• 정보과학회지
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• 제1권1호
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• pp.72-74
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• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.

• Structural Engineering and Mechanics
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• 제63권2호
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• 대한수학회보
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• 제41권1호
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• pp.137-145
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• 2004

In [13], we developed a theory of complex Finsler manifolds to investigate the global geometry of complex Finsler manifolds. There we proved a version of Bonnet-Myers' theorem for complex Finsler manifolds with a certain condition on the Finsler metric which is a generalization of the Kahler condition for the Hermitian metric. In this paper, we show that if the holomorphic sectional curvature of M is ${\geq}\;c^2\;>\;0$, then M is simply connected. This is a generalization of the Synge's theorem in the Riemannian geometry and the Tsukamoto's theorem for Kahler manifolds. The main point of the proof lies in how we can circumvent the convex neighborhood theorem in the Riemannian geometry. A second variation formula of arc length for complex Finsler manifolds is also derived.

• Computers and Concrete
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• 제20권2호
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• pp.129-143
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• 2017

Seismic design of reinforced concrete (RC) structures requires a certain minimum level of flexural ductility. For example, Eurocode EN1998-1 directly specifies a minimum flexural ductility for RC beams, while Chinese code GB50011 limits the equivalent rectangular stress block depth ratio at peak resisting moment to achieve a certain nominal minimum flexural ductility indirectly. Although confinement is effective in improving the ductility of RC beams, most design codes do not provide any guidelines due to the lack of a suitable theory. In this study, the confinement for desirable flexural ductility performance of both normal- and high-strength concrete beams is evaluated based on a rigorous full-range moment-curvature analysis. An effective strategy is proposed for flexural ductility design of RC beams taking into account confinement. The key parameters considered include the maximum difference of tension and compression reinforcement ratios, and maximum neutral axis depth ratio at peak resisting moment. Empirical formulae and tables are then developed to provide guidelines accordingly.

• 대한기계학회논문집
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• 제6권4호
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• pp.315-322
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• 1982

The slab analogy method was introduced in the 1920's for the first time as a new experimental stress analysis method. Notwithstanding its theoretical propriety, this method has not been recognized as efficient one because of its difficulty in practical measurement of the slab curvature. In this paper, aiming at experimental determination of two-dimensional stress intensity factors(S. I. F) of arbitrarily shaped cracks which had been regarded as almost impossible by conventional method, the slab analogy was reevaluated. Measuring of slab curvature was replaced by three simple measuring factors to overcome vital slab-analogy's shortcoming by joint use of the shadow-moire method. A determination formula was also derived from the theory of fracture mechanics. By this newly exploited method, it was found that the slab analogy still has its great advantage in determination of S.I.F. of arbitrarily shaped cracks with considerable accuracy compared with existent experimental methods.

• 대한기계학회논문집
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• 제17권10호
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• pp.2535-2542
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• 1993

Two-noded curved beam elements, CMLC (field-consistent membrane and linear curvature) and IMLC(field-inconsistent membrane and linear curvature) are developed on the basis of Timoshenko's beam theory and curvilinear coordinate. The curved beam element is developed by the separation of the radial deflection into the bending deflection. In the CMLC element, field-consistent axial strain interpolation is adapted for removing the membrane locking. The CMLC element shows the rapid and stable convergence on the wide range of curved beam radius to thickness. The field-consistent axial strain and the separation of radial deformation produces the most efficient linear element possible.

• 대한수학회보
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• 제51권4호
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• pp.957-964
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• 2014

In this paper, we prove that there is no branch point in the Lorentz space (M, d) which is the limit space of a sequence {($M_{\alpha},d_{\alpha}$)} of compact globally hyperbolic interpolating spacetimes with $C^{\pm}_{\alpha}$-properties and curvature bounded below. Using this, we also obtain that every maximal timelike geodesic in the limit space (M, d) can be expressed as the limit curve of a sequence of maximal timelike geodesics in {($M_{\alpha},d_{\alpha}$)}. Finally, we show that the limit space (M, d) satisfies a timelike triangle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.

• Journal of Mechanical Science and Technology
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• 제15권12호
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• pp.1655-1663
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• 2001

The objective of this paper is to develop a logical procedure to determine the center roller displacement, in the three-roll bending process, which is required in the fabrication of curved rectangular plates with a desired curvature. To this end, the mechanics of the process was analyzed by both analytical and finite element approaches. Comparisons of the results reveal that a simple analytical procedure, based on the beam theory, yields a reasonably accurate relationship between the center roller displacement and residual curvature. With further development and refinement, the proposed in this work has great premise for practical application, particularly automation of the process.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2007년도 추계학술대회 논문집
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• pp.107-114
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• 2007

In this paper, the equations of motion by which the natural vibration of rotating thick ring can be analyzed accurately are presented. These equations are derived from the theory of finite deformation and the principle of virtual work. The effects of variation in curvature across the ring cross-section can be considered in these equations. The ring models are called as thick ring model and thin ring model respectively as the effects of variation in curvature are considered or neglected. The radial displacement of ring which is rotating at constant angular velocity is determined by a non-linear equation derived from the principle of virtual work. The equations of the in-plane and out-of-plane vibrations at disturbed state are also formulated from the principle of virtual work. They can be expressed as the combination of the radial displacement at the steady state and the disturbed displacements about the steady state. The natural vibrations of rings with different thickness are analyzed by using the presented ring models and 3-dimensional finite element method to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 1988년도 학술세미나 강연집
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• pp.71-123
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• 1988

The aim of this paper is to examine the end bearing capacity of a pile in cohesionless soils. The ode of failure of soil due to pile installation is assumed from experimental observation of actual soil deformation. A new solution is proposed complying with the assumed mode of failure by employing the theory of cavity expansion. The effect of curvature of failure envelope is studied in relation to tile proposed solution. The influence of a curved failure envelope becomes larger with increasing degree of curvature and the level of confining stress. This effect in some cases or reduce the end bearing capacity by tore the 80 percent compared with that given by a straight failure envelope. For practical application of tile proposed solution, the method of determining the average volume change in the plastic zone is re-evaluated. The proposed solution is confirmed by comparing the theoretical values with experimental results obtained from model pile tests in a calibration chamber. The comparison shows that the proposed solution provides a reasonable prediction of end bearing capacity for both weak and strong grained soils.