Large thermal deflections of Timoshenko beams under transversely non-uniform temperature rise

Liu, Shirong; Song, Xi

doi:10.1016/j.mechrescom.2005.06.004

Cited by 32 publications

(13 citation statements)

References 8 publications

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“…The coupled non-linear ordinary di erential equations were numerically solved by the shooting method. The work has been extended to Timoshenko beams [4,5] subjected to thermomechanical loads.…”

Section: Introductionmentioning

confidence: 99%

Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation

Sun

Liu

Batra

2016

Journal of Thermal Stresses

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Buckling and post-buckling thermomechanical deformations of a functionally graded material (FGM) Timoshenko beam resting on a two-parameter nonlinear elastic foundation and subjected to only a temperature rise have been numerically investigated with the shooting method. The material properties are assumed to vary only in the thickness direction according to a power law function. Through-the-thickness temperature distribution is determined by numerically solving the one-dimensional heat conduction equation. Geometric non-linearities in the strain-displacement relations and the non-linear traction-displacement relations at the interface between the beam and the foundation are considered. For clamped-clamped and immovable simply supported beams, critical values of the ratio of temperatures of the top and the bottom surfaces of the beam for transitions in buckling modes to occur are determined. Post-buckled equilibrium paths and con gurations of the heated FGM beam are illustrated for di erent values of the elastic foundation sti ness parameters, exponent in the power law variation of material properties and the slenderness ratio. Results for the Timoshenko beam are compared with those of the corresponding homogeneous Euler-Bernoulli beam available in the literature. ARTICLE HISTORY

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Section: Introductionmentioning

confidence: 99%

Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation

Sun

Liu

Batra

2016

Journal of Thermal Stresses

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“…If shear deformation is further taken into account, the classical linear Timoshenko beam theory accounts for the above phenomena. For large deflection analysis based on the Timoshenko beam theory, Li and Song [26] solved large thermal deflections of Timoshenko beams under transverse non-uniform temperature rise. Mohyeddin and Fereidoon [27] formulated a method for calculating large deflections of a beam under three-point bending.…”

Section: Introductionmentioning

confidence: 99%

Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending

2016

Comptes Rendus. Mécanique

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Three-point bending of a beam is studied based on the Timoshenko beam theory. Large deflection and large rotation of a beam resting on simple supports with friction are calculated for a concentrated force acting at the midspan. Using the Lagrangian kinematic relations, a system of non-linear differential equations are obtained for a prismatic sheardeformable Timoshenko beam. Exact solutions for the deflection, horizontal displacement, and rotation of cross-section are derived analytically. Two deflections of small and large scale exist under three-point bending. The solutions corresponding to linearized model coincide with the well-known solutions to the classical Timoshenko beams. Numerical calculations are carried out to show the effect of the important parameters such as shear rigidity of the beam and the coefficient of friction at the contact position between the beam and supports on the deflection. The load-deflection curves are graphically presented. A comparison of large deflections and large rotations with their classical counterparts and with experimental data is made. The obtained results are useful in safety design of linear and non-linear beams subject to three-point bending.

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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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Large thermal deflections of Timoshenko beams under transversely non-uniform temperature rise

Cited by 32 publications

References 8 publications

Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation

Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation

Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending

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

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