• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.255-277
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• 2024

In this paper, we introduce the notion of stress-energy tensor Q of the traceless Ricci tensor for Riemannian manifolds (Mⁿ, g), and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when (M, g) satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.

• Structural Engineering and Mechanics
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• v.66 no.2
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• pp.195-201
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• 2018

From the structural safety point of view, ductility is an important parameter, a relatively high level of curvature ductility would provide to the structure an increased chance of survival against accidental impact and seismic attack. The ductility of reinforced concrete beams is very important, because it is the property that allows structures to dissipate energy in seismic zone. This paper presents a revision of an earlier formula for predicting the curvature ductility factor of unconfined HSC beams to make it simpler in the use. The new formula is compared with the earlier formula and other numerical and experimental results. The new formula regroups all parameters can affecting the curvature ductility of unconfined HSC beams and it has the same domain of application as the earlier formula.

• Proceeding of EDISON Challenge
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• 2016.03a
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• pp.228-233
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• 2016

Auxetic material is a material which has negative Poisson's ratio(NPR). Auxetic material shows some distinctive property like high energy absorbing property and high shear modulus. Among these, synclastic curvature is very interesting characteristic. When synclastic-curvature-material bends, it changes its shape like dome, contrary to non-auxetic material which changes its shape like saddle(anticlastic). This distinctive property could make it easy to manufacture curved structure like nose cone or wing panel in aerospace engineering. In this study, we studied a quantitative analysis about synclastic curvature of re-entrant panel with finite element model. We suggested a concept 'Degree of Synclasticity(DOS)', which means a ratio of curvature of load-direction and load-orthogonal direction. We studied the variation of DOS with two factor, unit cell inner angle(${\theta}$) and load position angle(${\phi}$). DOS decreases as ${\theta}$ increases because the unit cell goes out of auxetic-shape. As ${\phi}$ varies, DOS changes in a large range. So proper optimization of ${\phi}$ would be needed for application.

• Tunnel and Underground Space
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• v.6 no.1
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• pp.10-18
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• 1996

Arched openings are generally excavated in underground construction works. Since stress distribution around openings depends on geological structure in rock mass, any shape of arched openings fully conformed with in-situ stress condition should be recommended to maintain mechanical safety of structures. Shape of arched openings is specified by both roof curvature and height-width ratio, and especially this report presents deformation behaviors related with roof curvature. Scale model tests and numerical studies of various shaped openings are conducted, where rectangular opening shows the greatest convergence. Through the anlayses of various arched opengings, as radius of roof curvature is increased, roof lowering and sidewall closure are remarkably increased, whereas floor heaving is increased little by little. By the way, it is useful that displacements of openings are roughly estimated in the stage of preliminary investigation. To find out elastic displacements of arched openings with any roof curvature, regressional formula and charts by least square method are represented. In addition elastoplastic deformation behavoirs of arched openings concerning associated adn non-associated flow rule are discussed.

• Design & Manufacturing
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• v.12 no.3
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• pp.13-18
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• 2018

Flexible display tends to grow every year, It tends to be larger, slimmer, and higher in image quality. Therefore, accuracy is required in the manufacturing process of each part. In the curved monitor, the bottom chassis has a structure to which other parts can be attached. The accuracy of the curvature which the bottom chassis of the curve monitor monitors has is important. If the curvature error is large, serious defects such as cracks, warpage, twisting and the like occur. Curvature was analyzed using 3D scanner. In the Forming process and Restriking process steps, spring go occurred, and spring back occurred in the Notching process and Bending process steps. Even in the same process, it was confirmed that the curvature value varied depending on the formed shape.

• Computers and Concrete
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• v.12 no.6
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• pp.831-850
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• 2013

The high strength materials have been more widely used in reinforced concrete structures because of the benefits of the mechanical and durable properties. Generally, it is known that the ductility decreases with an increase in the strength of the materials. In the design of a reinforced concrete beam, both the flexural strength and ductility need to be considered. Especially, when a reinforced concrete structure may be subjected an earthquake, the members need to have a sufficient ductility. So, each design code has specified to provide a consistent level of minimum flexural ductility in seismic design of concrete structures. Therefore, it is necessary to assess accurately the ductility of the beam sections with high strength materials in order to ensure the ductility requirement in design. In this study, the effects of concrete strength, yield strength of reinforcement steel and amount of reinforcement including compression reinforcement on the complete moment-curvature behavior and the curvature ductility factor of doubly reinforcement concrete beam sections have been evaluated and a newly prediction formula for curvature ductility factor of doubly RC beam sections has been developed considering the stress of compression reinforcement at ultimate state. Based on the numerical analysis results, the proposed predictions for the curvature ductility factor are verified by comparisons with other prediction formulas. The proposed formula offers fairly accurate and consistent predictions for curvature ductility factor of doubly reinforced concrete beam sections.

• East Asian mathematical journal
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• v.36 no.3
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• pp.389-415
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• 2020

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, ξ, η, g) in a complex space form M_n+1(c), c ≠ 0. We denote by R_ξ and R'_X be the structure Jacobi operator with respect to the structure vector ξ and be R'_X = (∇_XR)(·, X)X for any unit vector field X on M, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_ξ𝜙 = 𝜙R_ξ and at the same time R'_ξ = 0, then M is a Hopf real hypersurfaces of type (A), provided that the scalar curvature ${\bar{r}}$ of M holds ${\bar{r}}-2(n-1)c{\leq}0$.

• East Asian mathematical journal
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• v.38 no.5
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• pp.549-581
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• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c), c≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that M satisfies R_𝜉S = SR_𝜉 and at the same time R_𝜉𝜙 = 𝜙R_𝜉, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.8
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• pp.29-39
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• 1997

The clamp, as the structure which is used for supporting the pipe in the atomic power plant, is produced with a certain degree of anticlastic curvature in the current manufacturing process. In this study, the structural analysis of the clamp and the pipe was performed using ABAQUS. And the finite element modelling for the analysis was made by an HyperMesh. The contact forces which are transferred between the clamp and the pipe for the external force are changed according to the binding force of bolts and keeps the clamp tightly and protects the slipping between the clamp and the pipe. The clamps with the anticlastic curvature and with the flat curvature are considered in order to invest the anticlastic effect. In this study, another case is suggested. The present case does not have the stiffness ring on the end of the clamp but the suggested case has the ring. For the present case, the results showed that the equivalent stress is higher in the anticlastic curvature case than in the flat curvature case and the equivalent stresses on the pipe are almost the same as the binding force increses. For the suggested case, the result showed that the equivalent stress in the anticlastic curvature case decreases until some binding force and increases as the binding forces increase and is lower in some range than in the flat curvature case. From this study, the clamp with the anticlastic curvature in the suggested method is better than the clamp with the flat curvature and the optimal binding force are given.

• Restorative Dentistry and Endodontics
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• v.28 no.1
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• pp.41-49
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• 2003

There are increasing usage of Nickel-Titanium rotary files in modern clinical endodontic treatment because it is effective and faster than hand filing due to reduced step. This study was conducted to evaluate the effect of canal preparations using 3 different rotary Nickel-Titanium files that has different cross sectional shape and taper on the maintenance of canal curvature. Simulated resin block were instrumented with Profile(Dentsply, USA), GT rotary files(Dentsply, USA), Hero 642(Micro-Mega France), and Pro-Taper(Dentsply, USA). The image of Pre-instrumentation and Post-instrumentation were acquired using digital camera and overspreaded in the computer. Then the total differences of canal diameter, deviation at the outer portion of curvature, deviation at the inner portion of curvature, movement of center of the canal and the centering ratio at the pre-determined level from the apex were measured. Results were statistically analyzed by means of ANOVA, followed by Scheffe test at a significance level of 0.05. The results were as follows； 1. Deviation at the outer portion of curvature, deviation at the inner portion of curvature were showed largest in Pro-Taper so also did in the total differences of canal diameter(p＜0.05). 2. All the groups showed movements of center Profile combined with GT rotary files and Hero 642 has no difference but Pro-Taper showed the most deviation(p＜0.05). 3. At the 1, 2, 3mm level from the apex movements of center directed toward the outer portion of curvature, but in 4, 5 mm level directed toward the inner portion of curvature(p＜0.05). As a results of this study, it could be concluded that combined use of other Nickel-Titanium rotary files is strongly recommended when use Pro-Taper file because it could be remove too much canal structure and also made more deviation of canal curvature than others.