• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.217-224
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• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.229-235
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• 2007

Measures of leverage in nonlinear regression models are discussed by extending the leverage in linear regression models. The connection between measures of leverage and nonlinearity of the models are explored. Illustrative example based on real data is presented.

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

• Honam Mathematical Journal
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• v.37 no.4
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• pp.487-504
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• 2015

For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

• Tunnel and Underground Space
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• v.34 no.4
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• pp.355-373
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• 2024

The Generalized Hoek-Brown (GHB) criterion is a nonlinear failure criterion specialized for rock engineering applications and has recently seen increased usage. However, the GHB criterion expresses the relationship between minimum and maximum principal stresses at failure, and when GSI≠100, it has disadvantage of being difficult to express as an explicit relationship between the normal and shear stresses acting on the failure plane, i.e., as a Mohr failure envelope. This disadvantage makes it challenging to apply the GHB criterion in numerical analysis techniques such as limit equilibrium analysis, upper-bound limit analysis, and the critical plane approach. Consequently, recent studies have attempted to express the GHB Mohr failure envelope as an approximate analytical formula, and there is still a need for continued interest in related research. This study presents improved formulations for the approximate GHB Mohr failure envelope, offering higher accuracy in predicting shear strength compared to existing formulas. The improved formulation process employs a method to enhance the approximation accuracy of the tangential friction angle and utilizes the tangent line equation of the nonlinear GHB failure envelope to improve the accuracy of shear strength approximation. In the latter part of this paper, the advantages and limitations of the proposed approximate GHB failure envelopes in terms of shear strength prediction accuracy and calculation time are discussed.