, with sinusoidal shear strain function, and the modified strain gradient theory (MSGT) for the first time. The Lagrange's principle combined with differential quadrature hierarchicalfinite element method (DQHFEM) are used to obtain the porous microbeam governing equations. The solutions are presented for the natural frequencies of the porous and homogeneoustype microbeam. The obtained results are validated with the analytical methods found in the literature, in order to confirm the accuracy of the presented resolution method. The influences of the shape of porosity distribution, slenderness ratio, microbeam thickness, and porosity coefficient on the free vibration of the porous microbeams are explored in detail. The results of this paper can be used in various design formetallic foammicro-structuresin engineering.

• Advances in nano research
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• v.7 no.6
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• pp.379-390
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• 2019

Putting emphasis on the effect of existence of porosity in the functionally graded materials (FGMs) on the dynamic responses of waves scattered in FG nanobeams resulted in implementation of a novel porosity-based homogenization method for FGMs and show its applicability in a wave propagation problem in the presence of axial pre-load for the first time. In the employed porosity-dependent method, the coupling between density and Young's moduli is included to consider for the effective moduli of the FG nanobeam by the means of a more reliable homogenization technique. The beam-type element will be modeled via the classical theory of beams, namely Euler-Bernoulli beam theory. Also, the dynamic form of the principle of virtual work will be extended for such nanobeams to derive the motion equations. Applying the nonlocal constitutive equations of Eringen on the obtained motion equations will be resulted in derivation of the nanobeam's governing equations. Depicted results reveal that the dispersion responses of FG nanobeams will be decreased as the porosity volume fraction is increased which must be noticed by the designers of advanced nanosize devices who are interested in employment of wave dispersion approach in continuous systems for specific goals.

• Advances in nano research
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• v.10 no.5
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• pp.493-507
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• 2021

This article focused on studying the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity based on first shear deformation and higher-order theory of tube. The nano-scale tube is simulated based on the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. The parametric study is performed to study the effects of different parameters such as axial and radial FG power indexes, porosity parameter, nonlocal gradient strain parameters on the buckling behavior of di-dimensional functionally graded porous tube.

• Structural Engineering and Mechanics
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• v.90 no.1
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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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• v.78 no.4
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• pp.379-386
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• 2021

A numerical and computer simulation for dynamic stability analysis of graded porous nanoplates has been provided using a Chebyshev-Ritz-Bolotin approach. The nanoplate has been formulated according to the nonlocal elasticity and a 3-unkown plate model capturing neutral surface location. All of material properties are assumed to be dependent of porosity factor which determines the amount or volume of pores. The nano-size plate has also been assumed to be under temperature and moisture variation. It will be shown that stability boundaries of the nanoplate are dependent on static and dynamical load factors, porosity factor, temperature variation and nonlocal parameter.