Thermoelastic Analysis of Functionally Graded Structures Accounting for Non-Linear Through-the-Thickness Temperature Profiles

Functionally graded materials are attractive for hypersonic and re-entry vehicle structures because they can combine thermal resistance at the exposed surface with mechanical load-carrying capability in the colder region. In these applications, however, the thermoelastic response is strongly affected not only by the material gradation, but also by the temperature field assumed through the thickness. This work investigates this aspect by combining conduction-consistent thermal profiles with refined structural models based on the Carrera Unified Formulation. The formulation accounts for spatially varying material properties and nonlinear temperature distributions, thereby avoiding the limitations of prescribed linear thermal fields. The implementation is first assessed on a reference FGM beam benchmark involving a nonuniform thermal load and three-dimensional stress recovery. The approach is then applied to a hypersonic-relevant FGM plate subjected to severe through-the-thickness heating. The results show that the use of a nonlinear, conduction-based temperature profile can noticeably modify both the displacement field and the recovered stresses.