• Steel and Composite Structures
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• v.43 no.1
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• pp.31-54
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• 2022

This paper is concerned with the buckling behavior of functionally graded graphene reinforced porous nanocomposite beams based on the finite element method (FEM) using two variables trigonometric shear deformation theory. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The finite element approach is developed using a nonlocal strain gradient theory. The governing equations derived here are solved introducing a 3-nodes beam element, and then the critical buckling load is calculated with different porosity distributions and GPL dispersion patterns. After a convergence and validation study to verify the accuracy of the present model, a comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern of GPL reinforcements on the Buckling behavior of the nanocomposite beam. The effects of various structural parameters such as the dispersion patterns for the graphene and porosity, thickness ratio, boundary conditions, and nonlocal and strain gradient parameters are brought out. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams, and the results allows to identify the most effective way to achieve improved buckling behavior of the porous nanocomposite beam.

• Steel and Composite Structures
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• v.20 no.3
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• pp.545-569
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• 2016

Stiffeners have widely been used in lateral load resisting systems to improve the buckling stability of shear panels in steel frames. However, due to major differences between plate girders and steel plate shear walls (SPSWs), use of plate girder equations often leads to uneconomical and, in some cases, incorrect design of stiffeners. Hence, this paper uses finite element analysis (FEA) to describe the effect of the rigidity and arrangement of stiffeners on the buckling behavior of plates. The procedures consider transverse and/or longitudinal stiffeners in various practical configurations. Subsequently, curves and formulas for the design of stiffeners are presented. In addition, the influence of stiffeners on the inward forces subjected to the boundary elements and the tension field angle is investigated as well. The results indicate that the effective application of stiffeners in SPSW systems not only improves the structural behavior, such as stiffness, overall strength and energy absorption, but also leads to a reduction of the forces that are exerted on the boundary elements.

• Advances in materials Research
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• v.12 no.3
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• pp.243-261
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• 2023

This study aims to analyze the mechanical buckling behavior of a single-walled carbon nanotube (SWCNT) integrated with a one-parameter elastic medium and modeled as a Kerr-type foundation under a longitudinal magnetic field. The structure is considered homogeneous and therefore modeled utilizing the nonlocal first shear deformation theory (NL-FSDT). This model targets thin and thick structures and considers the effect of the transverse shear deformation and small-scale effect. The Kerr model describes the elastic matrix, which takes into account the transverse shear strain and normal pressure. Using the nonlocal elastic theory and taking into account the Lorentz magnetic force acquired from Maxwell relations, the stability equation for buckling analysis of a simply supported SWCNT under a longitudinal magnetic field is obtained. Moreover, the mechanical buckling load behavior with respect to the impacts of the magnetic field and the elastic medium parameters considering the nonlocal parameter, the rotary inertia, and transverse shear deformation was examined and discussed. This study showed useful results that can be used for the design of nano-transistors that use the buckling properties of single-wall carbon nanotubes(CNTs) due to the creation of the magnetic field effect.

• Composites Research
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• v.13 no.5
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• pp.37-43
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• 2000

In this paper an analytical investigation pertaining to the elastic shear buckling behavior of transversely stiffened orthotropic plate under in-plane shear forces is presented. All edges of plate are assumed to be simply supported and the evenly placed stiffener is considered as a beam element neglecting its torsional rigidity. For the solution of the problem Rayleigh-Ritz method is employed. Using the derived equation, the limit of buckling stress of transversely stiffened plate is suggested as a graphical form. Based on the limit of buckling stress of stiffened plate, graphical form of results for finding the required stiffener rigidity is presented when one and two stiffeners are located, respectively.

• Advances in nano research
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• v.10 no.4
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• pp.313-325
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• 2021

This paper is concerned with the buckling behavior of 2D and quasi-3D problem of functionally graded nanobeam founded on high order shear deformation beams theory and made by two different types of porous distribution materials in Nano- and micro-scales. The used Quasi-3D formulation takes into account the transverse shear effect and uses only three variables. Both formulations do not include the correction factor that is required in the first shear deformation theory proposed by Timoshenko. Governing equations are derived using the principle of virtual work. Analytical resolutions for buckling of FG nanobeam are introduced under tow different boundary conditions, and the results obtained are compared to those proposed in literatures.

• Advances in nano research
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• v.4 no.1
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• pp.51-64
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• 2016

This paper investigates the effects of thermal load and shear force on the buckling of nanobeams. Higher-order shear deformation beam theories are implemented and their predictions of the critical buckling load and post-buckled configurations are compared to those of Euler-Bernoulli and Timoshenko beam theories. The nonlocal Eringen elasticity model is adopted to account a size-dependence at the nano-scale. Analytical closed form solutions for critical buckling loads and post-buckling configurations are derived for proposed beam theories. This would be helpful for those who work in the mechanical analysis of nanobeams especially experimentalists working in the field. Results show that thermal load has a more significant impact on the buckling behavior of simply-supported beams (S-S) than it has on clamped-clamped (C-C) beams. However, the nonlocal effect has more impact on C-C beams that it does on S-S beams. Moreover, it was found that the predictions obtained from Timoshenko beam theory are identical to those obtained using all higher-order shear deformation theories, suggesting that Timoshenko beam theory is sufficient to analyze buckling in nanobeams.

• Advances in nano research
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• v.7 no.6
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• pp.405-417
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• 2019

This research is devoted to study post-buckling analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) micro plate with cut out subjected to magnetic field and resting on elastic medium. The basic formulation of plate is based on first order shear deformation theory (FSDT) and the material properties of FG-CNTRCs are presumed to be changed through the thickness direction, and are assumed based on rule of mixture; moreover, nonlocal Eringen's theory is applied to consider the size-dependent effect. It is considered that the system is embedded in elastic medium and subjected to longitudinal magnetic field. Energy approach, domain decomposition and Rayleigh-Ritz methods in conjunction with Newton-Raphson iterative technique are employed to trace the post-buckling paths of FG-CNTRC micro cut out plate. The influence of some important parameters such as small scale effect, cut out dimension, different types of FG distributions of CNTs, volume fraction of CNTs, aspect ratio of plate, magnitude of magnetic field, elastic medium and biaxial load on the post-buckling behavior of system are calculated. With respect to results, it is concluded that the aspect ratio and length of square cut out have negative effect on post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the post-buckling behavior of plate and different distributions of CNTs in plate have diverse response. Meanwhile, nonlocal parameter and biaxial compression load on the plate has negative effect on post-buckling response. In addition, imposing magnetic field increases the post-buckling load of the microstructure.

• Advances in nano research
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• v.12 no.4
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• pp.427-440
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• 2022

In the present study, the nonlocal strain gradient theory is used to predict the size-dependent buckling and post-buckling behavior of geometrically imperfect nano-scale piezo-flexomagnetic plate strips in two modes of direct and converse flexomagnetic effects. The first-order shear deformation plate theory is used to analyze analytically nano-strips with simply supported boundary conditions. The nonlinear governing equations of equilibrium and associated boundary conditions are derived using the principle of minimum total potential energy with consideration of the von Kármán-type of geometric nonlinearity. A closed-form solution of governing differential equation is obtained, which is easily usable for engineers and designers. To validate the presented formulations, whenever possible, a comparison with the results found in the open literature is reported for buckling loads. A parametric study is presented to examine the effect of scaling parameters, plate slenderness ratio, temperature, the mid-plane initial rise, flexomagnetic coefficient, different temperature distributions, and magnetic potential, in case of the converse flexomagnetic effect, on buckling and post-buckling loads in detail.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.369-377
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• 2018

In this article, buckling and free vibration of functionally graded (FG) nanobeams resting on elastic foundation are investigated by developing various higher order beam theories which capture shear deformation influences through the thickness of the beam without the need for shear correction factors. The elastic foundation is modeled as linear Winkler springs as well as Pasternak shear layer. The material properties of FG nanobeam are supposed to change gradually along the thickness through the Mori-Tanaka model. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. From Hamilton's principle, the nonlocal governing equations of motion are derived and then solved applying analytical solution. To verify the validity of the developed theories, the results of the present work are compared with those available in literature. The effects of shear deformation, elastic foundation, gradient index, nonlocal parameter and slenderness ratio on the buckling and free vibration behavior of FG nanobeams are studied.

• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.547-567
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• 2013

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.