• Kyungpook Mathematical Journal
• /
• v.56 no.2
• /
• pp.583-595
• /
• 2016

Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle ${\Delta}ABP$. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane ${\mathbb{R}}^2$, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S={\frac{4}{3}}T$ for parabolas we study strictly locally convex curves in the plane ${\mathbb{R}}^2$ satisfying $S={\lambda}T+{\nu}U$, where ${\lambda}$ and ${\nu}$ are some functions on the curves. As a result, we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open arc of a parabola.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1994.04a
• /
• pp.95-102
• /
• 1994

A path-switching strategy by combining the use of generalized inverse and line search is proposed. A reliable predictor for the tangent vector to bifurcation path is first computed by using the generalized inverse approach. A line search in the direction of maximum gradient of total potential at the point of intersection between the above predictor and a constant loading plane introduced in the vicinity of the detected bifurcation point is then carried out for the purpose of obtaining an improved approximation for a point on bifurcation path. With this approximation obtained, an actual point on bifurcation path is then computed through iteration on the constant loading plane.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.571-579
• /
• 2015

Archimedes showed that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle ${\Delta}ABP$, where P is the point on the parabola at which the tangent is parallel to the chord AB. Recently, this property of parabolas was proved to be a characteristic property of parabolas. With the aid of this characterization of parabolas, using centroid of triangles associated with a curve we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be a parabola.

• Kyungpook Mathematical Journal
• /
• v.55 no.2
• /
• pp.473-484
• /
• 2015

Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $PG=\frac{3}{5}PV$. In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.

• Structural Engineering and Mechanics
• /
• v.11 no.1
• /
• pp.17-34
• /
• 2001

An improved method has been developed for the computation of the section forces and stiffness in nonlinear finite element analysis of RC plane frames. The need for a new approach arises because the conventional technique may have a questionable level of efficiency if a large number of layers is specified and a questionable level of accuracy if a smaller number is used. The proposed technique is based on automatically dividing the section into zones of similar state of stress and tangent modulus and then numerically integrating within each zone to evaluate the sectional stiffness parameters and forces. In the new system, the size, number and location of the layers vary with the state of the strains in the cross section. The proposed method shows a significant improvement in time requirement and accuracy in comparison with the conventional layered approach. The computer program based on the new technique has been used successfully to predict the experimental load-deflection response of a RC frame and good agreement with test and other numerical results have been obtained.

• Computers and Concrete
• /
• v.5 no.3
• /
• pp.217-241
• /
• 2008

In this paper, a total strain-based hysteretic material model based on MCFT is proposed for non-linear finite element analysis of reinforced concrete structures. Although many concrete models have been proposed for simulating behavior of structures under cyclic loading conditions, accurate simulations remain challenging due to uncertainties in materials, pitfalls of crude assumptions of existing models, and limited understanding of failure mechanisms. The proposed model is equipped with a fully generalized hysteresis rule and is formulated for 2D plane stress non-linear finite element analysis. The proposed model has been formulated in a tangent stiffness-based finite element scheme so that it can be used for most general finite element analysis packages. Moreover, it eliminates the need to check that tensile stresses can be transmitted across a crack. The tension stiffening model is a function of the bar orientation and any orientation can be accommodated. The proposed model has been verified with a series of experimental results of 2D RC planar panels. This study also demonstrates how parameters of the proposed model associated with cyclic damage modeling influences the pinched cyclic shear behavior.

• Journal of Korean Society of Steel Construction
• /
• v.21 no.5
• /
• pp.483-492
• /
• 2009

In this study, nonlinear analysis of steel plane frame was performed using the refined plastic hinge method of advanced analysis techniques. In deterioration of stiffness in plastic zone, influences by flexural bending, residual stress, geometrical non-linearity, and semi-rigid connection are considered. And also, further reduced tangent modulus was used for geometrical non-linearity, top and seat angle were chosen for semi-rigid connection. Furthermore, 3 parameter power model was used for moment-rotation behaviour of beam to column connection. The loading conditions are combined with axial and lateral force and the inverse triangle distribution of lateral and eight type of analytical models were used in analysis. The results of analyses were compared with semi-rigid and rigid connection on behaviour of numerical analysis models. And also, the behaviors of frame with changes of semi-rigidity were analyzed by using the results obtained from MIIDAS-GENw.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2006.10a
• /
• pp.256-267
• /
• 2006

After heavy rainfall, It was occurred massive plane failure along bedding plane of shale in the center of rock slope. It was observed filling material and trace of underground water leakage around of the slope. We tried to find the cause for slope failure, and the result of examination showed that primary factors of the failure were low shear strength of clay filling material and water pressure farmed within tension crack existed in the top of the slope. In this research, in order to examine the features of shear strength of filled rock joint, shear test of filled rock joint was conducted using of artificial filling material such as sand and clay. Also we made an investigation into the characteristics of shear strength with different thickness of filling materials.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.42 no.1
• /
• pp.286-290
• /
• 2017

In this paper, we have proposed a hexagonal patch UWB antenna with a band notch characteristic where the notch band of 5.15 ~ 5.85 GHz band of WLAN was induced by inserting a circular slit in the patch. The impedance bandwidth of the proposed antenna meet the band width criteria of UWB communication system where is mentioned as frequencies range form 3.1 ~ 11.8 GHz. The characteristic band at 5.2 ~ 5.8 GHz notch band was observed. The radiation pattern of the antenna shows a directinal radiation pattern at $0^{\circ}$ and $180^{\circ}$ in XZ-plane and YZ-plane is an omni-directional pattern, respectively. In addition, it is observed that increase in frequency results in increases of the antenna gain whereas the notch band section is decreased. The proposed antenna was designed TRF-45 substrate with thickness of 1.62 mm, a loss tangent of 0.0035, a relative permittivity of 4.5 and designed were used Ansys Inc. HFSS.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.14 no.1
• /
• pp.93-103
• /
• 1994

Two beam/column elements are developed in order to analyze the geometric nonlinear plane irames including the effects of internal hinge and transverse shear deformation. In the case of the first element (finite segment method), tangent stiffness matrix is derived by directly integrating the equilibrium equations whereas in the case of the second element (finite element method) elastic and goemetric stiffness matrices are calculated by using the hermitian polynomials including the effects of internal hinge and shear deformation as the shape function. Numerical results are presented for the selected test problems which demonstrate that both elements represent reliable and highly accurate tools.