Transient Thermoelastic Deformations of a Thick Functionally Graded Plate

Qian, Linfang; Batra, R.C.

doi:10.1080/01495730490440145

Cited by 118 publications

(50 citation statements)

References 41 publications

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“…[6][7][8][9], where U 0 , the radial displacement of a point on the mid-surface of the prebuckled plate, is the solution of the following boundary-value problem [5]:…”

Section: Equations For Infinitesimal Deformations Superimposed Upon Amentioning

confidence: 99%

“…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%

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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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“…[6][7][8][9], where U 0 , the radial displacement of a point on the mid-surface of the prebuckled plate, is the solution of the following boundary-value problem [5]:…”

Section: Equations For Infinitesimal Deformations Superimposed Upon Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration of Thermally Post-Buckled Orthotropic Circular Plates

Liu

Batra

2006

Journal of Thermal Stresses

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“…It is a truly mesh-free approach in terms of both interpolation of variables and integration of energy because it does not require a background mesh to evaluate various integrals appearing in the local weak formulation of the problem. Recently, the MLPG method has successfully been employed in the thermomechanical analysis of FGCs [Qian and Ching 2004;Qian and Batra 2004;Sladek et al 2003;Ching and Yen 2005;Ching and Chen 2006]. Most of the theoretical investigations reported so far have not taken into account the temperature dependence for the material properties.…”

Section: Introductionmentioning

confidence: 99%

Thermal stress analysis of functionally graded composites with temperature-dependent material properties

Ching

Chen

2007

JOMMS

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Thermomechanical deformation of a functionally graded composite (FGC) in elevated temperature environments is investigated by the meshless local Petrov-Galerkin method. The FGC is modeled as a 2-D linearly elastic solid which consists of ceramic ZrO 2 and alloy Ti-6Al-4V with the volume fraction varying along a predefined direction. Unlike most investigations performed so far, temperature-dependent thermophysical and thermomechanical properties are considered for both constituents in this work. The effective material properties of the FGC are evaluated with the micromechanical models. An FGC hollow cylinder under an internal temperature change is first studied; the numerical results agree very well with those computed by the finite element method. The parametric studies with respect to different profiles of graded FGCs are performed for a clamped-clamped thick beam and a square plate with a central hole, respectively. It is found that inclusion of temperature dependence for the material properties has a great impact on thermomechanical response prediction for FGCs in elevated temperature environments.

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“…However, the latter is easier to implement in programming. The compatible theory has been used for analyzing static and dynamic deformations of isotropic homogeneous [5], functionally graded (FG) thick plates [8,9]. we can expect quadrature formulas of the above form be exact for polynomials of degree up to 21 n  .…”

Section: Introductionmentioning

confidence: 99%