Thermal Buckling of Plates and Shells

Thornton, Earl A.

doi:10.1115/1.3120310

Cited by 170 publications

(55 citation statements)

References 62 publications

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“…Buckling and vibration of plates due to thermal loads play important roles in the design and analysis of aerospace, off-shore, under-water, nuclear, and electronic components/structures. Static and dynamic responses of plates and shells exposed to thermal environments have been reviewed by Tauchert [1] and Thorton [2]. Even though there have been extensive investigations on the thermal buckling of plates, the dynamic response of post-buckled circular plates has not been studied thoroughly.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Thermally Pre/Post-Buckled Circular Thin Plates Embedded with Shape Memory Alloy Fibers

Liu

Batra

2010

Journal of Thermal Stresses

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Axisymmetric deformations of a uniformly heated pre-buckled and post-buckled thin circular plate reinforced with shape memory alloy (SMA) fibers placed in the radial direction only are studied. Effects of von Kármán's nonlinearities are incorporated in the problem formulation. The matrix is assumed to be linear thermoelastic and the thermo-mechanical response of the SMA is modeled by one-dimensional constitutive relation. By assuming that plate's deflections can be additively decomposed into three parts, namely radial displacements of a pre-buckled plate, radial and lateral displacements during post-buckling deformations, and infinitesimal radial and lateral displacements during vibration of a post-buckled plate, boundary-value problems for determining these displacements for plate edges either simply supported or clamped have been formulated. The coupled nonlinear differential equations have been numerically solved by the shooting method that has been verified by good agreement between the presently computed results with those available in the literature. The dependence of the first three frequencies upon the temperature rise, for both pre-buckled and postbuckled plates, has been delineated. Characteristic curves relating the frequency with the temperature rise for different values of the volume fraction and the pre-strain in the SMA fibers are exhibited. It is found that reinforcement of an aluminum plate with SMA fibers changes plate's natural frequencies and enhances its resistance to buckling due to temperature rise.

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Section: Introductionmentioning

confidence: 99%

Free Vibration of Thermally Pre/Post-Buckled Circular Thin Plates Embedded with Shape Memory Alloy Fibers

Liu

Batra

2010

Journal of Thermal Stresses

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“…When T ≥ T cs , the buckled equilibria bifurcating from the trivial equilibrium through a pitchfork bifurcation are given by w(x, y) = ± (a/ h) 2 …”

Section: Post-buckling Analysis Of Linear-elastic Platementioning

confidence: 99%

“…Then the buckled equilibria are given by w(x, y) = ± (a/ h) 2 [16(1 + ν)α/(5π 2 )] T − 8 15 ×h sin(πx/a) sin(πy/a).…”

Section: Post-buckling Analysis When the Temperature Quasi-staticallymentioning

confidence: 99%

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Dynamic and buckling analysis of a thin elastic-plastic square plate in a uniform temperature field

Xiao

Chen

2005

ACTA MECH SINICA

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The nonlinear models of the elastic and elasticlinear strain-hardening square plates with four immovably simply-supported edges are established by employing Hamilton's Variational Principle in a uniform temperature field. The unilateral equilibrium equations satisfied by the plastically buckled equilibria are also established. Dynamics and stability of the elastic and plastic plates are investigated analytically and the buckled equilibria are investigated by employing Galerkin-Ritz's method. The vibration frequencies, the first critical temperature differences of instability or buckling, the elastically buckled equilibria and the extremes depending on the final loading temperature difference of the plastically buckled equillibria of the plate are obtained. The results indicate that the critical buckling value of the plastic plate is lower than its critical instability value and the critical value of its buckled equilibria turning back to the trivial equilibrium are higher than the value. However, three critical values of the elastic plate are equal. The unidirectional snap-through may occur both at the stress-strain boundary of elasticity and plasticity and at the initial stage of unloading of the plastic plate.

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“…Accordingly, static and dynamic responses of structures exposed to thermal environments have been studied by many investigators; e.g., see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Even though there are extensive investigations on the buckling of plates, there are very few works on the dynamic response of post-buckled configurations of plates buckled due to thermal loads.…”

Section: Introductionmentioning

confidence: 99%

Vibration of Thermally Post-Buckled Orthotropic Circular Plates

Liu

Batra

2006

Journal of Thermal Stresses

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Axisymmetric vibrations of a statically buckled polar orthotropic circular plate due to uniform temperature rise have been studied numerically. Effects of geometric nonlinearities have been incorporated into the problem formulation. The problem is challenging because the buckled configuration is unknown a priori. By assuming that the amplitude of plate's vibration and the additional strains induced in it are infinitesimal, and its response harmonic, the non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations; one for the thermal post-buckling, and the other for linear vibrations of the plate superimposed upon the post-buckled configuration. The plate's boundary is taken to be either clamped or simply supported but restrained from moving in the radial direction. The two sets of coupled boundary value problems are solved numerically by a shooting method. The dependence of the first three frequencies upon the temperature rise, for both pre-buckled and postbuckled plates, have been computed, and characteristic curves of the frequency versus temperature rise for different values of material anisotropy parameters are plotted. It is found that the three lowest frequencies of the pre-buckled plate decrease with an increase in the temperature, but those of a buckled plate increase monotonically with the temperature rise. The fundamental frequency of the deformed plate approaches zero at the onset of buckling.

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Thermal Buckling of Plates and Shells

Cited by 170 publications

References 62 publications

Free Vibration of Thermally Pre/Post-Buckled Circular Thin Plates Embedded with Shape Memory Alloy Fibers

Free Vibration of Thermally Pre/Post-Buckled Circular Thin Plates Embedded with Shape Memory Alloy Fibers

Dynamic and buckling analysis of a thin elastic-plastic square plate in a uniform temperature field

Vibration of Thermally Post-Buckled Orthotropic Circular Plates

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