A heat mixed variational theorem for thermoelastic multilayered composites

This paper presents for thermoelastic media the analogue of the Reissner’s mixed variational theorem (RMVT), initially developed for elastic media, by adding the transverse thermal field–temperature increment relation as a constraint via a Lagrange multiplier. The latter is shown to be the transverse (normal) heat flux, which continuity at the laminated composite interfaces can now be fulfilled in a natural way as is the case for transverse stresses in the RMVT. Hence, the resulting new heat mixed variational theorem (HMVT) will be well suited for modelling thermoelastic layered composites. Mixed coupled thermoelastic constitutive equations to be used in conjunction with the HMVT are also presented. Finally, discussions are made on the application of the HMVT to the quasi-static and steady-state classical cases leading to uncoupled heat transfer and thermal-stress analyses.