• 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.

• Smart Structures and Systems
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• v.19 no.1
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• pp.21-31
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• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• Advances in nano research
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• v.13 no.6
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• pp.545-559
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• 2022

This paper studies the buckling response of nonuniform functionally graded micro-sized tubes according to the high-order tube theory (HOTT) and classical beam theory (CBT) in addition to nonlocal strain gradient theory. The microtube is made of axially functionally graded material (AFGM). Both inner and outer tube radiuses are changed along the tube length; the microtube is the truncated conical type of tube. The nonlinear partial differential (PD) the formulations are obtained on the basis of the energy conservation method. Then, the linear and nonlinear results are computed via a powerful numerical approach. Finally, the impact of various parameters on the stability of axially functionally graded (AFG) microtube regarding the buckling analysis is discussed.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.04a
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• pp.166-171
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• 2004

In this study, shape optimization of micro-static mixer with a cantilever beam was accomplished for mixing the mixing efficiency by using successive response surface approximations. Variables were chosen as the length of cantilever beam and the angle between horizontal and the cantilever beam. Sequential approximate optimization method was used to deal with both highly nonlinear and non-smooth characteristics of flow field in a micro-static mixer. Shape optimization problem of a micro-static mixer can be divided into a series of simple subproblems. Approximation to solve the subproblems was performed by response surface approximation, which does not require the sensitivity analysis. To verify the reliability of approximated objective function and the accuracy of it, ANOVA analysis and variables selection method were implemented, respectively. It was verified that successive response surface approximation worked very well and the mixing efficiency was improved very much comparing with the initial shape of a micro-static mixer.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. 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. 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 lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.61-64
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• 2003

The finite element method based on the refined beam theory is applied to the vibration problem of rotation composite box beams. The present beam model includes a number of non-classical structural effects such as transverse shear, warping deformations, geometric non-linearities. The nonlinear finite element equations of motion are obtained from Hamilton's principle. Vibration characteristics versus various parameters such as ply angle, collective pitch angle, pretwist and precone are investigated for rotation box ben and relevant conclusions are outlined.

• Smart Structures and Systems
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• v.31 no.1
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• pp.13-27
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• 2023

Fatigue crack is a fatal problem for steel structures. Early detection and maintenance can help extend the service life and prevent hazards. This paper presents the ultrasonic guided waves-based (UGWs-based) fatigue crack detection of a steel I-beam. The semi-analytical finite element model has been built to obtain the wave propagation characteristics. Damage indices in both time and frequency domains were analyzed by considering the characteristic variations of UGWs including the amplitude, phase angle, and wave packet energy. The pulse-echo and pitch-catch methods were combined in the detection scheme. Lab-scale experiments were conducted on welded steel I-beams to verify the proposed method. Results show that the damage indices based on the characteristic variations in the time domain can identify and localize the fatigue crack before it enters the rapid growth stage. The damage severity can be reasonably evaluated by analyzing the time-domain damage indices. Two nonlinear damage indices in the frequency domain give earlier warnings of the fatigue crack than the time-domain damage indices do. The identification results based on the above two nonlinear indices are found to be less consistent under various excitation frequencies. More robust nonlinear techniques needed to be searched and tested for early crack detection in steel I-beams in further study.

• Advances in nano research
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• v.8 no.3
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• pp.255-264
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• 2020

Buckling and post-buckling cases are often occurred in aorta artery because it affected by higher pressure. Also, its stability has a vital importance to humans and animals. The loss of stability in arteries may lead to arterial tortuosity and kinking. In this paper, post-buckling analysis of aorta artery is investigated under axial compression loads on the basis of Euler-Bernoulli beam theory by using finite element method. It is known that post-buckling problems are geometrically nonlinear problems. In the geometrically nonlinear model, the Von Karman nonlinear kinematic relationship is employed. Two types of support conditions for the aorta artery are considered. The considered non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The aorta artery is modeled as a cylindrical tube with different average diameters. In the numerical results, the effects of the geometry parameters of aorta artery on the post-buckling case are investigated in detail. Nonlinear deflections and critical buckling loads are obtained and discussed on the post-buckling case.

• Journal of Fisheries and Marine Sciences Education
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• v.24 no.5
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• pp.699-711
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• 2012

An undergraduate course named computational structural analysis becomes more significant in recent years because of its important role in industries and the recent innovation in computer technology. Typically, the course consists of introduction to finite element method, utilization of general purpose finite element software, and examples focusing on static and linear analyses on various structural members such as a beam, truss, frame, arch, and cable. However, in addition to the static and linear analyses, current industries ask graduates to acquire basic knowledge on structural dynamics and nonlinear analysis, which are not listed in the conventional syllabus of the computational structural analysis. Therefore, this study develops geometrically nonlinear examples, which can help students to easily capture the fundamental nonlinear theory, software manipulation, and problem solving skills. For the purpose, five different examples are found, developed for the analyses of cables and cable nets, which naturally have strong geometrical non-linearity. In the paper, these examples are presented, discussed, and finally compared for a better subject development.

• Journal of Ocean Engineering and Technology
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• v.17 no.4
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• pp.59-65
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• 2003

In order to achieve the desired lightweight and robust design of a structure, it is preferable to design a structure and its control system, simultaneously, which is termed the combined optimal design. A constant-cross-sectional area cantilever beam was chosen as the optimum design method, An initial load and a time-varying disturbance were applied at the free end of the beam. Sliding mode control was selected, due to its insensitivity to the disturbance, compared with other modes. It is known that the sliding mode control is robust to the disturbance and is uncertain, only if a matching condition is met, after giving a switching hyper plane. In this study, the optimum method was used for the design of the switching hyper plane, and the objective function of the optimum switching hyper plane was assumed to be the objective of the control system. The total weight of the structure was treated as a constraint, and the cross sectional areas of the beam were considered as design variables, the result being a nonlinear programming problem. To solve it, the sequential linear programming method was applied. As a result of the optimum design, the effect of attenuating vibrations has been substantially improved. Moreover, the lightweight design of the structure became possible as a result of the relationship of the weight of the structure to the control objective function.