• Steel and Composite Structures
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• v.49 no.3
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• pp.293-306
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• 2023

This article focuses on the study of the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity, based on the first shear deformation and higher-order theory of the tube. The nano-scale tube is simulated using 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 a 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. A parametric study is performed to investigate the effects of different parameters, such as axial and radial FG power indices, porosity parameter, and nonlocal gradient strain parameters, on the buckling behavior of the bi-dimensional functionally graded porous tube. Keywords: Nonlocal strain gradient theory; buckling; Zhang-Fu's tube model; Timoshenko theory; Two-dimensional functionally graded materials; Nanotubes; Higher-order theory.

• 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.

• Advances in nano research
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• v.12 no.1
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• pp.101-115
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• 2022

Some researchers pointed out that the nonlocal cantilever models do not predict the dynamic softening behavior for nanostructures (including nanobeams) with clamped-free (CF) ends. In contrast, some indicate that the nonlocal cantilever models can capture the stiffness softening characteristics. There are substantial differences on this issue between them. The vibration analysis of porosity-dependent functionally graded nanoscale tubes with variable boundary conditions is investigated in this study. Using a modified power-law model, the tube's porosity-dependent material coefficients are graded in the radial direction. The theory of nonlocal strain gradients is used. Hamilton's principle is used to derive the size-dependent governing equations for simply-supported (S), clamped (C) and clamped-simply supported (CS). Following the solution of these equations by the extended differential quadrature technique, the effect of various factors on vibration issues was investigated further. It can be shown that these factors have a considerable effect on the vibration characteristics. It also can be found that our numerical results can capture the unexpected softening phenomena for cantilever tubes.

• Steel and Composite Structures
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• v.37 no.6
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• pp.711-731
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• 2020

This paper deals with free vibration of FG sandwich annular sector plates on Pasternak elastic foundation with different boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. The influence of carbon nanotubes (CNTs) waviness, aspect ratio, internal pores and graphene platelets (GPLs) on the vibrational behavior of functionally graded nanocomposite sandwich plates is investigated in this research work. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness of upper and bottom layers of the sandwich sectorial plates and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The core of structure is porous and the internal pores and graphene platelets (GPLs) are distributed in the matrix of core either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. A semi-analytic approach composed of 2D-Generalized Differential Quadrature Method (2D-GDQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.

• The Journal of Korean Academy of Prosthodontics
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• v.46 no.3
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• pp.307-319
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• 2008

STATEMENT OF PROBLEM: It is known that an anodic oxidation technique, one of the methods for the implant surface treatment, remarkably increased surface area, enhanced wettability and accelerated the initial bone healing. Purpose: This study was performed to evaluate the wettability of anodized titanium surface which has a nanotubular structure, to assess osseointegration after the placement of implant with nano-size tubes on tibia of rats and to analyze quantitatively transferable rhBMP-2 on each surface. MATERIAL AND METHOD: Four different kinds of surface-treated titanium discs (polished (machined surface) group, micro (blasting surface) group, nano (anodizedmachined surface) group, and nano-micro (anodized-blasting surface) group) were fabricated (n=10). Three different media were chosen to measure the surface contact angles; distilled water, plasma and rhBMP-2 solution. After a single drop (0.025 $m{\ell}$) of solution, the picture was taken with the image camera, and contact angle was measured by using image analysis system. For the test of osseointegration, 2 kinds of anodized surface (anodized-machined surface, anodized-blasting surface) implants having 2.0 mm in diameter and 5.0 mm in length inserted into the tibia of Wistar rats. After 3 weeks, tibia were harvested and the specimens were stained with hematoxylin and eosin for histological analysis. To test the possibility of drug delivery, after soaking sample groups in the concentration of 250 ng/$m{\ell}$l of rhBMP-2 for 48 hours, the excess solution of rhBMP-2 were removed. After that, they were lyophilized for 24 hours, and then the rhBMP-2 on the surface of titanium was resolved for 72 hours in PBS. All the extracted solution was analyzed by ELISA. One-way analysis of variance (ANOVA) was performed on the data. RESULTS: The wettability is improved by anodic oxidation. The best wettability was shown on the nano-micro group, and it was followed by nano group, micro group, and polished group. In the histological findings, all implants showed good healing and the new bone formation were observed along the implant surface. After 3 days, nano-micro group delivered the most amount of rhBMP-2, followed by nano group, micro group, and polished group. CONCLUSION: It indicated that anodic oxidation on blasting surface produce functionally graded nano-micro porous structure and enhance hydrophilicity of the surface and osseointegration. The findings suggest that the nano-micro porous structure could be a useful carrier of osteogenic molecules like rhBMP-2.