Fast approximations of dynamic stability boundaries of slender curved structures

Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, Michael

doi:10.1016/j.ijnonlinmec.2017.06.002

Cited by 7 publications

(3 citation statements)

References 67 publications

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“…For these higher dimension responses, the higher modes corresponding to the unstable equilibria of the system become quite relevant. The increased number of critical points was also correlated with an increase in the likelihood of chaotic responses [47] and with significantly less well defined snap-through boundaries [48].…”

Section: Perfect Parabolic Archesmentioning

confidence: 99%

A general condition for the existence of unconnected equilibria for symmetric arches

Zhou

Stanciulescu

2018

International Journal of Non-Linear Mechanics

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This paper presents a semi-analytical study of unconnected equilibrium states for symmetric curved beams. Using the Fourier series approximation, a general condition for the existence of unconnected equilibria for symmetric shallow arches is derived for the first time. With this derived condition, we can directly determine whether or not a shallow arch with specific initial configuration and external load has remote unconnected equilibria. These unconnected equilibria can not be obtained in experiments or nonlinear finite element simulations without performing a proper perturbation first. The derived general condition is then applied to curved beams with different initial shapes and external loads. It is found that initially symmetric parabolic arches under a uniformly distributed vertical force can have multiple groups of unconnected equilibria, depending on the initial rise of the structure. However, small symmetric geometric deviations are required for parabolic arches under a central point load, and half-sine arches under a central point load or a uniformly distributed load to have unconnected equilibria. The validity of the analytical derivations of the nonlinear equilibrium solutions and the general condition for the existence of unconnected equilibria are verified by nonlinear finite element methods.

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Section: Perfect Parabolic Archesmentioning

confidence: 99%

A general condition for the existence of unconnected equilibria for symmetric arches

Zhou

Stanciulescu

2018

International Journal of Non-Linear Mechanics

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“…Therefore, it is necessary to identify the dynamic stability limits that separate small amplitude responses from those occurring in the postcritical region. The dynamic snapthrough behavior is a strongly nonlinear phenomenon that generally has no analytical solution [3].…”

Section: Introductionmentioning

confidence: 99%

“…Zhou et al [3] proposed a scaling approach to highlight similarities between dynamic snap-through behavior in different thin-curved structures using variations between geometric and/or boundary conditions for fast dynamic stability limits approximations. Rosas [4] conducted studies on a sine-shaped sine-arch subjected to uniformly distributed loading, considering support conditions as discrete rotational springs.…”

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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Mathematical model of deformation of orthotropic shell structures under dynamic loading with transverse shears

Semenov

2019

Computers & Structures

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Fast approximations of dynamic stability boundaries of slender curved structures

Cited by 7 publications

References 67 publications

A general condition for the existence of unconnected equilibria for symmetric arches

A general condition for the existence of unconnected equilibria for symmetric arches

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

Mathematical model of deformation of orthotropic shell structures under dynamic loading with transverse shears

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