• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Structural Engineering and Mechanics
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• v.53 no.2
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• pp.373-392
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• 2015

In the present work, structural joints have been modeled as a pair of translational and rotational springs and frequency equation of the overall system has been developed using sub-structure synthesis. It is shown that using first few natural frequencies of the system, one can obtain a set of over-determined system of equations involving the unknown stiffness parameters. Method of multi-linear regression is then applied to obtain the best estimate of the unknown stiffness parameters. The estimation procedure has been developed first for a two parameter joint model and then for a three parameter model, in which cross coupling terms are also included. Two cases of structural connections have been considered, first with a cantilever beam with support flexibility and then a pair of beams connected through lap joint. The validity of the proposed method is demonstrated through numerical simulation and by experimentation.

• Coupled systems mechanics
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• v.6 no.4
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• pp.465-485
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• 2017

In this paper, free vibration and static response of magneto-electro-elastic (MEE) beams has been investigated. To this end, a 3D finite element formulation has been derived by minimization the total potential energy and linear constitutive equation. The coupling between elastic, electric and magnetic fields can have a significant influence on the stiffness and in turn on the static behaviour of MEE beam. Further, different Barium Titanate ($BaTiO_3$) and Cobalt Ferric oxide ($CoFe_2O_4$) volume fractions results in indifferent coupled response. Therefore, through the numerical examples the influence of volume fractions and boundary conditions on the natural frequencies of MEE beam is illustrated. The study is extended to evaluate the static response of MEE beam under various forms of mechanical loading. It is seen from the numerical evaluation that the volume fractions, loading and boundary conditions have a significant effect on the structural behaviour of MEE structures. The observations made here may serve as benchmark solutions in the optimum design of MEE structures.

• Journal of KSNVE
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• v.8 no.6
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• pp.1166-1171
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• 1998

The influences of the coupler consisting of stiffness and mass between neighboring two spans on mode localization are studied theoretically, and the results are confirmed by numerical examples. The mass of the coupler makes a structure sensitive to mode localization especially in higher modes while the stiffness does in all modes. A new type of delocalization phenomenon is observed for the first time in some modes for which mode localization does not occur or is very weak although structural disturbances are severe. A spring-mass system consisting of two substructures and a coupler connecting them is considered in the part of analytical study. As example structures for numerical analysis. simply supported continuous two-span beams with a coupler having a rotational stiffness and a mass moment of inertia on the mid support are considered.

• Wind and Structures
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• v.16 no.6
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• pp.579-601
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• 2013

Interference effects are of considerable concern for group hyperboloidal cooling towers, but evaluation methods and results are different from each other because of the insufficient understanding on the structure behavior. Therefore, the mechanical performance of hyperboloidal cooling tower shell under wind loads was illustrated according to some basic properties drawn from horizontal rings and cantilever beams. The hyperboloidal cooling tower shell can be regarded as the coupling of horizontal rings and meridian cantilever beams, and this perception is beneficial for understanding the mechanical performance under wind loads. Afterwards, the mean external latitude wind pressure distribution, CP(${\theta}$), was artificially adjusted to pursue the relationship between different CP(${\theta}$) and wind-induced responses. It was found that the maximum responses in hyperboloidal cooling tower shell are primarily dominated by the non-uniformity of CP(${\theta}$) but not the local pressure amplitude CP or overall resistance/drag coefficient CD. In all the internal forces, the maximum amplitude of meridian axial tension shows remarkable sensitivity to the variation of CP(${\theta}$) and it's also the controlling force in structure design, so it was selected as an indicator to evaluate the influence of CP(${\theta}$) on responses. Based on its sensitivity to different adjustment parameters of CP(${\theta}$), an comprehensive response influence factor, RIF, was deduced to assess the meridian axial tension for arbitrary CP(${\theta}$).

• Smart Structures and Systems
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• v.23 no.2
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• pp.141-153
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• 2019

This research deals with wave propagation of the functionally graded (FG) nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The FG nano-beam is resting in Winkler-Pasternak foundation. It is assumed that the material properties of the nano-beam changes continuously along the thickness direction according to simple power-law form. In order to include coupling of strain gradients and electrical polarizations in governing equations of motion, the nonlocal non-classical nano-beam model containg flexoelectric effect is used. Also, the effects of surface elasticity, dielectricity and piezoelectricity as well as bulk flexoelectricity are all taken into consideration. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory (FSDBT) and also considering residual surface stresses. The analytical method is used to calculate phase velocity of wave propagation in FG nano-beam as well as cut-off frequency. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface, bulk and residual surface stresses, Winkler and shear coefficients of foundation, power gradient index of FG material, and geometric dimensions on the wave propagation characteristics of FG nano-beam. The numerical results indicate that considering surface effects/flexoelectric property caused phase velocity increases/decreases in low wave number range, respectively. The influences of aforementioned parameters on the occurrence cut-off frequency point are very small.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.439-455
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• 2019

This research deals with thermo-electro-mechanical buckling analysis of the sandwich nano-beams with face-sheets made of functionally graded carbon nano-tubes reinforcement composite (FG-CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher-order shear deformation beam theories (HSDBT). The sandwich nano-beam with FG-CNTRC face-sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face-sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non-classical nano-beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano-beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano-beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.

• Smart Structures and Systems
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• v.26 no.6
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• pp.681-692
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• 2020

Conventional Piezoelectric Energy Harvesters (CPEH) have been extensively studied for maximizing their electrical output through material selection, geometric and structural optimization, and adoption of efficient interface circuits. In this paper, the performance of Stepped Piezoelectric Energy Harvester (SPEH) under harmonic base excitation is studied analytically, numerically and experimentally. The motivation is to compare the energy harvesting performance of CPEH and SPEHs with the same characteristics (resonant frequency). The results of this study challenge the notion of achieving higher voltage and power output through incorporation of geometric discontinuities such as step sections in the harvester beams. A CPEH consists of substrate material with a patch of piezoelectric material bonded over it and a tip mass at the free end to tune the resonant frequency. A SPEH is designed by introducing a step section near the root of substrate beam to induce higher dynamic strain for maximizing the electrical output. The incorporation of step section reduces the stiffness and consequently, a lower tip mass is used with SPEH to match the resonant frequency to that of CPEH. Moreover, the electromechanical coupling coefficient, forcing function and damping are significantly influenced because of the inclusion of step section, which consequently affects harvester's output. Three different configurations of SPEHs characterized by the same resonant frequency as that of CPEH are designed and analyzed using linear electromechanical model and their performances are compared. The variation of strain on the harvester beams is obtained using finite element analysis. The prototypes of CPEH and SPEHs are fabricated and experimentally tested. It is shown that the power output from SPEHs is lower than the CPEH. When the prototypes with resonant frequencies in the range of 56-56.5 Hz are tested at 1 m/s2, three SPEHs generate power output of 482 μW, 424 μW and 228 μW when compared with 674 μW from CPEH. It is concluded that the advantage of increasing dynamic strain using step section is negated by increase in damping and decrease in forcing function. However, SPEHs show slightly better performance in terms of specific power and thus making them suitable for practical scenarios where the ratio of power to system mass is critical.

• Journal of Korean Association for Spatial Structures
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• v.11 no.1
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• pp.47-56
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• 2011

In general, shear walls are employed as lateral resistance system. Most of shear wall structures require openings in shear walls and thus shear walls are linked by floor slabs or coupling beams resulting in the coupled shear wall structures. In this study, an LRB (lead rubber bearing) was introduced in the middle of the coupling beam of the coupled shear wall structures and the wind-induced response reduction effect of this system was investigated. In order to evaluate the control performance of the proposed method, 20- and 30-story building structures were used as example structures and boundary nonlinear time history analyses have been performed using artificial wind excitation. Japanese vibration evaluation criteria was employed to evaluate whether the proposed system could improve the serviceability of the tall coupled shear wall structures under wind excitation. Based on analytical results, it has been shown that the proposed method that connects shear walls with LRBs can improve the wind-induced response control effect.

• Steel and Composite Structures
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• v.23 no.4
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• pp.409-420
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• 2017

This paper theoretically studies the cyclic behavior of hybrid connections between steel coupling beams and concrete shear walls with embedded steel columns. Finite element models of connections with long and short embedded steel columns are built in ABAQUS and validated against the test results in the companion paper. Parametric studies are carried out using the validated FE model to determine the key influencing factors on the load-bearing capacity of connections. A close-form solution of the load-bearing capacity of connections is proposed by considering the contributions from the compressive strength of concrete at the interface between the embedded beam and concrete, shear yielding of column web in the tensile region, and shear capacity of column web and concrete in joint zone. The results show that the bond slip between embedded steel members and concrete should be considered which can be simulated by defining contact boundary conditions. It is found that the loadbearing capacity of connections strongly depends on the section height, flange width and web thickness of the embedded column. The accuracy of the proposed calculation method is validated against test results and also verified against FE results (with differences within 10%). It is recommended that embedded steel columns should be placed along the entire height of shear walls to facilitate construction and enhance the ductility. The thickness and section height of embedded columns should be increased to enhance the load-bearing capacity of connections. The stirrups in the joint zone should be strengthened and embedded columns with very small section height should be avoided.