• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.17 no.10
• /
• pp.300-309
• /
• 2016

Curved beams are increasingly used in buildings, vehicles, ships, and aircraft, which has resulted in considerable effort towards developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic curved beams has been the subject of many investigations. Solutions to the relevant differential equations have traditionally been obtained by the standard finite difference or finite element methods. However, these techniques require a great deal of computer time for a large number of discrete nodes with conditions of complex geometry and loading. One efficient procedure for the solution of partial differential equations is the differential quadrature method (DQM). This method has been applied to many cases to overcome the difficulties of complex algorithms and high storage requirements for complex geometry and loading conditions. Out-of-plane buckling of curved beams with rotatory inertia were analyzed using DQM under uniformly distributed radial loads. Critical loads were calculated for the member with various parameter ratios, boundary conditions, and opening angles. The results were compared with exact results from other methods for available cases. The DQM used only a limited number of grid points and shows very good agreement with the exact results (less than 0.3% error). New results according to diverse variation are also suggested, which show important roles in the buckling behavior of curved beams and can be used for comparisons with other numerical solutions or experimental test data.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.20 no.5
• /
• pp.612-620
• /
• 2019

The increasing use of curved beams in buildings, vehicles, ships, and aircraft has results in considerable effort being directed toward developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic curved beams has been the subject of a large number of investigations. Solutions of the relevant differential equations have traditionally been obtained by the standard finite difference. These techniques require a great deal of computer time as the number of discrete nodes becomes relatively large under conditions of complex geometry and loading. One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method(DQM) has been applied to a large number of cases to overcome the difficulties of the complex algorithms of programming for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. In this study, the in-plane extensional vibration for asymmetric curved beams with linearly varying cross-section is analyzed using the DQM. Fundamental frequency parameters are calculated for the member with various parameter ratios, boundary conditions, and opening angles. The results are compared with the result by other methods for cases in which they are available. According to the analysis of the solutions, the DQM, used only a limited number of grid points, gives results which agree very well with the exact ones.

• Proceedings of the Korean Institute of Industrial Safety Conference
• /
• 2001.11a
• /
• pp.111-117
• /
• 2001

The problem of the vibration of arches has become a subject of interest for many investigators due to Its importance in many practical applications. The early investigators into the in-plane vibration of rings were Hoppe $^{1)}$ and Love $^{2)}$ . Love $^{2)}$ improved on Hoppe's theory by allowing for stretching of the ring. Lamb $^{3)}$ investigated the statics of incomplete ring with various boundary conditions and the dynamics of an incomplete free-free ring of small curvature.(omitted)

• Communications of Mathematical Education
• /
• v.12
• /
• pp.281-301
• /
• 2001

본 논문은 고등학교 제7차 교육과정 중 수학 I 과 미분적분학에서 나오는 적분 단원의 교수 학습을 위해 Visual Basic을 사용하여 제작한 프로그램의 설계과정과 그 기능을 기술하였다. 먼저, 적분의 개념을 이끌어 내기 위한 도구인 “구분구적법”의 설명을 위해 원을 포함하는 사각형과 원에 포함된 사각형들의 개수와 면적에 대해 원을 나누는 사각형의 한 변의 길이를 조절해감으로서 원의 실제 면적에 접근해 가는 과정을 보여줄 수 있으며, 또한 “정적분”, “넓이”, “두 곡선 사이의 넓이”를 구하는 프로그램을 이용하여 학생들이 각각의 개념을 프로그램을 실행하며 시각적으로 확인할 수 있도록 설계하였다. 이 프로그램은 일선 학교에서 구분구적법과 적분, 넓이의 개념을 시각적으로 이해할 수 있는 자료로 활용될 수 있을 것이다.

• Proceedings of the Korean Institute of Industrial Safety Conference
• /
• 2000.11a
• /
• pp.17-26
• /
• 2000

The early investigators into the in-plane vibration of rings were Hoppe $Hoppe ^{1)}$ and $Love ^{2)}$. $Love ^{2)}$ Improved on Hoppe's theory by allowing for stretching of the ring. $Lamb ^{3)}$ investigated the statics of incomplete ring with various boundary conditions and the dynamics of an incomplete free-free ring of small curvature. Den $Hartog ^{4)}$ used the Rayleigh-Ritz method for finding the lowest natural frequency of circular arcs with simply supported or clamped ends and his work was extended by Volterra and $Morell ^{5)}$ for the vibrations of arches having center lines in the form of cycloids, catenaries or parabolas.(omitted)

• Journal of the Korean Society of Safety
• /
• v.14 no.1
• /
• pp.199-207
• /
• 1999

The differential quadrature method (DQM) is applied to computation of eigenvalues of the equations of motion governing the free in-plane and out-of-plane vibrations for circular curved beams. Fundamental frequencies are calculated for the members with various end conditions and opening angles. The results are compared with existing exact solutions and numerical solutions by other methods (Rayleigh-Ritz, Galerkin or FEM) for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.19 no.11
• /
• pp.205-212
• /
• 2018

In order to overcome shortcomings of commercial analysis program for solving certain geotechnical problems, finite element method adopting isoparametric quadrilateral element was selected as a tool for analyzing soil behavior and calculating process was programmed. Two examples were considered in order to verify reliability of the developed program. One of the two examples is the case of acting isotropic confining pressure on finite element and the other is the case of acting shear stress on the sides of the finite element. Isoparametric quadrilateral element was considered as the finite element and displacements in the element can be expressed by node displacements and shape functions in the considered element. Calculating process for determining strain which is defined by derivatives using global coordinates was coded using the Jacobian and the natural coordinates. Four point Gauss rule was adopted to convert double integral which defines stiffness of the element into numerical integration. As a result of executing analysis of the finite element under isotropic confining pressure, calculated stress corresponding to four Gauss points and center of the element were equal to the confining pressure. In addition, according to the analyzed results for the element under shear stress, horizontal stresses and vertical stresses were varied with positions in the element and the magnitudes and distribution pattern of the stresses were thought to be rational.