Stability of shallow arches under constant load

Ha, Junhong; Gutman, Semion; Shon, Sudeok; Lee, Seungjae

doi:10.1016/j.ijnonlinmec.2013.08.004

Cited by 16 publications

(7 citation statements)

References 20 publications

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“…The governing equation of motion is expressed in the following equation when the shape and coordinate system of the shallow arches are defined as in Figure 1 (Lin and Chen [21]; Ha et al [18]). In this figure, the two ends of the arch are separated from each other by the distance .…”

Section: Nonlinear Equations Of Motionmentioning

confidence: 99%

“…which yields the following nonlinear partial differential equations governing the motion of the shallow arch system (Ha et al [18]):…”

Section: Nonlinear Equations Of Motionmentioning

confidence: 99%

“…These early researches on shallow arches resulted in rebounding studies of chaotic motion or global dynamic behavior (Blair et al [9]; Levitas et al [10]), accurate solution of free-vibration (Tseng et al [11]; De Rosa and Franciosi [12]), internal resonance (Bi and Dai [13]; Lacarbonara and Rega [14]), and buckling under boundary condition and moving load (Kong et al [15]; Chen and Lin [16,17]). Recently, many investigations for design and construction of shallow arch roofs have been conducted, including the identification and stability for shallow arches (Ha et al [18]), and sensitivity of shallow arch (Virgin et al [19]). On the other hand, the initially 2 Mathematical Problems in Engineering curved or buckled microbeams in mechanics (Farokhi and Ghayesh [20]) have been studied in terms of nonlinearity, geometrical imperfection, resonance, and chaotic behaviors.…”

Section: Introductionmentioning

confidence: 99%

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A Semianalytical Approach for Nonlinear Dynamic System of Shallow Arches Using Higher Order Multistep Taylor Method

Shon

Ahn²,

Lee

et al. 2018

Mathematical Problems in Engineering

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This study aimed at obtaining a semianalytical solution for nonlinear dynamic system of shallow arches. Taylor method was applied to find the analytical solution, and an investigation of their dynamic characteristic was carried out to verify the applicability of this methodology for the shallow arches under step or periodic excitation. A polynomial solution can be obtained from this multistep approach with respect to time, and direct buckling as well as indirect buckling of the shallow arches can be observed, also. The results indicated that the dynamic buckling load level was higher with higher shape factor. Additionally, a change of attractor in phase space was investigated. Coupling in symmetric mode as well as asymmetric mode was observed in case of indirect buckling, and a sensitive response was also manifested during sinusoidal and beating excitation. These results of applying multistep Taylor series for the investigation of displacement response and attractor change revealed that this analytical approach was valid in explaining the dynamic buckling behavior of shallow arches under direct and indirect snapping.

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Section: Nonlinear Equations Of Motionmentioning

confidence: 99%

“…which yields the following nonlinear partial differential equations governing the motion of the shallow arch system (Ha et al [18]):…”

Section: Nonlinear Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Semianalytical Approach for Nonlinear Dynamic System of Shallow Arches Using Higher Order Multistep Taylor Method

Shon

Ahn²,

Lee

et al. 2018

Mathematical Problems in Engineering

Self Cite

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“…The solution proposed by them can be applied to arbitrary arches with arbitrary geometric imperfections. Ha et al [7] analyzed the asymptotic stability of shallow arches, achieving the analytical response when the initial shape of the arch and the acting load, assumed to be independent of time, are linear combinations of sinusoidal functions. Virgin et al [8] verified the response to a shallow arch subjected to loading and the influence of changes in the thermal environment.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Instability in Shallow Arches under Transversal Forces and Plane Frames with Semirigid Connections

Fernandes

Vasconcellos

Greco

2018

Mathematical Problems in Engineering

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Structural engineering demands increasingly lighter systems, which can cause instability problems and compromise performance. A high slenderness index of a structural element makes it susceptible to instability. It is important to understand the problem, the limits of stability, and its postcritical behavior. An example that can occur in collapsed arches under a cross load is the dynamic snap-through behavior, where the structure in a given equilibrium condition jumps to a new remote equilibrium setting, causing usually sudden curvature. The semirigid connections are a source of physical nonlinearity and can influence the overall stability of the structural system, in addition to the distribution of stresses in the same system. Conventional approaches make use of static considerations. However, instability problems are inherently evolutionary processes, so a transient analysis is necessary for a complete description of structural behavior. The present work evaluates the geometrically nonlinear dynamic behavior of collapsed arches subjected to transverse force and plane frames with semirigid connections. The time domain responses, via Newmark's Method and positional formulation of the Finite Element Method, were obtained in terms of displacements, velocities, acceleration, and phase diagrams.

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“…in derivation of the non-linear longitudinal normal strain for shallow parabolic arches, which have been used in large span roof structures as reported in [35] and bridges as reported in [36]. This assumption of Eq.…”

Section: Introductionmentioning

confidence: 99%

Effects of approximations on non-linear in-plane elastic buckling and postbuckling analyses of shallow parabolic arches

Bradford¹,

Pi²,

Yang³

et al. 2015

Engineering Structures

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Stability of shallow arches under constant load

Cited by 16 publications

References 20 publications

A Semianalytical Approach for Nonlinear Dynamic System of Shallow Arches Using Higher Order Multistep Taylor Method

A Semianalytical Approach for Nonlinear Dynamic System of Shallow Arches Using Higher Order Multistep Taylor Method

Dynamic Instability in Shallow Arches under Transversal Forces and Plane Frames with Semirigid Connections

Effects of approximations on non-linear in-plane elastic buckling and postbuckling analyses of shallow parabolic arches

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