A Linear,First-order Shell Model for Transverse Isotropic Material under a Uniform Change of Temperature

A first-order shell model is derived for describing the behaviour of a thin, arbitrarily curved structure made from homogeneous, transverse isotropic material under the influence of a uniform change of temperature. Transverse isotorpy means that the elastic behaviour and the thermal expansion is isotropic in in-plane directions but different in thickness direction. The influence of the different thermal expansion is incorporated by equivalent stress couples and bending moments. Thus, a higher-order approximation in thickness direction is not necessary. However, the so-called ‘second approximation of shell theory’ must be used which deals with more accurate constitutive relations than the standard theory. Further the question is investigated in which cases a stress-free transverse isotropic thermal deformation exists.