Thermo-mechanics of undamaged and damaged multilayered composite plates: a sub-laminates finite element approach Marco Gherlone * , Marco Di Sciuva 1 Department of Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy Available online 18 September 2006 Abstract In this work a plate mixed finite element based on a refined zig-zag plate model is formulated for the analysis of multilayered com- posite plates subjected to thermal and mechanical loads. The zig-zag plate model is characterised by: (i) through-the-thickness cubic in- plane displacements and linear transverse displacement, (ii) transverse shear stresses continuity, (iii) satisfaction of traction equilibrium conditions on top and bottom faces of the laminate thus allowing for the presence of tangential distributed loads, (iv) the transverse normal deformability is taken into account by means of a r 33 supposed constant along the thickness and by the use of the complete con- stitutive equations of orthotropic materials, (v) use, as degrees of freedom of the model, of displacements and transverse shear stresses of external faces of the laminate. In particular, this last property may be extended to the associated plate finite element that, having its nodal degrees of freedom on the external faces, allows a through-the-thickness discretisation in some sub-domains called sub-laminates. Some numerical results are presented in order to show that the use of more sub-laminates improves the capability of the approach to capture with high accuracy the though-the-thickness distributions of transverse displacements, strains and stresses also for very thick plates. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Multilayered plates; Thermo-mechanics; Transverse deformability; Sub-laminates; Plate mixed finite element 1. Introduction Multilayered composite plates and shells are extensively used in the field of aeronautical, civil and marine engineer- ing due to their high specific stiffness and strength. The increasing use of composite components as primary struc- tural parts of more complex structures leads to the adop- tion of very thick panels and beams; high thick-to-side length ratios exacerbate some of the peculiar aspects of multilayered composite structures [1–5]: • transverse anisotropy: remarkable variations in the mechanical properties from layer to layer are, for exam- ple, typical of the more and more successful sandwich structures; transverse anisotropy leads to a more com- plex interaction among the different deformation modes (membrane, flexing, shear) of a composite structure and gives to the strain and stress states a more evident 3D nature; • high transverse deformability: typical composite materi- als (fibre reinforced plastics) exhibit shear moduli-to- in-plane moduli ratios that are lower than those of isotropic materials, thus, also for thin structures, the transverse shear deformability may be remarkable; also transverse normal deformability may be not negligible when thick laminates are considered; • damage sensibility: composite structures may experience damage as a consequence of operating conditions or manufacturing operations; in any case, due to the dis- continuous nature of a multilayered structure, the dam- age occurrence probability and the effects of damages on the load carrying capabilities of composite structures are issues of main importance; • load carrying capacity under environmental constraints: fibre reinforced plastics are particularly sensitive to the action of temperature variations, moisture, radiations; 0263-8223/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2006.08.004 * Corresponding author. Tel.: +39 0115646817; fax: +39 0115646899. E-mail addresses: marco.gherlone@polito.it (M. Gherlone), marco. disciuva@polito.it (M. Di Sciuva). 1 Tel.: +39 0115646808; fax: +39 0115646899. www.elsevier.com/locate/compstruct Composite Structures 81 (2007) 125–136