• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.989-993
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• 2001

This paper deals with the free vibrations of horizontally curved beams supported by non-homogeneous elastic foundation. Taking into account the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which the linear elastic foundation is considered as the non-homogeneous foundation. Differential equations are solved numerically to calculate natural frequencies. In numerical examples, the parabolic curved member is considered. The parametric studies are conducted and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms.

• Tunnel and Underground Space
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• v.3 no.2
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• pp.142-151
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• 1993

In this study, the deformation characteristics of atrtificially fractured joints of granite under normal and shear loading were investigated. To obtain the characteristics of joint deformation, compression and shear tests were performed in the laboratory on three different sizes of rock specimens. The rock used in the experimens was Iksan granite. Joints were produced artificially by fracturing using the apparatus for generating extension-joint. Joint normal deformability was studied by conducting cyclic loading tests on the joints. Joint closure varied non-linearly with normal stress through cyclic loadings. As normal stress increased, the joints gradually reached a state of maximum joint closure. The relation between normal stress and joint closure for mated and unmated joints was well described by the hyperbolic and exponential function, respectively. Joint shear deformability was studied by performing direct shear tests under normal stresses on the joints. it was shown that the behaviour in the prepeak range was non-linear and joint shear stiffness depended on the size of specimen and the normal stress.

• Structural Engineering and Mechanics
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• v.56 no.1
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• pp.85-106
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• 2015

Postbuckling of thick plates made of functionally graded material (FGM) subjected to in-plane compressive, thermal and thermomechanical loads is investigated in this work. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation. Thermomechanical non-homogeneous properties are considered to be temperature independent, and graded smoothly by the distribution of power law across the thickness in the thickness in terms of the volume fractions of constituents. By employing the higher order shear deformation plate theory together the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect FGM plates are derived. The Galerkin technique is used to determine the buckling loads and postbuckling equilibrium paths for simply supported plates. Numerical examples are presented to show the influences of power law index, foundation stiffness and imperfection on the buckling and postbuckling loading capacity of the plates.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.2
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• pp.124-129
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• 2011

The thick plate produced by rolling process is used as the basic members of a ship structure. In this paper, we present a setup model to control the asymmetric factors causing plate bending in the upper or lower direction during rolling. A series of finite element analysis are conducted to predict the relationship between various asymmetric factors and plate bending. The setup model is developed by regressing the relationship to the linear equations with several non-dimensional parameters. The setup model is verified by a pilot rolling test and applied to actual rolling conditions. Results show that the model is substantial to predict the asymmetric deformation in the plate rolling process.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.127-134
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• 1996

In general, seismic isolators which are made of laminated rubber and shim plate have characteristics of complex hysteretic behavior. When shear deformation of the seismic isolator is small, the isolator hassimple hysteretic almost bi-linear behabior. But on large shear deformation hardening effects may occur. This paper proposes a moldeling method of the seimic isolator with modified hysteretic bi-linear model which can consider the hardening effects. From the results of the seismic analyses of the isolated system it is shown that the responses are singificantly reduced compared with those of the non-isolated system. The modified hysteretic bi-linear model of the isolator gives larger ZPA(zero period acceleration) than those of the simple hysteretic bi-linear model and the equivalunt spring-damper model.

• Computers and Concrete
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• v.7 no.4
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• pp.317-329
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• 2010

The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non-linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a non-linear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.

• Steel and Composite Structures
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• v.31 no.2
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• pp.187-199
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• 2019

This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (${\sigma}_{xx}$, ${\sigma}_{yy}$ and ${\tau}_{xy}$) within the FG cylindrical panel. These stresses are evaluated by minimizing the membrane energy via Ritz method. Using these stresses the partial differential equations of FG cylindrical panel are formulated by applying Hamilton's principal assuming higher order shear deformation theory (HSDT) and von-$K{\acute{a}}rm{\acute{a}}n$ non-linearity. The non-linear governing partial differential equations are converted into a set of Mathieu-Hill equations via Galerkin's method. Bolotin method is adopted to trace the boundaries of instability regions. The linear and non-linear dynamic responses in stable and unstable region are plotted to know the characteristics of instability regions of FG cylindrical panel. Moreover, the non-linear frequency-amplitude responses are obtained using Incremental Harmonic Balance (IHB) method.

• Smart Structures and Systems
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• v.18 no.2
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• pp.267-291
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• 2016

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) sandwich plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present refined theory. The non-linear governing equations are solved for plates subjected to simply supported and clamped boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.05a
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• pp.111-112
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• 2010

• Journal of Korean Association for Spatial Structures
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• v.13 no.1
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• pp.8-16
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• 2013