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.

Novel first and second order numerical differentiation techniques and their application to nonlinear analysis of Kirchhoff–Love shells

“…On the other hand, substituting x = x 0 + t(e i + e j ) in (25), one can also obtain that (27) being the Taylor expansion of y i j (t) around t = 0. Thus, the second-order derivative…”

“…IGA is based on interpolation spline functions (like, e.g., B-splines or NURBS), which make it possible to fulfil the continuity requirement easily, particularly suitable for problems which require haigh order derivatives. Isogemetric analysis has attracted the attention of many researchers in the context of different applications based on various mechanical models (see, e.g., [27,28,30,33,36,37]). Moreover, interesting industrial applications have been presented recently for the optimization of post-buckling behaviour of aeronautical specimens made of advanced composite materials in [19,34].…”

Direct Evaluation of the Sensitivity of the Nonlinear Critical Point to Geometrical Imperfections

“…The convergence of the gradient-based path to the minimum can be improved using a line search or the Globally convergent method of moving asymptotes (GCMMA) [6], with a multi-start approach [7] or deflation techniques to deal with multiple local minima.…”

A Koiter reduction technique for the nonlinear thermoelastic analysis of shell structures prone to buckling

“…55 Moreover, the reduction technique gives remarkable advantages in optimal design strategies of composite structures. 4,5,[56][57][58] The Koiter ROM can be also employed in standard incremental-iterative strategies as an accurate nonlinear predictor 59,60 followed by Newton's iterations on the full model. When the ROM accuracy decreases, a new one is constructed.…”

“…Recently, Koiter's method has been employed to analyze the postbucking behavior using a specialized hybrid‐Trefftz FE for composite structures 55 . Moreover, the reduction technique gives remarkable advantages in optimal design strategies of composite structures 4,5,56‐58 . The Koiter ROM can be also employed in standard incremental‐iterative strategies as an accurate nonlinear predictor 59,60 followed by Newton's iterations on the full model.…”