• Structural Engineering and Mechanics
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• 제85권5호
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• pp.665-677
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• 2023

In the present study, the limit point buckling and postbuckling behaviors of sinusoidal, shallow arches with pinned supports subjected to localized sinusoidal loading, based on the Euler-Bernoulli beam theory, are numerically analyzed. There are some studies on the buckling of sinusoidal shallow arches under the effect of sinusoidal loading. However, in these studies, the sinusoidal loading acts along the horizontal projection of the entire shallow arch. No study has been found in the relevant literature pertaining to the stability of the shallow arches subjected to various lengths of sinusoidal loading. Therefore, the purpose of this paper is to contribute to the literature by examining the effect of the length of the localized sinusoidal loading and the initial rise of the shallow arch on the limit point buckling and postbuckling behaviors. Equilibrium paths corresponding to certain values of the length of the localized sinusoidal loading and various values of the initial rise parameter are presented. It has been observed that the length of the sinusoidal loading and the initial rise parameter affects the transition from no buckling to limit point instability remarkably. The deformed configurations of the sinusoidal shallow arch under localized loading regarding buckling and postbuckling states are illustrated, as well. The effects of the length of the localized sinusoidal loading on the internal forces of the shallow arch are investigated during various stages of the loading.

• 한국공간구조학회논문집
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• 제20권1호
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• pp.95-102
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• 2020

The structural design of arch roofs or bridges requires the analysis of their unstable behaviors depending on certain parameters defined in the arch shape. Their maintenance should estimate the parameters from observed data. However, since the critical parameters exist in the equilibrium paths of the arch, and a small change in such the parameters causes a significant change in their behaviors. Thus, estimation to find the critical ones should be carried out using a global search algorithm. In this paper we study the parameter estimation for a shallow arch by a quantum-inspired evolution algorithm. A cost functional to estimate the system parameters included in the arch consists of the difference between the observed signal and the estimated signal of the arch system. The design variables are shape, external load and damping constant in the arch system. We provide theoretical and numerical examples for estimation of the parameters from both contaminated data and pure data.

• Structural Engineering and Mechanics
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• 제35권5호
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• pp.555-570
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• 2010

Shallow fixed arches have a nonlinear primary equilibrium path with limit points and an unstable postbuckling equilibrium path, and they may also have bifurcation points at which equilibrium bifurcates from the nonlinear primary path to an unstable secondary equilibrium path. When a shallow fixed arch is subjected to a central step load, the load imparts kinetic energy to the arch and causes the arch to oscillate. When the load is sufficiently large, the oscillation of the arch may reach its unstable equilibrium path and the arch experiences an escaping-motion type of dynamic buckling. Nonlinear dynamic buckling of a two degree-of-freedom arch model is used to establish energy criteria for dynamic buckling of the conservative systems that have unstable primary and/or secondary equilibrium paths and then the energy criteria are applied to the dynamic buckling analysis of shallow fixed arches. The energy approach allows the dynamic buckling load to be determined without needing to solve the equations of motion.

• 한국터널지하공간학회 논문집
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• 제11권4호
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• pp.419-425
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• 2009

최근에 저토피 및 터널 갱구부에 반개착식 공법을 적용하여 구조적인 안전성과 자연친화성을 높인 사례가 증가하고 있다. 반개착식 공법은 저토피구판에시 원지반을 터널 천단아치에 해당하는 기초까지만 굴착하고 아치형 구조달을 설치하여 복토한 후에 터널하반을 굴착하여 기존 개착공법에서 발생되는 지반 과다절취에 따른 대절토 비탈면 발생과 굴착면 보강에 따른 고비용과 불안정성 증대 문제를 해결할 수 있는 공법이다. 본 논문에서는 저토피 구간에서 반개착식으로 굴착한 Braced Rib Arch의 거동에 대하여 연구하였다. 아치형구조물의 Rib Arch는 지간이 1.8 m인 아치형 강재를 간격재는 목재를 사용하였으며 1:10의 축척으로 4.0 m(폭)$\times$3.3 m(높이)$\times$4.0 m(연장)의 크기를 가진 대형토조에서 실험을 수행하였다. 모형실험결과 아치형 구조물에 작용하는 성토하중은 기존 개착터널에서 사용하는 하부구조물의 폭에 해당하는 상부토체의 크기보다 작은 것으로 나타났다.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.49-64
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• 2024

When setting up a structure with an embedded shallow arch, there is a phenomenon where the end of the arch moves. To study the so-called moving domain problem, one try to transform a considered noncylindrical domain into the cylindrical domain using the transform operator, as well as utilizing the method of penalty and other approaches. However, challenges arise when calculating time derivatives of solutions in a domain depending on time, or when extending the initial conditions from the non-cylindrical domain to the cylindrical domain. In this paper, we employ the transform operator to prove the existence and uniqueness of weak solutions of the shallow arch equation on the moving domain as clarifying the time derivatives of solutions in the moving domain.

• 한국터널지하공간학회 논문집
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• 제7권3호
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• pp.227-237
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• 2005

본 연구에서는 수평 불연속면 하부에 굴착한 얄은 섬도의 2-Arch 터널의 거동을 실험적으로 규명하고자 하였다. 이를 위하여 토피고와 불연속면의 위치를 변화시켜가며 모형실험을 수행하였다. 모형실험은 실제 2-Arch 터널의 Pilot 터널굴착에서 본선터널불착에 이르는 시공단계가 반영된 실험순서에 따라 진행되었다. 연구결과로 부터 토피고에 따른 2-Arch 터널 주변지반의 하중전이 메커니즘의 변화와 불연속면 위치에 따른 이완영역의 분포 및 범위의 변화를 확인하였다. 또한 시공단계에 따른 중앙필러의 역학적 거동을 규명하였으며 불연속면 위치가 터널에 근접할수록 중앙필러 작용하중이 증가하는 것을 확인하였다.

• 한국공간구조학회논문집
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• 제20권2호
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• pp.77-85
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• 2020

This paper examined the dynamic instability of a shallow arch according to the response characteristics when nearing critical loads. The frequency changing feathers of the time-domain increasing the loads are analyzed using Fast Fourier Transformation (FFT), while the response signal around the critical loads are analyzed using Hilbert-Huang Transformation (HHT). This study reveals that the models with an arch shape of h = 3 or higher exhibit buckling, which is very sensitive to the asymmetric initial conditions. Also, the critical buckling load increases as the shape increases, with its feather varying depending on the asymmetric initial conditions. Decomposition results show the decrease in predominant frequency before the threshold as the load increases, and the predominant period doubles at the critical level. In the vicinity of the critical level, sections rapidly manifest the displacement increase, with the changes in Instantaneous Frequency (IF) and Instant Energy (IE) becoming apparent.

• 한국전산구조공학회논문집
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• 제15권2호
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• pp.367-377
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• 2002

이 논문은 탄성지반 위에 놓인 낮은 아치의 자유진동에 관한 연구이다. Pasternak가 제안한 두 개의 매개변수로 표현되는 지반모형을 채택하여 대상아치의 자유진동을 지배하는 미분방정식을 유도하였다. 양단회전 및 양단고정의 단부 조건을 갖는 두 종류의 아치선형을 유도된 지배방정식에 적용하여 Galerkin method로 해석함으로써 최저차 대칭 및 역대칭 고유진동수 방정식을 산출하였다 아치높이, Winkler지반계수 및 전단지반계수가 고유진동수에 미치는 영향을 분석하였으며, 아치선형이 고유진동수에 미치는 영향을 분석하였다.

• 대한수학회지
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• 제54권3호
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• pp.945-966
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• 2017

The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 봄 학술발표회 논문집
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• pp.457-464
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• 1998

The equilibrium path of shallow sinusoidal arches supported by hinges at both ends is investigated. The displacement increment method is used to get the solution of the nonlinear differential equations for these structures and to plot the equilibrium paths by the results. Using the equilibrium paths, the relations between the position of buckling point and buckling type for the case of sinusoidal distributed loads are inferred. From the result that the buckling type changes according to the normalized rise of arch, it is also shown that the arch rise is the governing factor to stability regions