• Advances in materials Research
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• 제3권2호
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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.

• Structural Engineering and Mechanics
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• 제25권2호
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• pp.161-180
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• 2007

A first endeavor is made to exploit the differential quadrature method (DQM) as a simple, accurate, and computationally efficient numerical tool for the large deformation analysis of thin laminated composite skew plates, which has very strong singularity at the obtuse vertex. The geometrical nonlinearity is modeled by using Green's strain and von Karman assumption. A recently developed DQ methodology is used to exactly implement the multiple boundary conditions at the edges of skew plates, which is a major draw back of conventional DQM. Using oblique coordinate system and the DQ methodology, a mapping-DQ discretization rule is developed to simultaneously transform and discretize the equilibrium equations and the related boundary conditions. The effects of skew angle, aspect ratio and different types of boundary conditions on the convergence and accuracy of the presented method are studied. Comparing the results with the available results from other numerical or analytical methods, it is shown that accurate results are obtained even when using only small number of grid points. Finally, numerical results for large deflection behavior of antisymmetric cross ply skew plates with different geometrical parameters and boundary conditions are presented.

• 대한기계학회논문집A
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• 제26권9호
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• pp.1905-1913
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• 2002

Using the finite element method, this study investigates the dynamic time responses of a flexible spinning disk of which axis of rotation is misaligned with the axis of symmetry. The misalignment between the axes of symmetry and rotation is one of the major vibration sources in optical disk drives such as CD-ROM, CD-R, CD-RW and DVD drives. Based upon the Kirchhoff plate theory and the von-Karman strain theory, three coupled equations of motion for the misaligned disk are obtained: two of the equations are for the in-plane motion while the other is for the out-of-plane motion. After transforming these equations into two weak forms for the in-plane and out-of-plane motions, the weak forms are discretized by using newly defined annular sector finite elements. Applying the generalized-$\alpha$ time integration method to the discretized equations, the time responses and the displacement distributions are computed and then the effects of the misalign ment on the responses and the distributions are analyzed. The computation results show that the misalignment has an influence on the magnitudes of the in-plane displacements and it results in the amplitude modulation or the beat phenomenon in the time responses of the out-of-plane displacement.

• Smart Structures and Systems
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• 제8권5호
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• pp.433-447
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• 2011

The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.

• Advances in Computational Design
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• 제2권3호
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• pp.165-194
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• 2017

The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).

• 대한기계학회논문집A
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• 제24권9호
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• pp.2201-2210
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• 2000

Vibration of a rotating disk-spindle system is analyzed by using Hamilton's principle, FEM and substructure synthesis. A rotating disk undergoes the rigid body motion and the elastic deformation. It s equation of motion is derived by Kirchhoff plate theory and von Karman nonlinear strain. A rotating shaft is described by Rayleigh beam theory considering the axial rigid body motion. The stationay shaft supporting the rotating disk-spindle-bearing system is modeled by Euler beam theory, and the stiffness of ball bearing is determined by A.B.Jones' theory. FEM is used to solve the derived governing equations, and substructure synthesis is introduced to assemble each structure of the rotating disk-spindle system. The developed theory is applied to the spindle system of a 35' computer hard disk drive with 3 disks to verify the simulation results. The simulation results agree very well with the experimental ones. The proposed theory may be effectively expanded to the complex structure of a disk-spindle system.

• Structural Engineering and Mechanics
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• 제59권3호
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• pp.431-454
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• 2016

In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• Smart Structures and Systems
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• 제9권2호
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• pp.127-143
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• 2012

The present paper deals with the nonlinear analysis of the functionally graded piezoelectric (FGP) annular plate with two smart layers as sensor and actuator. The normal pressure is applied on the plate. The geometric nonlinearity is considered in the strain-displacement equations based on Von-Karman assumption. The problem is symmetric due to symmetric loading, boundary conditions and material properties. The radial and transverse displacements are supposed as two dominant components of displacement. The constitutive equations are derived for two sections of the plate, individually. Total energy of the system is evaluated for elastic solid and piezoelectric sections in terms of two components of displacement and electric potential. The response of the system can be obtained using minimization of the energy of system with respect to amplitude of displacements and electric potential. The distribution of all material properties is considered as power function along the thickness direction. Displacement-load and electric potential-load curves verify the nonlinearity nature of the problem. The response of the linear analysis is investigated and compared with those results obtained using the nonlinear analysis. This comparison justifies the necessity of a nonlinear analysis. The distribution of the displacements and electric potential in terms of non homogenous index indicates that these curves converge for small value of piezoelectric thickness with respect to elastic solid thickness.

• Structural Engineering and Mechanics
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• 제42권4호
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• pp.589-608
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• 2012

In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.