Abstract
The problem of deducing two-dimensional theory from three-dimensional theory for a thermoelastic isotropic body is investigated. Based on thermoelasticity theory, the refined plate theory is derived by using Biot's solution of thermoelasticity and Lur'e method without ad hoc assumptions. For the homogeneous boundary conditions, the exact equations and solutions are derived and the equations can be decomposed into four governing differential equations: the biharmonic equation, the shear equation, the transcendental equation and the temperature equation. Moreover, the approximate equations and solutions for the plate under anti-symmetrical transverse loadings and temperature distribution are derived directly from the refined plate theory. By omitting coupling effect and higher-order terms, the refined plate theory can be degenerated into other well-known elastic and thermoelastic theoretical models.
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