• Structural Engineering and Mechanics
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• v.85 no.5
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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.

• Journal of Korean Association for Spatial Structures
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• v.20 no.1
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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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• v.35 no.5
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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.

• Journal of Korean Tunnelling and Underground Space Association
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• v.11 no.4
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• pp.419-425
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• 2009

Recently, the number of shallow tunnel construction increases to improve the structural safety and environment-friendliness. In Semi-Cut and Cover Method, ground is excavated to the crown arch level and braced rib arch is set to backfill before the excavation of lower face. Semi-Cut and Cover Method is proposed to solve the problems occurred by the conventional Cut and Cover Method, such as unstability, high-cost and the large cutting slope to be reinforced. In this paper, the behaviors of Braced Rib Arch in shallow tunnel excavated by semi-cut and cover method was studied. Model tests in 1:10 Scale were performed in real construction sequences. The distance between supports of rib arch was 1.8 m and the length of spacer was 1.0 m. the size of test pit was 4.0 m (width)$\times$3.3 m (length) 4.0 m (height) in dimension. Tests results show that backfill load acting on arch was smaller than that in the conventional Open-Cut Method.

• Journal of applied mathematics & informatics
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• v.42 no.1
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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.

• Journal of Korean Tunnelling and Underground Space Association
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• v.7 no.3
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• pp.227-237
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• 2005

In this study, the behavior of shallow 2-Arch tunnel due to excavation under horizontal discontinuity plane was verified experimentally. The model tests were carried out by varying the overburden height and the location of the discontinuity plane. The model tests followed exactly the real 2-Arch tunnel construction stages. As a result, it is discovered that stress-transfer mechanism and loosening area around the 2-Arch tunnel depends on the overburden heights and the location of the discontinuity plane. And central pillar load is also dependent on overburden height, location of discontinuity plane and construction stages.

• Journal of Korean Association for Spatial Structures
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• v.20 no.2
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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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.2
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• pp.367-377
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• 2002

This paper deals with the free vibrations of shallow arches resting on elastic foundations. Foundations we assumed to follow the hypothesis proposed by Pasternak. The governing differential equation is derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. Two arch shapes with hinged-hinged and clamped-clamped end constraints we considered in analysis. The frequency equations (lowest symmetrical and antisymmetrical frequency equations) we obtained by Galerkin's method. The effects of arch rise, Winkler foundation parameter and shear foundation parameter on the lowest two natural frequencies are investigated. The effect of initial arch shapes on frequencies is also studied.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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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