Sensitivity in the structural behavior of shallow arches

Virgin, Lawrence N.; Wiebe, Richard; Spottswood, S. Michael; Eason, Thomas

doi:10.1016/j.ijnonlinmec.2013.10.003

Cited by 45 publications

(18 citation statements)

References 23 publications

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“…The buckling and postbuckling response of elastic arches has been, and continues to be, a subject of immense engineering importance, with a vast number of publications, studies and books involved. Within our limitations, not even a short overview of them can be given, but the reader may address the references of some indicative papers [1][2][3][4][5][6][7][8], as well as books [9][10][11][12][13][14] on the issue. To this end, we will limit ourselves to a general qualitative overview, and then focus on the problem dealt with herein.…”

Section: Short Overview On the Buckling Of Archesmentioning

confidence: 99%

05.41: A unified catastrophe theory approach for the in‐plane buckling of steel arches under point gravitational loading

Pantazi

Sophianopoulos

2017

ce papers

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The problem of the buckling response of various types of steel arches has been the subject of a vast number of earlier as well as recent papers and chapters of books. Namely, the majority of all these works aimed -via analytical and/or computational approaches -to establish the nature of the postbuckling response of the foregoing structures. It has been found over the years that two types of loss of in-plane stability are dominant: (a) snap-through, a characteristic of shallow (flat) arches (low height to span ratio), in a symmetric or asymmetric mode (limit point or bifurcation), and (b) sideways buckling (deep arches). In the latter situation, the axial inextensibility (being a justified simplifying assumption) becomes dominant and in the case of radial load and circular arch configuration the whole analysis is rather easy and convenient, using equilibrium considerations. On the other hand, low arches (with unavoidable shortening of their center line) can be thought of as curved beams; hence their buckling analysis may be performed from the viewpoint of energy. However, there not seems to be a unified approach overall, especially since the geometry of arches may be significantly varying, from circular to elliptical, parabolic, sinusoidal and catenary, and hence the height at the crown and the span are not the only parameters this geometry is dependent on. Moreover, if one considers a point gravitational loading acting on the arch, a case scarcely reported, then the whole analysis is multiparametric, since it involves (a) the value of the load and its position, (b) the cross-sectional and material characteristics and (c) the geometrical configuration parameters. This work aims to provide a unified approach for the foregoing problem based on the Theory of Catastrophes. The total potential energy function involving all the parameters is firstly established, and furthermore all restrictions related to boundary conditions, geometry, material and cross-sectional properties. Using an approximate 4 th order polynomial postbuckling shape, it was found that the problem at hand is governed by a singularity that strongly resembles the butterfly. The work is ongoing and will hopefully reveal interesting future results for structural design purposes.

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Section: Short Overview On the Buckling Of Archesmentioning

confidence: 99%

05.41: A unified catastrophe theory approach for the in‐plane buckling of steel arches under point gravitational loading

Pantazi

Sophianopoulos

2017

ce papers

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“…Considering equation (2.14a), we can estimate N as the following average value 18) where the average thermal axial forceÑ T can be calculated from equation (2.16a) as…”

Section: (B) Governing Equations Of Initially Curved Functionally Gramentioning

confidence: 99%

“…However, for the asymmetric bifurcation, the arch may exhibit one of the asymmetric deformations shown in figure 1b. Studies on the symmetric snap-through and asymmetric bifurcation of homogeneous macro/micro/nanobeams have been largely reported in the literature, and the influences of the initial arch rise, beam thickness, residual axial force, uniform temperature variation, size effect and surface effects have been systematically investigated [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Recently, functionally graded materials (FGMs) have been proposed to be used in MEMS [22,23] for their combined properties of improved stress distribution, enhanced thermal resistance and high fracture toughness [24,25].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

Chen¹,

Meguid²

2016

Proc. R. Soc. A.

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In this paper, we investigate the symmetric snapthrough buckling and the asymmetric bifurcation behaviours of an initially curved functionally graded material (FGM) microbeam subject to the electrostatic force and uniform/non-uniform temperature field. The beam model is developed in the framework of Euler-Bernoulli beam theory, accounting for the through-thickness power law variation of the beam material and the physical neutral plane. Based on the Galerkin decomposition method, the beam model is simplified as a 2 d.f. reduced-order model, from which the necessary snap-through and symmetry breaking criteria are derived. The results of our work reveal the significant effects of the power law index on the snap-through and symmetry breaking criteria. Our results also reveal that the non-uniform temperature field can actuate the FGM microbeam and induce the snap-through and asymmetric bifurcation behaviours.

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“…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. Chandra et al [9] have obtained experimental and computational results of the transient behavior of arches culled under harmonic distributed load, establishing the ranges of parameters that lead to snapthrough and chaotic responses.…”

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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Sensitivity in the structural behavior of shallow arches

Cited by 45 publications

References 23 publications

05.41: A unified catastrophe theory approach for the in‐plane buckling of steel arches under point gravitational loading

05.41: A unified catastrophe theory approach for the in‐plane buckling of steel arches under point gravitational loading

Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

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

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