Thermoelasticity of Heterogeneous Aeolotropic Plates

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Abstract
A general thermoelastic theory for thin aeolotropic plates that are heterogeneous in the thickness direction may be formulated in terms of two simultaneous equations for the transverse deflection, w, and the Airy stress function, F. From these equations, thermal coupling terms appear, in addition to the interaction of stretching and bending. Applying the theory to the case of uniform heating of long rectangular heterogeneous plates yields explicit equations for the transverse deflection, the in-plane forces, and couples that arise in a uniformly heated plate. A cross-thermoelastic phenomenon is exemplified in the stress-resultants and couples relations. The linear theory may be extended to include finite deflections. The pre-thermal and post-thermal buckling states, in a heterogeneous plate, require the simultaneous determination of w and F.

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