A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties

Abstract

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 di erent 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 e ective elastic properties (to be used at the macro-scale) must be conceived. To this purpose, in this rst paper, we present the numerical homogenisation technique as well as the related nite element model of the unit cell which makes use of solid elements instead of the usual shell ones. A numerical study to determine the e ective 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.

Numerical study on thermal buckling of CFRP–Al honeycomb sandwich composites based on homogenization–localization analysis

“…Catapano and Montemurro [6] developed an optimization strategy for the design of sandwich panels. In the study, the equivalent properties of the hexagonal core were calculated through homogenization analysis based on the averaging scheme [7]. The obtained properties were in a good agreement with analytical results in provided by [8].…”

Effective elastic properties of periodic hexagonal honeycombs

“…Therefore, some researchers have used numerical approaches (e.g. FE based) to better understand and predict the elastic behaviour of honeycombs (Chamis et al, 1988;Grediac, 1993;Silva et al, 1995;Vougiouka et al, 1998;Guo and Gibson, 1999;Meraghni et al, 1999;Hohe and Becker, 2001;Chen, 2011;Catapano and Montemurro, 2014a). However, only few of them (Vougiouka et al, 1998;Hohe and Becker, 2001;Chen, 2011;Catapano and Montemurro, 2014a), have actually attempted to predict all the elastic constants for generally orthotropic honeycombs and compare them with available analytical estimates or experimental data.…”

“…FE based) to better understand and predict the elastic behaviour of honeycombs (Chamis et al, 1988;Grediac, 1993;Silva et al, 1995;Vougiouka et al, 1998;Guo and Gibson, 1999;Meraghni et al, 1999;Hohe and Becker, 2001;Chen, 2011;Catapano and Montemurro, 2014a). However, only few of them (Vougiouka et al, 1998;Hohe and Becker, 2001;Chen, 2011;Catapano and Montemurro, 2014a), have actually attempted to predict all the elastic constants for generally orthotropic honeycombs and compare them with available analytical estimates or experimental data. Most researchers, employed shell (Chamis et al, 1988;Grediac, 1993;Vougiouka et al, 1998;Meraghni et al, 1999;Hohe and Becker, 2001;Chen, 2011) or beam (Silva et al, 1995;Guo and Gibson, 1999) elements for their numerical models.…”

“…Moreover, most shell elements have limitations in capturing the true variation of normal and shear stresses through the shell thickness. As pointed out by Catapano and Montemurro (2014a), this makes the validity of these numerical models questionable, especially for honeycombs with thick cell walls.…”

A New Paradigm for the Optimum Design of Variable Angle Tow Laminates

“…The authors and their co-workers already made use of the MS2L procedure for the design and optimisation of several classes of hybrid anisotropic structures in the past [4,5,6,17,18,19,20,25]. The MS2L design strategy employed in the previous works is a very general methodology for designing composites structures: it is characterised on the one hand by the refusal of the simplifying hypotheses and classical rules usually employed in the framework of the design process of laminates, and on the other hand by a proper and complete mathematical formalisation of the optimum design problem at each characteristic scale (micro-meso-macro).…”