• Earthquakes and Structures
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• v.13 no.3
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• Journal of Computational Design and Engineering
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• v.3 no.3
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• pp.215-225
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• 2016

In recent years, the automotive industry has known a remarkable development in order to satisfy the customer requirements. In this paper, we will study one of the components of the automotive which is the twist beam. The study is focused on the multicriteria design of the automotive twist beam undergoing linear elastic deformation (Hooke's law). Indeed, for the design of this automotive part, there are some criteria to be considered as the rigidity (stiffness) and the resistance to fatigue. Those two criteria are known to be conflicting, therefore, our aim is to identify the Pareto front of this problem. To do this, we used a Normal Boundary Intersection (NBI) algorithm coupling with a radial basis function (RBF) metamodel in order to reduce the high calculation time needed for solving the multicriteria design problem. Otherwise, we used the free form deformation (FFD) technique for the generation of the 3D shapes of the automotive part studied during the optimization process.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.1
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• pp.12-20
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• 1997

In this paper, we analyze the thermal deformation of mask frame assembly using finite element method(FEM) and predict the beam landing shift during tube operation. For realistic analysis, the apparent thermal conductivity and the apparent elastic modulus are calculated and the shadow mask is modeled as shell without aperatures. Also, all parts inside the tube are modeled and the each radiative effect is considered. Then the finite element analysis is performed for transient thermo-elastic deformation of the mask frame assembly and the beam landing shift is calculated. Experiments are eprformed for 17" cathode ray tube (CRT) to validate the FEM analysis. The temperatures of all parts inside the tube and beam landing shift on the panel are measured and the results are discussed in comparison with the results of the FEM analysis.ysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.43-50
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• 2002

Main goal of this study is to develop MATLAB programming for exact analysis of distortional deformation of the straight box girder. For this purpose, a theory for distortional deformation theory is firstly summarized and then a BEF (Beam on Elastic Foundation) theory is presented using analogy of the corresponding variables. Finally, the governing equation of the beam-column element on elastic foundation is derived. An element stiffness matrix of the beam element is established via a generalized linear eigenvalue problem. In order to verify the efficiency and accuracy of the element using exact dynamic stiffness matrix, buckling loads for the continuous beam structures with elastic foundation and distortional deformations of box girders are calculated.

• Advances in nano research
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• v.5 no.2
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• pp.113-126
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• 2017

This paper proposes a new nonlocal higher-order hyperbolic shear deformation beam theory (HSBT) for the static bending and vibration of nanoscale-beams. Eringen's nonlocal elasticity theory is incorporated, in order to capture small size effects. In the present model, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the upper and bottom surfaces of the nanobeams without using shear correction factor. Employing Hamilton's principle, the nonlocal equations of motion are derived. The governing equations are solved analytically for the edges of the beam are simply supported, and the obtained results are compared, as possible, with the available solutions found in the literature. Furthermore, the influences of nonlocal coefficient, slenderness ratio on the static bending and dynamic responses of the nanobeam are examined.

• Structural Engineering and Mechanics
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• v.73 no.2
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• pp.109-121
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• 2020

This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.

• Computers and Concrete
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• v.25 no.5
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• pp.427-432
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• 2020

In this research, the buckling analysis of sandwich beam with composite reinforced by graphene platelets (GPLs) in two face sheets is investigated. Three type various porosity patterns including uniform, symmetric and asymmetric are considered through the thickness direction of the core. Also, the top and bottom face sheets layers are considered composite reinforced by GPLs/CNTs based on Halpin-Tsai micromechanics model and extended mixture rule, respectively. Based on various shear deformation theories such as Euler-Bernoulli, Timoshenko and Reddy beam theories, the governing equations of equilibrium using minimum total potential energy are obtained. It is seen that the critical buckling load decreases with an increase in the porous coefficient, because the stiffness of sandwich beam reduces. Also, it is shown that the critical buckling load for asymmetric distribution is lower than the other cases. It can see that the effect of graphene platelets on the critical buckling load is higher than carbon nanotubes. Moreover, it is seen that the difference between carbon nanotubes and graphene platelets for Reddy and Euler-Bernoulli beam theories is most and least, respectively.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.348-353
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• 2008

A vibration analysis for a rotating cantilever beam with the tapered cross section is presented in this study. The stiffness changes due to the stretching caused by centrifugal inertia forces when a tapered cantilever beam rotates about the axis perpendicular to its longitudinal axis. When the cross section of cantilever beam are assumed to decrease constantly, the mass and stiffness also change according to the variation of the thickness and width ratio of a tapered cantilever beam. Such phenomena result in variations of natural frequencies and mode shapes. Therefore it is important to the equations of motion in order to be obtained accurate predictions of these variations. The equations of motion of a rotating tapered cantilever beam are derived by using hybrid deformation variable modeling method and numerical results are obtained along with the angular velocity and the thickness and width ratio.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.4
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• pp.363-369
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• 2009

A vibration analysis for a rotating cantilever beam with the tapered cross section is presented in this study. The stiffness changes due to the stretching caused by centrifugal inertia forces when a tapered cantilever beam rotates about the axis perpendicular to its longitudinal axis. When the cross section of cantilever beam are assumed to decrease constantly, the mass and stiffness also change according to the variation of the thickness and width ratio of a tapered cantilever beam. Such phenomena result in variations of natural frequencies and mode shapes. Therefore it is important to the equations of motion in order to be obtained accurate predictions of these variations. The equations of motion of a rotating tapered cantilever beam are derived by using hybrid deformation variable modeling method and numerical results are obtained along with the angular velocity and the thickness and width ratio.

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.205-212
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• 2017

Based on the coupled elastic bending deformation features and relationships between the internal force and deformation of pre-twisted Euler beam, the generalized strain, the equivalent constitutive equation and the equilibrium equation of pre-twisted Euler beam are developed. Based on the properties of the dual-antisymmetric matrix, the general solution of pre-twisted Euler beam is obtained. By comparison with ANSYS solution by using straight Beam-188 element based on infinite approach strategy, the results show that the developed method is available for pre-twisted Euler beam and also provide an accuracy displacement interpolation function for the subsequent finite element analysis. The effect of pre-twisted angle on the mechanical property has been investigated.