• Journal of the Korean Society of Hazard Mitigation
• /
• v.8 no.2
• /
• pp.39-43
• /
• 2008

Determination of strain associated with shear modulus and damping ratio during torsional test is complicated. This is due to nonuniform stress-strain variation occurring linearly with radius in a soil specimen in torsion. A conventional equivalent radius approach proposed by Chen and Stokoe appears to be adequate for evaluating strain associated with shear modulus at low to intermediate strain levels. This approach is less accurate for damping measurement, particularly at high strain. Modified equivalent radius approach was used to account for the nonuniform stress-strain effect more precisely. The modified equivalent radius approach was applied for hyperbolic, modified hyperbolic, and Ramberg-Osgood models. The results illustrate the usefulness of the modified equivalent radius approach and suggest that using a single value of equivalent radius ratio to calculate strains is not appropriate.

• The Pure and Applied Mathematics
• /
• v.6 no.2
• /
• pp.87-93
• /
• 1999

A holomorphic function f on D = {z : │z│ ＜ 1} is called uniformly locally univalent if there exists a positive constant $\rho$ such that f is univalent in every hyperbolic disk of hyperbolic radius $\rho$. We establish a characterization of uniformly locally univalent functions and investigate uniform local univalence of holomorphic universal covering projections.

• Journal of the Korean Society of Hazard Mitigation
• /
• v.8 no.2
• /
• pp.97-103
• /
• 2008

Determination of stress-strain relationship in torsional tests is complicated due to nonuniform stress-strain variation occurring linearly with the radius in a soil specimen in torsion. The equivalent radius approach is adequate when calculating strain at low to intermediate strains, however, the approach is less accurate when performing the test at higher strain levels. The modified equivalent radius approach was developed to account for the problem more precisely. This approach was extended to generate the plots of equivalent radius ratio versus strain using modified hyperbolic and Ramberg-Osgood models. Results showed the effects of soil nonlinearity on the equivalent radius ratio curves were observed. Curve fitting was also performed to find the stress-strain relationship by fitting the theoretical torque-rotation relationship to measured torque-rotation relationship.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.12 no.1
• /
• pp.43-55
• /
• 2008

The complexity of determining strain associated with shear modulus and damping ratio in torsional tests has been resolved by means of several approaches. Particularly, the modified equivalent radius approach is adequate to when generating the plots of equivalent radius ratio versus strain more effectively over any range of strains in resonant column and torsional shear (RC/TS) tests. The modified equivalent radius approach was applied for hyperbolic, modified hyperbolic, and Ramberg-Osgood models in evaluating damping ratio. Results showed that using a single value of equivalent radius ratio based on conventional equivalent radius approach is not appropriate. A new model was developed to consider the soil damping behavior at small strains as well as hysteretic damping and it was attempted to determine adjustments are required in evaluating strain associated damping when combining the two damping components.

• Korean Journal of Optics and Photonics
• /
• v.12 no.5
• /
• pp.352-355
• /
• 2001

A null lens is designed for testing the hyperbolic mirror which is the first mirror of the off-axis three mirror anastigmat(TMA) designed as a high resolution camera for remote sensing. To choose a better null lens system for the hyperbolic surface under test, both autostigmatic and mixed type null lenses are designed and analysed for sensitivity with respect to change of each surface parameter such as the radius of curvature and the thickness.

• Journal of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.587-599
• /
• 1996

We assume throughout the paper that f(z) is a conformal function in the ipen unit disk $D = {z : $\mid$z$\mid$ < 1}$. In the rest of paper, conformal means analytic and locally univalent.

• Structural Engineering and Mechanics
• /
• v.84 no.6
• /
• pp.707-722
• /
• 2022

In this study, a new refined hyperbolic shear deformation theory (RHSDT) is developed using an equivalent single-layer shell displacement model for the static bending and free vibration response of cross-ply laminated composite spherical shells. It is based on a new kinematic in which the transverse displacement is approximated as a sum of the bending and shear components, leading to a reduction of the number of unknown functions and governing equations. The proposed theory uses the hyperbolic shape function to account for an appropriate distribution of the transverse shear strains through the thickness and satisfies the boundary conditions on the shell surfaces without requiring any shear correction factors. The shell governing equations for this study are derived in terms of displacement from Hamilton's principle and solved via a Navier-type analytical procedure. The validity and high accuracy of the present theory are ascertained by comparing the obtained numerical results of displacements, stresses, and natural frequencies with their counterparts generated by some higher-order shear deformation theories. Further, a parametric study examines in detail the effect of both geometrical parameters (i.e., side-to-thickness ratio and curvature-radius-to-side ratio), on the bending and free vibration response of simply supported laminated spherical shells, which can be very useful for many modern engineering applications and their optimization design.

• Journal of Korean Association for Spatial Structures
• /
• v.16 no.3
• /
• pp.67-78
• /
• 2016

Determining of the shape in the process of design for natural draught cooling tower is very important, because the shape of hyperbolic shell is respond sensitively to dynamic behavior of the whole cooling tower against wind load. In engineering practice, the geometric parameters have been determining based on the natural frequency. This study analyses influence of the tower shell geometric parameters on the structural behavior. For three representative models were selected, they were analyzed based on evaluation of damage by means of nonlinear FE-method. As a result, a hyperbolic rotational shell with the small radius overall was the lowest damage index induced by sufficient capacity of the stress redistribution and thus a wind-insensitive structure.

• Structural Engineering and Mechanics
• /
• v.82 no.5
• /
• pp.629-641
• /
• 2022

This study deals with the spinning impact on flap-wise vibration characteristics of nonlocal functionally graded (FG) cylindrical beam based on the Hyperbolic shear deformation beam theory. The nonlocal strain gradient theory is used to investigate the small-scale impact on the nonlocal motion equation as well as corresponding nonlocal boundary conditions. Based on the mathematical simulation and according to the Hamilton principle, the computerized modeling of a rotating functionally graded nanotube is generated, and then, via a numerical approach, the obtained mathematical equations are solved. The calculated outcomes are helpful to the production of Nano-electro-mechanical-systems (NEMS) by investigating some designed parameters such as rotating speed, hub radius, length-scale parameters, volume fraction parameters, etc.

• Honam Mathematical Journal
• /
• v.34 no.1
• /
• pp.103-111
• /
• 2012

Wetzel[5] proved if ${\Gamma}$ is a closed curve of length L in $E^n$, then ${\Gamma}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.