• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.431-454
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• 2016

In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear 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 Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• Advances in nano research
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• v.16 no.3
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• pp.273-288
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• 2024

The geometrical nonlinear vibrations of the gold nanoscale rod are investigated for the first time by considering the internal modals interactions using different nonlinear beam theories. This phenomenon is usually one of the important features of nonlinear vibration systems. For a more detailed analysis, the von-Karman effects, preserving all the nonlinear terms in the strain-displacement relationships of gold nanoscale rods in three displacement directions, are considered to analyze the nonlinear axial vibrations of gold nanoscale rods. It uses highly accurate analytical-numerical solutions for the clamped-clamped and clamped-free boundary conditions of nanoscale gold rods. Also, with the help of Hamilton's principle, the governing equation and boundary conditions are derived based on Eringen's theory. The influence of nonlinear and nonlocal factors on axial vibrations was investigated separately for all three theories: Simple (ST), Rayleigh (RT) and Bishop (BT). Using different theories, the effects of inertia and shear on the internal resonances of gold nanorods were studied and compared in terms of twoto-one and three-to-one internal resonances. As the nonlocal parameter of the gold nanorod increases, the maximum nonlinear amplitude occurs. So, by adding nonlocal effects in a gold nanorod, the internal modal interactions resulting from the unique structure can be enhanced. It is worth noting that shear and inertial analysis have a significant effect on internal modal interactions in gold nanorods.

• Computational Structural Engineering
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• v.8 no.2
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• pp.115-121
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• 1995

The object of this study is to propose a rational method of resistance strength and flexural deformation for structures using high strength concrete(400-700kgf/cm/sup 2/). The material property(stress-strain relationship) is to be modelize using regression analysis of experimental result. And the applicability of trapezoidal stress model is to be verified. An analytical method is used by the moment-curvature relationship which is based on stress-strain relationships of material for discreted element of section. The evaluation method of moment-curvature of high strength concrete structures is also proposed by using the Monte Carlo Simulation based on a probabilistic concept that could minimize an error due to iterated calculations and random variable of material properties.

• Geomechanics and Engineering
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• v.5 no.3
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• pp.241-261
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• 2013

The bearing mechanism of pile during installation and loading process which controls the deformation and distribution of strain and stress in the soil surrounding pile tip is complex and full of much uncertainty. It is pointed out that particle crushing occurs in significant stress concentrated region such as the area surrounding pile tip. The solution to this problem requires the understanding and modeling of the mechanical behavior of granular soil under high pressures. This study aims to investigate the sand behavior around pile tip considering the characteristics of sand crushing. The numerical analysis of model pile loading test under different surcharge pressure with constitutive model for sand crushing is presented. This constitutive model is capable of predicting the dilatancy of soil from negative to positive under low confining pressure and only negative dilatancy under high confining pressure. The predicted relationships between the normalized bearing stress and normalized displacement are agreeable with the experimental results during the entire loading process. It is estimated from numerical results that the vertical stress beneath pile tip is up to 20 MPa which is large enough to cause sand to be crushed. The predicted distribution area of volumetric strain represents that the distributed area shaped wedge for volumetric contraction is beneath pile tip and distributed area for volumetric expansion is near the pile shaft. It is demonstrated that the finite element formulation incorporating a constitutive model for sand with crushing is capable of producing reasonable results for the pile loading problem.

• Steel and Composite Structures
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• v.42 no.1
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• pp.139-149
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• 2022

To simplify the design and reduce the construction cost of traditional multi-girder structural systems, twin I-girder structures are widely used in many countries in recent years. Due to the concern on post-fracture redundancy, however, twin girder bridges are currently classified as fracture critical structures in AASHTO specifications for highway bridges. To investigate the after-fracture behavior of such structures, a composite steel and concrete twin girder specimen was built and an artificial fracture through the web and the bottom flange was created on one main girder. The static loading test was performed to investigate its mechanical performance after a severe fracture occurred on the main girder. Applied load and vertical displacement curves, and the applied load versus strain relationships at key sections were measured. To investigate the load distribution and transfer capacities between two steel girders, the normal strain development on crossbeams was also measured during the loading test. In addition, both shear and normal strains of studs were also measured in the loading test to explore the behavior of shear connectors in such bridges. The functions and structural performance of structural members and possible load transfer paths after main girder fractures in such bridges were also discussed. The test results indicate in this study that a typical twin I-girder can resist a general fracture on one of its two main girders. The presented results can provide references for post-fracture performance and optimization for the design of twin I-girder bridges and similar structures.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.559-564
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• 1998

The object of this thesis is an analytical study on shear deformation of reinforced concrete members using monte carlo method. Using the established experimental data that has been presented in various documents the stress-strain relationships curves of reinforced concrete (300kgf/$\textrm{cm}^2$~400kgf/$\textrm{cm}^2$) models are proposed. Finally, the theoretical values calculated using the analytical method developed in this study have been investigated in comparison with the experimental ones which were carried out earlier in order to prove its validity. From the results it has been shown that theoretical values agree quite well with experimental ones, and it could be pointed out that the presented analytical method is widely acceptable for the practical analysis of shear displacement of reinforced concrete members.

• Tunnel and Underground Space
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• v.8 no.1
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• pp.1-7
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• 1998

In order to get the information of the deformational behavior of rock masses with time in waste disposal repository, it is necessary to measure the relationships between stress and strain and time for temperature. A creep law is used in conjunction with the elastic moduli to calculate stress and displacement following waste emplacement. Exponential-time law's parameters consist of stress and temperature. In this study, thermal creep test was carried out for Whangdeung granite. The measured creep deformation behavior was well explained by exponential time law and generalized Kelvin's rheological model. Mechanicla coefficients for exponential-time creep law showed the clear tendency of temperature dependent while those for Kelvein's model didn't.

• Journal of KSNVE
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• v.11 no.1
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• pp.156-166
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• 2001

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

• Journal of the Korean Society of Safety
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• v.14 no.2
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• pp.116-121
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• 1999

When plate anchors are embedded in soft clay, they may undergo a deformation under the pressure of sustained load. The critical depth at which the transition from a shallow to a deep anchor takes place depends on the properties of soil. Laboratory model tests were performed for the short-term net ultimate uplift capacity of a circular anchors with respect to various embedment depths and moisture content in saturated kaolinite. The tests have been conducted with the anchor at two different moisture contents. Based on the model test results, empirical relationships between the net load, rate of strain, and time have been developed. In creep tests of kaolinite for load versus ultimate uplift capacity, the displacement of plate anchors rapidly increases during the primary stage but thereafter becomes constant over a period of time.