• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.497-517
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• 2015

In this study, nonlocal nonlinear buckling analysis of embedded polymeric temperature-dependent microplates resting on an elastic matrix as orthotropic temperature-dependent elastomeric medium is investigated. The microplate is reinforced by single-walled carbon nanotubes (SWCNTs) in which the equivalent material properties nanocomposite are estimated based on the rule of mixture. For the carbon-nanotube reinforced composite (CNTRC) plate, both cases of uniform distribution (UD) and functionally graded (FG) distribution patterns of SWCNT reinforcements are considered. The small size effects of microplate are considered based on Eringen's nonlocal theory. Based on orthotropic Mindlin plate theory along with von K$\acute{a}$rm$\acute{a}$n geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the buckling load of system. The effects of different parameters such as nonlocal parameters, volume fractions of SWCNTs, distribution type of SWCNTs in polymer, elastomeric medium, aspect ratio, boundary condition, orientation of foundation orthtotropy direction and temperature are considered on the nonlinear buckling of the microplate. Results indicate that CNT distribution close to top and bottom are more efficient than those distributed nearby the mid-plane for increasing the buckling load.

• Advances in materials Research
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• v.3 no.2
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• pp.77-89
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• 2014

In the present article, the thermal buckling of zigzag single-walled carbon nanotubes (SWCNTs) is studied using a nonlocal refined shear deformation beam theory and Von-Karman geometric nonlinearity. The model developed simulates both small scale effects and higher-order variation of transverse shear strain through the depth of the nanobeam. Furthermore the present formulation also accommodates stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. The equivalent Young's modulus and shear modulus for zigzag SWCNTs are derived using an energy-equivalent model. The present study illustrates that the thermal buckling properties of SWCNTs are strongly dependent on the scale effect and additionally on the chirality of zigzag carbon nanotube. Some illustrative examples are also presented to verify the present formulation and solutions. Good agreement is observed.

• Steel and Composite Structures
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• v.15 no.5
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• pp.481-505
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• 2013

This paper focuses on thermal post-buckling analysis of functionally graded beams with temperature dependent physical properties by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces and therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In this study, the differences between temperature dependent and independent physical properties are investigated for functionally graded beams in detail in post-buckling case. With the effects of material gradient property and thermal load, the relationships between deflections, critical buckling temperature and maximum stresses of the beams are illustrated in detail in post-buckling case.

• Steel and Composite Structures
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• v.24 no.1
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• pp.65-77
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• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.433-450
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• 1997

The objective of this work is to predict the failure loads, associated maximum transverse displacements, locations and the modes of failure, including the onset of delamination, of thin, flat, square symmetric laminates under the action of uni-axial compression. Two progressive failure analyses, one using Hashin criterion and the other using Tensor polynomial criteria, are used in conjunction with the finite element method. First order shear deformation theory and geometric nonlinearity in the von Karman sense have been employed. Five different types of lay-up sequence are considered for laminates with all edges simply supported. In addition, two boundary conditions, one with all edges fixed and other with mixed boundary conditions for $(+45/-45/0/90)_{2s}$ quasi-isotropic laminate have also been considered to study the effect of boundary restraints on the failure loads and the corresponding modes of failure. A comparison of linear and nonlinear results is also made for $({\pm}45/0/90)_{2s}$ quasi-isotropic laminate. It is observed that the maximum difference between the failure loads predicted by various criteria depend strongly on the laminate lay-ups and the flexural boundary restraints. Laminates with clamped edges are found to be more susceptible to failure due to the transverse shear and delamination, while those with the simply supported edges undergo total collapse at a load slightly higher than the fiber failure load.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.5
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• pp.85-98
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• 1993

A method of analysis for the material and geometric nonlinear analysis of planar prestressed concrete cable-stayed bridges including the time-dependent effects due to load history, creep, shrinkage, aging of concrete and relaxation of prestress is described. The analysis procedure, based on the finite element method, is capable of predicting the response of these structures through elastic, cracking, inelastic and ultimate ranges. The nonlinear formulation for the description of motion is based on the updated Lagrangian approach. To account for the material nonlinearity, nonlinear stress-strain relationship and cracking of concrete, nonlinear stress-strain relationships of reinforcing steel, prestressing steel, and cable, including load reversal are given. Results from a numerical examples on ultimate analyses of cable-stayed bridges are presented to illustrate the analysis method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.9
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• pp.879-888
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• 2012

This study aims to apply multistage homotopy perturbation method(MHPM) to space truss composed of discrete members to obtain a semi-analytical solution. For the purpose of this research, a nonlinear governing equation of the structures is formulated in consideration of geometrical nonlinearity, and homotopy equation is derived. The result of carrying out dynamic analysis on a simple model is compared to a numerical method of 4th order Runge-Kutta method(RK4), and the dynamic response by MHPM concurs with the numerical result. Besides, the displacement response and attractor in the phase space is able to delineate dynamic snapping properties under step excitations and the responses of damped system are reflected well the reduction effect of the displacement.

• Structural Engineering and Mechanics
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• v.44 no.1
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• pp.109-125
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• 2012

Post-buckling behavior of Timoshenko beams subjected to uniform temperature rising with temperature dependent physical properties are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The beams considered in numerical examples are made of Austenitic Stainless Steel (316). The convergence studies are made. In this study, the difference between temperature dependent and independent physical properties are investigated in detail in post-buckling case. The relationships between deflections, thermal post-buckling configuration, critical buckling temperature, maximum stresses of the beams and temperature rising are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.797-816
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• 2014

Cooling tower is analyzed as an assembly of layered nonlinear shell elements. Geometric representation of the shell is enabled through layered nonlinear shell elements to define the different layers of reinforcements and concrete by considering the material nonlinearity of each layer for the cooling tower shell. Modal analysis using Ritz vector analysis and nonlinear time history analysis by direct integration method have been carried out to study the effects of the inclination of the supporting columns of the cooling tower shell on its dynamic characteristics. The cooling tower is supported by I-type columns and ${\Lambda}$-type columns supports having the different inclination angles. Relevant comparisons of the dynamic response of the structural system at the base level (at the junction of the column and shell), throat level and at the top of the tower have been made. Dynamic response of the cooling tower is found to be significantly sensitive to the change of the inclination of the supporting columns. It is also found that the stiffness of the structure system increases with increase in inclination angle of the supporting columns, resulting in decrease of the period of the structural system. The participation of the stiffness of the tower in structural response of the cooling tower is fund to be dependent of the change in the inclination angle and even in the types of the supporting columns.

• Advances in nano research
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• v.1 no.1
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• pp.1-11
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• 2013

The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.