Postbuckling Analysis of Slender Elastic Rods Subjected to Uniform Thermal Loads

Vaz, Murilo Augusto; Solano, Rafael Familiar

doi:10.1080/01495730306293

Cited by 31 publications

(13 citation statements)

References 12 publications

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“…By accurately considering the axial extension, Conffin and Bloom [1] first presented an elliptic integral solution for the hygrothermal postbuckling response of a linear-elastic beam with two ends pinned. By taking into account of a nonlinear thermal straintemperature relation, Vaz and Solano [2][3] investigated postbuckling deformations of pinnedpinned rods and presented a closed-form solution via uncoupled elliptic integrals, in which an axial elastic support at the end was considered. Based on the accurate consideration for the axial extension, Li and Cheng [4] , Li et al [5] , and Li and Batra [6] geometrically developed the nonlinear governing equations of the Euler-Bernoulli beams in terms of seven basic unknowns including the displacements of the axial line, the rotational angle of the cross section, and the internal resultant forces.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, more attention has been paid on the research of the thermal postbuckling and vibration in the vicinity of the postbuckling configurations of elastic beams/rods subjected to thermal loadings [1][2][3][4][5][6][7][8] . By accurately considering the axial extension, Conffin and Bloom [1] first presented an elliptic integral solution for the hygrothermal postbuckling response of a linear-elastic beam with two ends pinned.…”

Section: Introductionmentioning

confidence: 99%

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Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Liu

Chang-jun

2009

Appl. Math. Mech.-Engl. Ed.

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Free vibration of statically thermal postbuckled functionally graded material (FGM) beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electromechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Liu

Chang-jun

2009

Appl. Math. Mech.-Engl. Ed.

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“…Using a shooting method in conjunction with the concept of analytical continuation, the nonlinear boundaryvalue problem consisting of nonlinear ordinary differential equations was numerically solved. Finally, Vaz and Solano [17] developed a closed-form analytical 368 M. A. VAZ AND R. F. SOLANO solution via uncoupled elliptical integrals for the postbuckling analysis of slender elastic rods subjected to uniform thermal loads with nonmovable hinged ends, where the thermal strain-temperature relationship was considered nonlinear.…”

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confidence: 99%

Thermal Postbuckling of Slender Elastic Rods With Hinged Ends Constrained by a Linear Spring

Vaz¹,

Solano²

2004

Journal of Thermal Stresses

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“…These techniques have only recently been extended to the solution of thermal and snap-through problems [15,16,17]. This is most likely due to the increased ease of solving the equations numerically, e.g., by shooting methods [18,19].…”

Section: Introductionmentioning

confidence: 99%

A lower bound on snap-through instability of curved beams under thermomechanical loads

Stanciulescu

Mitchell

Chandra

et al. 2012

International Journal of Non-Linear Mechanics

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A nonlinear finite element formulation (three dimensional continuum elements) is implemented and used for modeling dynamic snap-through in beams with initial curvature. We identify a nontrivial (nonflat) configuration of the beam at a critical temperature value below which the beam will no longer experience snap-through under any magnitude of applied quasistatic loadfor beams with various curvatures. The critical temperature is shown to successfully eliminate snap-through in dynamic simulations at quasistatic loading rates. Thermomechanical coupling is included in order to model a physically minimal amount of damping in the system, and the resulting post-snap vibrations are shown to be thermoelastically damped. We propose a test to determine the critical snap-free temperature for members * Corresponding author. Tel.: +1713 348 4704; fax: +1713 348 5268. of general geometry and loading pattern; the analogy between mechanical prestress and thermal strain that holds between the static and dynamic simulations is used to suggest a simple method for reducing the vulnerability of thin-walled structural members to dynamic snap-through in members of large initial curvature via the introduction of initial pretension.

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Postbuckling Analysis of Slender Elastic Rods Subjected to Uniform Thermal Loads

Cited by 31 publications

References 12 publications

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Thermal Postbuckling of Slender Elastic Rods With Hinged Ends Constrained by a Linear Spring

A lower bound on snap-through instability of curved beams under thermomechanical loads

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