Thermo-mechanics of undamaged and damaged multilayered composite plates: a sub-laminates finite element approach

Abstract

In this work a plate mixed finite element based on a refined zig-zag plate model is formulated for the analysis of multilayered composite 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 σ33 supposed constant along the thickness and by the use of the complete constitutive 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.