For this reason the need for a better knowledge of the deflections and stresses induced by thermal loads arose. Elevated thermal stresses at layer interfaces induce the origin of failure mechanisms such as the debonding of layers and the developing of longitudinal cracks. Thus, an accurate description of local stress fields in each layer becomes mandatory also in the first stages of the design. Most of the early works represent an attempt to include the effects of thermal loadings to the previous models for the elastic analysis of multilayered plates such as the Classical Laminate Theory (CLT), First Shear Deformation Theory (FSDT) or Higher-order Shear Deformation Theory (HSDT). Murakami [1] asserted the superiority of the layer-wise description of the unknowns since the intrinsic through-the-thickness variation of thermal loadings. Bhaskar and Varadan [2], Ali et al. [3] recently pointed out the importance of refined theories to handle thermal loadings accurately with respect to mechanical ones. An assessment of the theories for thermoelastic analysis of laminated structures has been given in [4]. Therefore, it appears clearly that appropriate structural modeling of multilayered plates are required to satisfy what was summarized by the Carrera [4] with the acronym -requirements. These are conditions on the displacement and stress fields. In particular, they take into account the so-called zig-zag form of the displacement field and the Interlaminar continuity for transverse stress field. On the basis of a unified formulation, recently Carrera [5] investigated the influence of the temperature profile through the thickness of the plate. The aim of that work has been to investigate the errors introduced with the usual assumption of a linear through the thickness profile of temperature. Indeed Tungikar and Rao [6] demonstrated, by solving the heat conduction problem, how for a thick anisotropic laminate the temperature profile shows a layerwise form differing considerably from the linear one. It is clear how the inhomogeneity in the material properties causes a sever layerwise distortion of the normal to the mid-surface for the moderately thick and thick beams [7]. In this work, a finite element model based on the unified formulation introduced by Carrera is proposed and applied. The possibility to develop both Equivalent Single Layer (ESL) and Layer Wise (LW) descriptions of the unknown and to consider up to fourth-order expansions along the thickness allows to compare and verify inside the same formulation several different theories. Two different profile of temperature have been compared on cross-ply simply supported plates: 1) the linear one 2) the actual profile obtained by solving the heat conduction problem. A complete range of thickness ratios have been considered in order to show how the transverse shear plays a even more significant role increasing the thickness of the plate. The accuracy of the present model has been verified comparing the results obtained with available exact solutions present in literature.

1

H. Murakami, "Assessment of plate theories for treating the thermomechanical response of layered plates", Composite Engineering, vol.3, no.2, pp.137-143, 1993. doi:10.1016/0961-9526(93)90038-L

2

K. Bhaskar, T.K. Varadan, J.S.M. Ali, "Thermoelastic Solution for Orthotropic and Anisotropic Composites Laminates", Composites Part B, vol. 27, pp. 415-420, 1986. doi:10.1016/1359-8368(96)00005-4

3

J.S.M. Ali, K. Bhaskar, T.K. Varadan, " new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates", Composite Structures, vol. 45, pp. 227-232, 1999. doi:10.1016/S0263-8223(99)00028-8

4

E. Carrera, "An assessment of mixed and classical theories for thermal stress analysis of orthotropic plates", Journal of Thermal Stresses, vol 23, pp 797-831, 2000. doi:10.1080/014957300750040096

5

E. Carrera, "Temperature Profile Influence on Layered Plates Response Considering Classical and Advanced Theories", American Institute of Aeronautics and Astronautics Journal, vol 40, pp 1885-1896, 2002. doi:10.2514/2.1868

6

V.B. Tungikar, K.M. Rao, "Three dimensional exact solution of thermal stresses in rectangular composite laminate", Composite Structures, vol.27, pp.419-430,1994. doi:10.1016/0263-8223(94)90268-2

7

Kapuria S., Dumir P.C., Ahmed A., "An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading", International Journal of Solids and Structures, vol.40, pp.6613-6631, 2003. doi:10.1016/j.ijsolstr.2003.08.014

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