Transformed function representations of plane solutions for anisotropic elasticity and thermoelasticity

Abstract

Abstract A generalized two-dimensional deformation of an anisotropic elastic solid is considered. The transformed function method is employed to remove the breakdown limitation of the Stroh formalism for a degenerate anisotropic solid with multiple characteristic roots. The anisotropic elastic formalism for a general solution of elastic fields does not breakdown, and the closed form expressions of elastic fields for the degenerate anisotropic materials are obtained. A general solution of the thermoelastic fields in an anisotropic material under steady-state heat conduction is also derived. The thermoelastic formalism is shown to be valid for an anisotropic solid with distinct thermoelastic characteristic roots and a degenerate anisotropic solid with multiple thermoelastic characteristic roots.