Issue 30

D. Tumino et alii, Frattura ed Integrità Strutturale, 30 (2014) 317-326; DOI: 10.3221/IGF-ESIS.30.39 319 continuity of the matrix resin. The space between the corrugate and skin laminates is filled by PVC foam, whose main contribution is to strengthen the core GRP webs against buckling. The work provides an analytical formulation of the equivalent elastic constants of the homogenised model, which are also compared with those derived by a 3D FEM simulation of the elementary sandwich cell. The homogenised model has then been implemented in a typical shell element in ANSYS. Experimental tests have been performed on both beams and panels manufactured in-house by hand lay-up lamination. The beams have been tested in three point bending, along and perpendicular to the corrugation, in order to uncouple the relative bending stiffness. Specific loading conditions for the panels have also been implemented in order to reproduce pure torsional and coupled torsional-bending conditions. Results from all the experimental evaluations have matched very well the numerical predictions based on the homogenised model. A NALYTICAL MODEL OF HOMOGENISATION n Fig. 1 left, the geometry of the sandwich considered for the homogenisation is sketched. It can be noted that the core has a trapezoidal shape in the transversal section of the corrugated laminate, symmetric with respect to mid- plane of the sandwich and constant along x. Because of its geometry, the corrugated laminate has an intrinsic orthotropy, in fact in-plane and out-of-plane behaviour changes between x and y direction. Homogenisation can be obtained once the unit cell is defined: in Fig. 1 middle its transversal section is depicted. It represents the repeated element of the periodic structure of the corrugated core, under the assumption of indefinite length in x. In Fig. 1 right the equivalent homogenised cell is depicted: we can consider it as a portion of a thin plate subjected to small deformation which elastic constant must be equal to those of the unit cell with the corrugated core. These constants are: in-plane stiffness (E x , E y , G xy ), flexural stiffness (D x and D y ) and torsional stiffness (D xy ) and shear transversal stiffness (D Qx and D Qy ). The procedure exposed so far is the same as the one in [22] where some basic assumption were made: - Small deflections, - Elastic modulus of the equivalent plate in z is infinite, - Linear segments normal to the mid-plane remain linear but not necessarily normal to the mid-plane because of the shear effect, - Thickness of the skins small compared to the core, Under these assumptions, in [22] expressions of the elastic properties of the equivalent cell were derived from the geometric parameters of the unit cell of the corrugated sandwich, for isotropic materials and symmetric transversal section of the core. In the present work, the limitation of an isotropic material has been removed for both skin and core. Two assumptions were added to the ones previously cited and are: - Skins and core have the same layup, - The layup is symmetric. Procedure followed to obtain the expressions of the in-plane and out-of-plane stiffness is similar to the one in [22] but with the difference that, due to orthotropy of the laminate, the elastic constants of the material must be defined for the two directions x and y, in particular: E x , E y ,  xy and G xy . For purposes of the present work, only the out of plane equivalent properties are of interest. In-plane elastic stiffness were obtained too and are reported in Appendix for completeness but they don’t play any role in the simulation and tests of the following paragraphs. Flexural elastic stiffness are: 2 1 2 x x s x c D E t h E I   (1)     2 2 2 2 2 2 1 2 2 2 2 s c x y s y x s c xy yx s xy yx c xy y s t h I E E t h D E t h I t h I E t h            (2) where I c is the moment of inertia, per unit width, of the corrugation cross section with respect to its mid-plane, and ij  are flexural Poisson coefficients of the laminate. And for the torsional stiffness: 2 xy mxy s D G t h  (3) I