• Structural Engineering and Mechanics
• /
• v.51 no.4
• /
• pp.601-625
• /
• 2014

Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.551-561
• /
• 2010

In this paper we give a new characterization of real hypersurfaces of type B, that is, a tube over a totally geodesic $\mathbb{Q}P^n$ in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$, where m = 2n, with the Reeb vector $\xi$ belonging to the distribution $\mathfrak{D}$, where $\mathfrak{D}$ denotes a subdistribution in the tangent space $T_xM$ such that $T_xM$ = $\mathfrak{D}{\bigoplus}\mathfrak{D}^{\bot}$ for any point $x{\in}M$ and $\mathfrak{D}^{\bot}=Span{\xi_1,\;\xi_2,\;\xi_3}$.

• Magazine of the Korea Concrete Institute
• /
• v.2 no.3
• /
• pp.73-80
• /
• 1990

This research program is directed at studying the behavior and the strength of reinforced concrete slabs sub¬jected to certain combination of punching shear and in-plane tension. Major variables to be investigated are the shear span to depth ratio of reinforced concrete slabs and the degree of the in-plane tensile force which is act¬ing tangent to the slabs. The experimental results are used for understanding of the degree of tbe interaction between the two loadings, and for developing a new practical design equation.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.10a
• /
• pp.327-334
• /
• 2001

This paper presents a non-linear analysis procedure for plane frame structures by finite element formulation with assumptions of Timoshenko beam theory. Finite element displacement method based on Lagrangian formulation is used and two-noded and isoparametric line element is adopted to represent finite element model. The layered approach is used for the elasto-plastic analysis of the plane frame structures with rectangular and I cross sections. A load incremental method combined with the tangent stiffness and the initial stiffness methods for each load increment is used for the solution of non-linear equations. Numerical examples are presented to investigate the behavior and the accuracy of the elasto-plastic non-linear application and the results of this study are compared with other solutions using the concept of plastic hinge.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.407-417
• /
• 2022

Archimedes proved 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 of the region bounded by the parabola X and the chord AB is four thirds of the area of the triangle ∆ABP. This property was proved to be a characteristic of parabolas, so called the Archimedean characterization of parabolas. In this article, we study strictly convex curves in the plane ℝ². As a result, first using a functional equation we establish a characterization theorem for quadrics. With the help of this characterization we give another proof of the Archimedean characterization of parabolas. Finally, we present two related conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open arc of a parabola.

• Maxillofacial Plastic and Reconstructive Surgery
• /
• v.15 no.4
• /
• pp.329-337
• /
• 1993

Improvement of orthognathic surgical techniques make it possible to design esthetic surgical correction for total esthetic face. In order to find the esthetic line which guide esthetic surgical correction in patients of orthognathic surgery, cephalometric soft tissue analysis of esthetic faces were performed. In esthetic Korean young adults, 25 males and 25 females who were within 1 S.D. of E-line, ANB, P/A facial height ratio, were analyzed in natural position keeping their face eye level. 1. Sn position is constant in males and females. The Sn-N'-N' Vertical plane angle is $5.3^{\circ}$ in both sexes. Sn is positioned in front of 5 mm in female 7 mm in male from the N' vertical plane. 2. The Sn-Ls line make constant angle to horizontal plane with $72.5^{\circ}$ in both sexes, which is called "upper esthetic line". The Ls-Pg' line makes constant angle to $72.4^{\circ}$ (range $72.2^{\circ}$ in female to $72.6^{\circ}$ in male), which is called "lower esthetic line". 3. When inter-esthetic line angle (the Sn-Ls line to Ls-Pg' line) has $144.9^{\circ}$, lower third face has esthetic upper and lower lip. 4. In treatment planning, Sn is first corrected in proper position, and then upper and lower esthetic line are established with the angle of 144.9. The maxilla is moved to tangent Ls to the upper esthetic line, and mandible is moved to tangent Li and Pg' to the lower esthetic line, according to the "y"-shaped esthetic lines, then lower third face showes esthetics.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.2103-2114
• /
• 2013

Archimedes knew 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 AB. We consider whether this property (and similar ones) characterizes parabolas. We present five conditions which are necessary and sufficient for a strictly convex curve in the plane to be a parabola.

• Journal of the Korean Data and Information Science Society
• /
• v.20 no.5
• /
• pp.913-917
• /
• 2009

The measures of leverage in linear regression has been extended to nonlinear regression models. We consider several curvature measures of nonlinearity in an estimation situation. The relationship between measures of leverage and statistical curvature are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a tangent plane leverage are discussed in connection with the effective residual curvature of the nonlinear model.

• 제어로봇시스템학회:학술대회논문집
• /
• 1992.10a
• /
• pp.407-411
• /
• 1992

A method for optimal route planning is presented with the assumption that the overall defended area is known in terms of threat potential function. This approach employes tangent plane to reduce the dimension of the state space for optimal programming problems with a state equality constraint. One-dimensional search algorithm is used to select the optimal route among the extermal fields which are obtained by integrating three differential equations from the initial values. In addition to being useful for the route planning through threat potential area, the trajectory planning will be suitable for general two-dimensional searching problems.

• Structural Engineering and Mechanics
• /
• v.3 no.1
• /
• pp.35-48
• /
• 1995

This paper presents new frequency results for elliptical and semi-elliptical Mindlin plates of various aspect ratios, thicknesses and boundary conditions. The results were obtained using the recently developed computerized Rayleigh-Ritz method for thick plate analysis. For simply supported elliptical plates, it is proposed that the penalty function method be used to enforce the condition of zero rotation of the midplane normal in the tangent plane to the plate boundary.