Issue 30

D. Tumino et alii, Frattura ed Integrità Strutturale, 30 (2014) 317-326; DOI: 10.3221/IGF-ESIS.30.39 321 E x [GPa] E y [GPa] G xy [GPa]  xy p [mm] f [mm] h [mm] t s [mm] t c [mm] 10 17 1.85 0.1 80 14 24.2 1.11 0.96 Table 1 : Elastic properties of the laminate and geometric parameters of the sandwich. Results obtained from the three load and boundary configuration in Fig. 2 are given in terms of total reaction to an applied rotation (flexural or torsional). Each component of stiffness can be calculated by the ratio between the reaction calculated and the rotation. In Tab. 2, analytical results given by the proposed formulation in eq. (1,2,3) are compared with numerical results obtained with FEM with this procedure. D x [Nmm] D y [Nmm] D xy [Nmm] Analytical eq. (1,2,3) 4.26E6 5.61E6 1.20E6 Numerical FEM 4.39E6 5.88E6 1.15E6 Table 2 : Comparison between the analytical model and FEM method Numerical implementation of the analytical model The behavior of a sandwich structure with a corrugate core can be effectively numerically simulated by using suitable finite shell elements that implement the homogenized analytical model. In this way, an equivalent model of the real structure is obtained where only the mid-surface of the sandwich is considered. Advantages of this technique with respect to a full 3D model mainly consist in remarkable time saving in modeling and numerical computation. In the present work, the SHELL99 element of the ANSYS library has been used [39]. This element has eight nodes with six degrees of freedom each (three displacements and three rotations) and can be customized via the direct definition of its stiffness matrix D that relates the vector of moments M with the vector of curvatures k . This relation is expressed with the following expression: 11 12 13 12 22 23 13 23 33 0 1 1 0 1 1 0 0 2 yx x x xy yx xy yx x x x yx x y y y y xy yx xy yx xy xy xy xy D D M D D D k k D D M D D D k k M D D D k k D                                                                              (4) where coupling terms between flexural and torsional behaviour (D 13 and D 23 ) are null in a cross-ply layup [38] and where ij  are Poisson flexural coefficients of the whole sandwich, coming from Poisson coefficients of the laminate skins via these expressions [21]: xy xy    and y yx xy x D D    (5) Submatrices A and B of the complete formulation of the stiffness matrix of a laminate are not considered in this work because only out-of-plane behaviour are simulated and symmetrical layups are assumed. E XPERIMENTAL TESTS Preparation of samples orrugated core sandwich panels have been prepared using unidirectional glass fiber fabric (with 220 g/m 2 unit weight) and polyester resin. From a PVC panel (Klegecell® R45 by DIAB) several prismatic bars with trapezoidal section have been cut off. The presence of the PVC was due both for the manufacturing process and to reduce the possibility of local indentation of the sandwich. Sandwich has been assembled following this procedure (see also Fig. 4 left for a detailed view): stacking of glass fiber fabrics by hand layup to obtain the bottom skin, positioning of the PVC C