Optimal Design of CNT-Nanocomposite Nonlinear Shells

Abstract

Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generation lightweight structures in advanced applications due to the superior multifunctional properties combined with lightness. Here material optimization of carbon nanotube/polymer nanocomposite beams and shells is tackled via ad hoc nonlinear finite element schemes so as to control the loss of stability and overall nonlinear response. Three types of optimizations are considered: variable through-the-thickness volume fraction of random carbon nanotubes (CNTs) distributions, variable volume fraction of randomly oriented CNTs within the mid-surface, aligned CNTs with variable orientation with respect to the mid-surface. The collapse load, which includes both limit points and deformation thresholds, is chosen as the objective/cost function. An efficient computation of the cost function is carried out using the Koiter reduced order model obtained starting from an isogeometric solid-shell model to accurately describe the point-wise material distribution. The sensitivity to geometrical imperfections is also investigated. The optimization is carried out making use of the Global Convergent Method of Moving Asymptotes. The extensive numerical analyses show that varying the volume fraction distribution as well as the CNTs orientation can lead to significantly enhanced performances towards the loss of elastic stability making these lightweight structures more stable. The most striking result is that for curved shells, the unstable postbuckling response of the baseline material can be turned into a globally stable response maintaining the same amount of nanostructural reinforcement but simply tailoring strategically its distribution.

Keywords

• CNT nanocomposite shells
• post-buckling optimization
• composite optimal design
• Koiter method
• isogeometry
• NURBS interpolation