Higher-order zig-zag model for analysis of thick composite beams with inclusion of transverse normal stress and sublaminates approximations

C0 Layerwise Model with Fixed Degrees of Freedom and Variable In- and Out-of-Plane Kinematics by Strain Energy Updating Technique

“…It is reminded that in [55] this model has been already proven to be accurate and computationally efficient when closed form solutions are considered, since it achieves the accuracy of layerwise models with just five d.o.f. Therefore, the aim of present numerical results is neither that of: a) discussing the advantages of the zigzag modeling approach here used, nor discussing the advantages offered by its variable kinematics, as both aspects have been already comprehensively overviewed in [43,[51][52][53][54][55][56]; b) nor discussing the relative merits of a physically-based zigzag representation like the present one over the Murakami's zigzag function just based upon kinematic assumptions, because both modeling options have been already compared and extensively discussed in [17]; c) finally, nor comparing the available displacement-based and mixed theories incorporating zigzag functions to other existing models and nor to discuss their fidelity to 3D exact elasticity or finite element solutions, since assessments were already given among many others in the references quoted in [17] that have shown their value.…”

“…The damage is simulated reducing the elastic moduli, according to the ply discount theory. Simply-supported, sandwich beams with damaged faces and/or core, undergoing sinusoidal transverse loading are considered and, in addition, the damage is assumed to be distributed over the entire length, because in this case the exact elasticity solution can be still found [43] and used for comparisons. Owing to the reduction of elastic moduli used for simulating the damage rise, intricate through-the-thickness distributions of out-of-plane stresses take place as a consequence of asymmetric, distinctly different properties, which make the samples considered a very severe test case for the models.…”

“…Sublaminate models (SBZZ) that combine the concepts of zigzag and discrete-layer models have been recently developed by Averill and coworkers [41,42], Icardi [43] and Gherlone and Di Sciuva [44] having kinematic variables at the top and bottom surfaces of computational layers as functional d.o.f., instead of classical mid-plane variables. With these models, the analysis can be carried out using a single computational layer, stacking several computational layers or even subdividing a physical layer into one or more computational layers.…”

“…Because the transverse normal stress has a significant bearing for keeping equilibrium when temperature gradients across the thickness cause thermal stresses and when describing the core's crushing behavior of sandwiches, Icardi and coworkers [43,[51][52][53][54][55][56][57][58][59] incorporated into zigzag models a variable kinematic representation of displacements across the thickness that can adapt to the variation of solutions, where a progressively refined description of the piecewise variation of the transverse displacement was also considered. Accordingly, the representation can be refined like with discrete layer models, though the functional d.o.f.…”

“…Because the enforcement of the physical constraints is satisfied without increasing the number of unknowns, accurate results are obtained with a computational effort not considerably larger than for equivalent single-layer models, thus considerably lower than for the available discrete-layer and high-order layerwise models, as shown in [55][56][57][58][59] and also by the results reported hereafter, where the processing time by the present model is compared to that by the first-order shear deformation theory-FSDPT. In many sample cases [43,[51][52][53][54][55][56], a successful application to variable stiffness composites was shown, which proven the progressively refined "adaptive" zigzag models based on enforcement of physical conditions suited to find solutions in closed form of static and dynamic cases. i.e., natural frequencies, low velocity impact and blast pulse loading using overall trial functions, i.e., Galerkin's and Rayleigh-Ritz's methods.…”