Stroh-like formalism for Kirchhoff anisotropic thermoelastic plates

Xu Wang, Peter Schiavone

A Stroh-like formalism is developed for the heat conduction and the coupled stretching and bending deformations of a laminated anisotropic thermoelastic thin plate based on Kirchhoff theory. For the heat conduction problem, a Stroh-like quartic formalism is developed. Twodimensional generalized temperature and heat flux function vectors are introduced. The structure of the introduced 4×4 fundamental plate matrix for heat conduction is the same as that of the 8×8 fundamental elasticity matrix in the Stroh sextic formalism for generalized plane strain elasticity. Consequently, the orthogonality and closure relations for heat conduction in thin plates is established. For the thermoelastic problem, an inhomogeneous particular solution is derived rigorously. We obtain an octet formalism in which the general solution is composed of the well-known homogeneous solution developed by Cheng and Reddy (isothermal case) and the inhomogeneous particular solution arising from the thermal effect.