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International audience; This work deals with the problem of the optimum design of a sandwich panel. The design process is based on a general two-level optimisation strategy involving different scales: the meso-scale for both the unit cell of the core and the constitutive layer of the laminated skins and the macro-scale for the whole panel. Concerning the meso-scale of the honeycomb core, an appropriate model of the unit cell able to properly provide its effective elastic properties (to be used at the macro-scale) must be conceived. To this purpose, in this first paper, we present the numerical homogenisation technique as well as the related finite element model of the unit cell which makes use of solid elements instead of the usual shell ones. A numerical study to determine the effective properties of the honeycomb along with a comparison with existing models and a sensitive analysis in terms of the geometric parameters of the unit cell have been conducted. Numerical results show that shell-based models are no longer adapted to evaluate the core properties, mostly in the context of an optimisation procedure where the parameters of the unit cell can get values that go beyond the limits imposed by a 2D model.

A linear static analysis of composite beams is presented in this work. Simply supported, cross-ply laminated beams are examined. Beams with different values of length-to-thickness ratio subjected to bending loadings are considered. Carrera’s Unified Formulation is adopted to derive several hierarchical theories. The kinematic field is imposed above the cross-section via a N-order polynomials approximation of the displacements unknown variables. The governing equations and boundary conditions are variationally obtained through the Principle of Virtual Displacements. A closed form, Navier-type solution is adopted. Thanks to this formulation, quasi three-dimensional strain and stress fields can be obtained. Classical beam models, such as Euler–Bernoulli’s and Timoshenko’s, are obtained as particular cases. Results are validated in terms of accuracy and computational costs towards three-dimensional FE models implemented in the commercial code ANSYS. Numerical investigations show that good results are obtained as long as the appropriate expansion order is used.