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

• Communications of the Korean Mathematical Society
• /
• v.17 no.4
• /
• pp.625-633
• /
• 2002

Recently, Chen establishes sharp relationship between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. In this paper, we establish sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in quaternion projective spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.639-648
• /
• 2013

In this paper, we study Finsler metrics of constant S-curvature. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (${\alpha}$, ${\beta}$)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen' construction.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.63-76
• /
• 2003

In this article, we establish relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a slant submanifold in a Sasakian space form of constant $\varphi-sectional$ curvature with arbitrary codimension.

• Structural Engineering and Mechanics
• /
• v.43 no.2
• /
• pp.147-161
• /
• 2012

This paper presents a curvature method for analysis of beam-columns with different materials and arbitrary cross-section shapes and subjected to combined biaxial moments and axial load. Both material and geometric nonlinearities (the p-delta effect in this case) were incorporated. The proposed method considers biaxial curvatures and uniform normal strains of discrete cross-sections of beam-columns as basic unknowns, and seeks for a solution of the column deflection curve that satisfies force equilibrium conditions. A piecewise representation of the beam-column deflection curve is constructed based on the curvatures and angles of rotation of the segmented cross-sections. The resulting bending moments were evaluated based on the deformed column shape and the axial load. The moment curvature relationship and the beam-column deflection calculation are presented in matrix form and the Newton-Raphson method is employed to ensure fast and stable convergence. Comparison with results of analytic solutions and eccentric compression tests of wood beam-columns implies that this method is reliable and effective for beam-columns subjected to eccentric compression load, lateral bracings and complex boundary conditions.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.189-201
• /
• 2005

In this article, we establish relations between the sectional curvature function K and the shape operator, and also relationship between the k-Ricci curvature and the shape operator for slant submanifolds in generalized complex space forms with arbitrary codimension.

• Communications for Statistical Applications and Methods
• /
• v.18 no.1
• /
• pp.131-136
• /
• 2011

The original Bates-Watts framework applies only to the complete parameter vector. Thus, guidelines developed in that framework can be misleading when the adequacy of the linear approximation is very different for different subsets. The subset curvature measures appear to be reliable indicators of the adequacy of linear approximation for an arbitrary subset of parameters in nonlinear models. Given the specific mean shift outlier model, the standard approaches to obtaining test statistics for outliers are discussed. The accuracy of outlier tests is investigated using subset curvatures.

• Journal of the Chungcheong Mathematical Society
• /
• v.34 no.4
• /
• pp.369-378
• /
• 2021

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L²-norm of the traceless second fundamental form. If M is weakly stable, then λ₁(M) is bounded above by n² + O(n^2+s) for arbitrary s > 0.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2003.06a
• /
• pp.806-809
• /
• 2003

In this paper, extracting design information from arbitrary aspherical lens shape in reverse engineering is introduced. Deformation terms and sphere data equation with various variables compose asphere equation. Aspherical lens shape is expressed with complicated polynomial expression that includes deformation terms and sphere data. Deformation term and vertex curvature have direct influence on a geometric shape and an optical characteristics of aspherical lens. Hence, extracting these information mean that design information could be derived and analyzed from shape data of arbitrary aspherical lens. Furthermore, sharing designer's experience and knowledge for aspherical lens design could be expected.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.1
• /
• pp.100-114
• /
• 1996

In this paper, a new thin-walled beam finite elcment is developed to overmome the difficulties in the analysis of real structures by existing beam elements. The element is formulated by extending Benscoter's assumption and also by adopting the concept of the curvature-based element. It is applicable to the analysis of the beams with arbitrary cross-sectional shapes. The results obtained show that the element is locking-free and the accuracy of the finite element solutions is remarkably improved.