• 대한기계학회논문집A
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• 제24권1호
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• pp.182-189
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• 2000

This paper presents the real time control method of 5-axis NC machine for high precision and productivity based on the curvature theory, of a ruled surface. The trajectory, of NC machine is described by, way of a ruled surface generated by the points on part surface and tool axis direction vector. The curvature theory, of a ruled surface is then applied to deter-mine the motion parameters of the 5-axis machine for control. The controller computes position, orientation, and differential motion parameters of the tool in each sampling period. The real-time approach produces smoother surfaces and requires substantially less machining time compared to conventional off-line approaches. The propose real-time control method based of the curvature theory of a ruled surface may give new methodology of precision 5-axis machine control.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2002년도 추계학술대회 논문집
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• pp.482-487
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• 2002

This paper presents a robot trajectory generation method based on the dual curvature theory of ruled surfaces. Robot trajectory can be represented as a ruled surface generated by the TCP(Tool Center Point) and my unit vector among the tool frame. Dual curvature theory of ruled surfaces provides the robot control algorithm with the motion property parameters. With the differential properties of the ruled surface, the linear and angular motion properties of the robot end effector can be utilized in the robot trajectory planning.

• Steel and Composite Structures
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• 제21권6호
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• pp.1347-1368
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• 2016

In this article, an exact analytical solution for mechanical buckling analysis of symmetrically cross-ply laminated plates including curvature effects is presented. The equilibrium equations are derived according to the refined nth-order shear deformation theory. The present refined nth-order shear deformation theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments The most interesting feature of this theory is that it accounts for a parabolic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Buckling of orthotropic laminates subjected to biaxial inplane is investigated. Using the Navier solution method, the differential equations have been solved analytically and the critical buckling loads presented in closed-form solutions. The sensitivity of critical buckling loads to the effects of curvature terms and other factors has been examined. The analysis is validated by comparing results with those in the literature.

• 대한수학회지
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• 제56권1호
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• pp.113-125
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• 2019

In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a directed regular graph to be Ricci-flat. Moreover, we calculate the Ricci curvature of the cartesian product of directed graphs.

• Structural Engineering and Mechanics
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• 제7권5호
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• pp.457-471
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• 1999

In this paper, different curvature-rates are controlled to highlight the characteristic of viscoplastic response in cyclic bending tests. The curvature-ovalization apparatus, which was designed by Pan et al. (1998), is used for conducting the curvature-controlled experiments on thin-walled tubular specimens for AISI 304 stainless steel under cyclic bending. The results reveals that the faster the curvature-rate implies, the fast degree of hardening of the metal tube. However, the ovalization of the tube cross-section increases when the curvature-rate increases.

• 대한수학회보
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• 제58권1호
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• pp.1-20
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• 2021

We examine the theory of surfaces in the isotropic three-space, with emphases on the surfaces related to the zero mean curvature.

• International Journal of Ocean System Engineering
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• 제2권2호
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• pp.63-70
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• 2012

This paper presents a new curvature based kinematic displacement theory and a numerical method to calculate the planar displacement of structures from a geometrical viewpoint. The theory provides an opportunity to satisfy the kinematic equilibrium of a planar structure using a progressive numerical approach, in which the cross sections are assumed to remain plane, and the deflection curve was evaluated geometrically using the curvature values despite being solved using differential equations. The deflection curve is parameterized with the arc-length, and was taken as an assembly of the chains of circular arcs. Fast and accurate solutions of most complex deflections can be obtained with few inputs.

• Steel and Composite Structures
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• 제10권3호
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• pp.245-260
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• 2010

In this paper, experimental and theoretical investigations on the response and collapse of 310 stainless steel tubes with different diameter-to-thickness ratios subjected to cyclic bending are discussed. The tube-bending device and curvature-ovalization measurement apparatus were used to conduct the experiment. The endochronic theory combined with the principle of virtual work and finite element software, ANSYS, were used to simulate the moment-curvature and ovalization-curvature relationships. It is shown that although the two methods lead to good simulation of the moment-curvature relationship, the endochronic theory combined with the principle of virtual work has the better simulation of the ovalization-curvature response when compared with experimental data and the simulation by ANSYS. In addition, the theoretical formulations proposed by Kyriakides and Shaw (1987) and Lee et al. (2001) were used to simulate the controlled curvature-number of cycles to produce buckling relationship. It is shown that the theoretical formulations effectively simulate the experimental data.

• Steel and Composite Structures
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• 제5권5호
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• pp.359-374
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• 2005

This paper presents the experimental and theoretical results of the viscoplastic response and collapse of 316L stainless steel tubes subjected to cyclic bending. The tube bending machine and curvature-ovalization measurement apparatus, which was designed by Pan et al. (1998), were used for conducting the cyclic curvature-controlled experiment. Three different curvature-rates were controlled to highlight the characteristic of viscoplastic response and collapse. Next, the endochronic theory and the principle of virtual work were used to simulate the viscoplastic response of 316L stainless steel tubes under cyclic bending. In addition, a proposed theoretical formulation (Lee and Pan 2001) was used to simulate the relationship between the controlled cyclic curvature and the number of cycles to produce buckling under cyclic bending at different curvature-rates (viscoplastic collapse). It has been shown that the theoretical simulations of the response and collapse correlate well with the experimental data.

• International Journal of Ocean System Engineering
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• 제2권3호
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• pp.195-199
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• 2012

This paper reports a new analytical method to calculate the planar displacement of structures. The cross-sections were assumed to remain in plane and the deflection curve was evaluated using the curvature values geometrically, despite being solved with differential equations. The deflection curve was parameterized with the arc-length of the curvature values, and was taken as an assembly of chains of circular arcs. Fast and accurate solutions of complex deflections can be obtained easily. This paper includes a comparison of the nonlinear displacements of an elastic tapered cantilever beam with a uniform moment distribution among the proposed analytical method, numerical method of the theory and large deflection FEM solutions.