Localized loading and nonlinear instability and post-instability of fixed arches

Lu, Hanwen; Liu, Airong; Pi, Yong‐Lin; Bradford, Mark A.; Fu, Jiyang; Huang, Yonhui

doi:10.1016/j.tws.2018.06.019

Cited by 25 publications

(12 citation statements)

References 42 publications

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“…where w � w/R and v � v/R are defined as the dimensionless axial displacement and radial displacement, respectively. Substituting equations (10) and 11into equation (9) can be obtained as…”

Section: Differential Equations Of Equilibriummentioning

confidence: 99%

“…where v b and w b are the dimensionless radial and axial instability displacements, respectively. In order to perform an antisymmetric bifurcation instability analysis, secondorder terms of the strain (v ′ + w) 2 /2 need to be included in the strain of equation (10), which can be expressed as…”

Section: Instability Analysismentioning

confidence: 99%

“…In practical engineering, a fixed arch under a linear temperature gradient field and a uniformly distributed radial load caused by fire may lose its bearing capacity due to instability which has received concerns recently. Analytical investigations on the buckling of arches subject to a uniformly distributed radial load or a radial point load are extensive [1][2][3][4][5][6][7][8][9][10][11][12][13]. Besides the external load, arches may also be under temperature field.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

In‐Plane Instability of Fixed Arches under Linear Temperature Gradient Field and Uniformly Distributed Radial Load

Song

Liu

et al. 2019

Mathematical Problems in Engineering

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This paper focuses on an in-plane instability analysis of fixed arches under a linear temperature gradient field and a uniformly distributed radial load, which has not been reported in the literature. Combining a linear temperature gradient field and uniformly distributed radial load leads to the changes in axial expansion and curvature of arches, producing the complex in-plane nonuniform bending moment and axial force. Therefore, it is necessary to explore the in-plane thermoelastic mechanism behavior of fixed arches under a linear temperature gradient field and a uniformly distributed radial load in the in-plane instability analysis. Based on the energy method and the exact solutions of internal force before instability, the analytical solutions of the critical uniformly distributed radial load considering the linear temperature gradient field associated with in-plane thermoelastic instability of arches are derived. Comparisons show that agreements of analytical solutions against FE (finite element) results are excellent. Influences of various factors on in-plane instability are also studied. It is found that the change of the linear temperature gradient field has significant influences on the in-plane instability load. The in-plane instability load decreases as the temperature differential of the linear temperature gradient field increases.

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Section: Differential Equations Of Equilibriummentioning

confidence: 99%

Section: Instability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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In‐Plane Instability of Fixed Arches under Linear Temperature Gradient Field and Uniformly Distributed Radial Load

Song

Liu

et al. 2019

Mathematical Problems in Engineering

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“…(Pi et al, 2017) revealed in-plane buckling of fixed shallow circular arches with the arbitrary radial point load. (Lu et al, 2018) explored the nonlinear in-plane buckling and post-buckling behavior of the fixed arches subjected to a localized uniform radial load. (Lu et al, 2020) also explored effects of movement and rotation of supports on nonlinear instability of fixed shallow arches under a localized uniform radial load.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Buckling of Fixed Functionally Graded Material Arches Under a Locally Uniformly Distributed Radial Load

Zhou

Yang

et al. 2021

Front. Mater.

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Functionally graded material (FGM) arches may be subjected to a locally radial load and have different material distributions leading to different nonlinear in-plane buckling behavior. Little studies is presented about effects of the type of material distributions on the nonlinear in-plane buckling of FGM arches under a locally radial load in the literature insofar. This paper focuses on investigating the nonlinear in-plane buckling behavior of fixed FGM arches under a locally uniformly distributed radial load and incorporating effects of the type of material distributions. New theoretical solutions for the limit point buckling load and bifurcation buckling loads and nonlinear equilibrium path of the fixed FGM arches under a locally uniformly distributed radial load that are subjected to three different types of material distributions are derived. The comparisons between theoretical and ANSYS results indicate that the theoretical solutions are accurate. In addition, the critical modified geometric slendernesses of FGM arches related to the switches of buckling modes are also derived. It is found that the type of material distributions of the fixed FGM arches affects the limit point buckling loads and bifurcation buckling loads as well as the nonlinear equilibrium path significantly. It is also found that the limit point buckling load and bifurcation buckling load increase with an increase of the modified geometric slenderness, the localized parameter and the proportional coefficient of homogeneous ceramic layer as well as a decrease of the power-law index p of material distributions of the FGM arches.

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“…For example, Pi et al. 9–13 comprehensively studied the shallow circular arch's static deformation under uniform radial pressure, central concentrated force, localized radial loading and considered the boundary conditions including pinned, fixed, rotationally restrained BCs. Cai and Feng 14–17 analyzed the in-plane elastic stability of shallow arch of parabolic shape considering the rotational restraint which is depending on the axial force 14 and temperature variations.…”

Section: Introductionmentioning

confidence: 99%

Static and dynamic symmetric snap-through of non-uniform shallow arch under a pair of end moments considering critical slowing-down effect

Yan

Shen

Jin

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper presents analytical analysis of static and dynamic symmetric snap-through of non-uniform shallow circular shallow arch under a pair of end moments with the same magnitude. The non-uniformity is characterized by dividing the arch into three piecewise constant-stiffness segments. Hamilton's principle is used to derive the governing differential equations by assuming negligible axial inertia. The snap-through load and snap-through criterion are analyzed in detail and by an index plot, the stiffer center case is shown to behave distinctly when stiffer end case is compared. The dynamic snap-through when the moment is slightly higher than the snap-through moment is analyzed analytically by a perturbation method, and a critical slowing effect is observed when the moment is approaching to the snap-through moment. Comparison with dynamic FEA shows a good agreement with the analytical result and analysis on theoretical finite time blow-up phenomenon reveals that when geometric parameters are corresponding to the critical snap-through condition, the initial quadratic phase's motion is slow and relatively blow-up phase's motion is fast. The analytical formulations have been extended to include two limiting cases including rigid end case and rigid center case by using the constrained Hamilton's principle by Lagrangian multipliers. Snap-through criteria analysis reveals closed-form criterion for rigid center case and an asymptotic result for rigid end case. This paper serves to enhance the knowledge on snap-through and critical slowing down for shallow arches with non-uniformity under end moments.

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Localized loading and nonlinear instability and post-instability of fixed arches

Cited by 25 publications

References 42 publications

In‐Plane Instability of Fixed Arches under Linear Temperature Gradient Field and Uniformly Distributed Radial Load

In‐Plane Instability of Fixed Arches under Linear Temperature Gradient Field and Uniformly Distributed Radial Load

Nonlinear Buckling of Fixed Functionally Graded Material Arches Under a Locally Uniformly Distributed Radial Load

Static and dynamic symmetric snap-through of non-uniform shallow arch under a pair of end moments considering critical slowing-down effect

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