• Advances in concrete construction
• /
• v.9 no.1
• /
• pp.43-54
• /
• 2020

This paper presents an innovative stress-function variational approach in formulating the interfacial shear and normal stresses in an externally bonded concrete joint using carbon fiber-reinforced plastic (CFRP) plies. The joint is subjected to surface traction loadings applied at both ends of the concrete substrate layer. By introducing two interfacial shear and normal stress functions on the CFRP-concrete interface, based on Euler-Bernoulli beam idea and static stress equations of equilibrium, the entire stress fields of the joint were determined. The complementary strain energy was minimized in order to solve the governing equation of the joint. This yields an ordinary differential equation from which the interfacial normal and shear stresses were proposed explicitly, satisfying all the multiple traction boundary conditions. Lamination theory for composite materials was also employed to obtain the interfacial stresses. The proposed approach was validated by the analytic models in the literature as well as through a comprehensive computational code generated by the authors. Furthermore, a numerical verification was carried out via the finite element software ABAQUS. In the end, a scaling analysis was conducted to analyze the interfacial stress field dependence of the joint upon effective issues using the devised code.

• Steel and Composite Structures
• /
• v.21 no.5
• /
• pp.1045-1067
• /
• 2016

Concrete bridges with corrugated steel webs and prestressed by both internal and external tendons have emerged as one of the promising bridge forms. In view of the different behaviour of components and the large shear deformation of webs with negligible flexural stiffness, the assumption that plane sections remain plane may no longer be valid, and therefore the classical Euler-Bernoulli and Timoshenko beam models may not be applicable. In the design of this type of bridges, both the ultimate load and ductility should be examined, which requires the estimation of full-range behaviour. An analytical sandwich beam model and its corresponding beam finite element model for geometric and material nonlinear analysis are developed for this type of bridges considering the diaphragm effects. Different rotations are assigned to the flanges and corrugated steel webs to describe the displacements. The model accounts for the interaction between the axial and flexural deformations of the beam, and uses the actual stress-strain curves of materials considering their stress path-dependence. With a nonlinear kinematical theory, complete description of the nonlinear interaction between the external tendons and the beam is obtained. The numerical model proposed is verified by experiments.

• Advances in nano research
• /
• v.8 no.3
• /
• pp.245-254
• /
• 2020

This work examines the fundamental vibrational characteristics of a spinning CNT-based nano-rotor assuming a nonlocal elasticity Euler-Bernoulli beam theory. The rotary inertia, gyroscopic, and rotor mass unbalance effects are all taken into consideration in the beam model. Assuming a nonlocal theory, two coupled 6th-order partial differential equations governing the vibration of the rotating SWCNT are first derived. In order to acquire the natural frequencies and dynamic response of the nano-rotor system, the nonlinear equations of motion are numerically solved. The nano-rotor system frequency spectrum is shown to exhibit two distinct frequencies: one positive and one negative. The positive frequency is known as to represent the forward whirling mode, whereas the negative characterizes the backward mode. First, the results obtained within the framework of this numerical study are compared with few existing data (i.e., molecular dynamics) and showed an overall acceptable agreement. Then, a thorough and detailed parametric study is carried out to study the effect of several parameters on the nano-rotor frequencies such as: the nanotube radius, the input angular velocity and the small scale parameters. It is shown that the vibration characteristics of a spinning SWCNT are significantly influenced when these parameters are changed.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.3
• /
• pp.514-520
• /
• 2002

A new non-linear modelling of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends. Using the Euler-Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton's principle are derived the coupled non-linear equations of motion for the longitudinal and transverse displacements. These equations of motion are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the generalized-$\alpha$ time integration method to the non-linear discretized equations. The validity of the new modelling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by Paidoussis.

• Proceedings of the KSME Conference
• /
• 2004.11a
• /
• pp.793-798
• /
• 2004

The vibration of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the extended Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the vibration characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. From these results, we should consider the geometric nonlinearity to analyze the dynamics of a curved pipe conveying fluid more precisely.

• Structural Engineering and Mechanics
• /
• v.66 no.6
• /
• pp.737-748
• /
• 2018

The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

• Smart Structures and Systems
• /
• v.13 no.1
• /
• pp.55-80
• /
• 2014

The present work pays emphasis on investigating the effect of different types of debonding on the bending behaviour of active sandwich beam, consisting of both extension and shear actuators. An active sandwich beam finite element is formulated by using Timoshenko's beam theory, characterized by first order shear deformation for the core and Euler-Bernoulli's beam theory for the top and bottom faces. The problem of debondings of extension actuator and face are dealt with by employing four-region model for inner debonding and three-region model for the edge debonding respectively. Displacement based continuity conditions are enforced at the interfaces of different regions using penalty method. Firstly, piezoelectric actuation of healthy sandwich beam is assessed through deflection analysis. Then the effect of actuators' debondings with different boundary conditions on bending behavior is computationally evaluated and experimentally clamped-free case is validated. The results generated will be useful to address the damage tolerant design procedures for smart sandwich beam structures with structural control and health monitoring applications.

• Interaction and multiscale mechanics
• /
• v.2 no.3
• /
• pp.223-233
• /
• 2009

This paper presents a new nonlocal stress variational principle approach for the transverse free vibration of an Euler-Bernoulli cantilever nanobeam with an initial axial tension at its free end. The effects of a nanoscale at molecular level unavailable in classical mechanics are investigated and discussed. A sixth-order partial differential governing equation for transverse free vibration is derived via variational principle with nonlocal elastic stress field theory. Analytical solutions for natural frequencies and transverse vibration modes are determined by applying a numerical analysis. Examples conclude that nonlocal stress effect tends to significantly increase stiffness and natural frequencies of a nanobeam. The relationship between natural frequency and nanoscale is also presented and its significance on stiffness enhancement with respect to the classical elasticity theory is discussed in detail. The effect of an initial axial tension, which also tends to enhance the nanobeam stiffness, is also concluded. The model and approach show potential extension to studies in carbon nanotube and the new result is useful for future comparison.

• Smart Structures and Systems
• /
• v.18 no.5
• /
• pp.1029-1062
• /
• 2016

In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton's principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon.

• Structural Engineering and Mechanics
• /
• v.64 no.4
• /
• pp.403-411
• /
• 2017

In this article, analytical solution for free vibration of micro composite laminated beam on elastic medium based on modified couple stress are presented. The surrounding elastic medium is modeled as the Winkler elastic foundation. The governing equations and boundary conditions are obtained by using the principle of minimum potential energy for EulerBernoulli beam. For investigating the effect of different parameters including material length scale, beam thickness, some numerical results on different cross ply laminated beams such as (90,0,90), (0,90,0), (90,90,90) and (0,0,0) are presented on elastic medium. Free vibration analysis of a simply supported beam is considered utilizing the Fourier series. Also, the fundamental frequency is obtained using the principle of Hamilton for four types of cross ply laminations with hinged-hinged boundary conditions and different beam theories. The fundamental frequency for different thin beam theories are investigated by increasing the slenderness ratio and various foundation coefficients. The results prove that the modified couple stress theory increases the natural frequency under the various foundation for free vibration of composite laminated micro beams.