Postbuckling Analysis of Variable Stiffness Laminates via R-Function Method
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Over the past years, innovative variable stiffness (VS) laminates, in which the fibers can vary their orientation as a function of the planar position, have received increasing attention due to the improved thermo-mechanical response. These VS laminates are associated to a larger number of degrees of freedom. Fast formulations based on the Ritz method are nowadays available, however one typical restriction regards the shape of the domain. More advanced formulations are thus needed to explore the potential of the elastic tailoring of VS laminates in the postbuckling field. In fact, complex domains are typically characterized by undesired load concentrations, e.g. in correspondence of cut-outs, that can lead to structural damages. In this context, the potential of VS laminates can be exploited to achieve a better shaping of the stiffness distribution and to redirect the load path in presence of these load concentrations. To overcome the above mentioned issues, a semi-analytical formulation is presented, based on the Ritz-method and the R-functions theory. R-functions are here used to represent the panel geometry and to enforce the boundary conditions. Any complex domain can be obtained as the composition of primitive geometries. In addition, the R-functions are exploited to build the boundary functions for the Ritz approximation. Any set of boundary and thermo-mechanical loading conditions can be considered. Starting from the approach developed in, this work exploits the R-functions theory to investigate the potential given by the elastic tailoring of VS laminates in the postbuckling regime. Aiming at assessing the potential of the so-obtained tool, several test cases are presented and compared to commercial finite element simulations. In addition, parametric studies are conducted on the fibers’ path to achieve better load redistributions in the postbuckling field. Overall, the present method shows an improved ability to explore complex panel configurations with reduced computational time.