Bio-inspired cellular nanocomposite shells: stability analysis

The pressing global issues of climate change, sustainability, and energy efficiency spark an urgent demand for resilient lightweight structures. Consequently, porous cellular materials have emerged as a promising category of lightweight materials, capable of concurrently meeting various requirements, ranging from structural stiffness to thermal insulation. While the majority of metal foam studies focus on random porosity, recent research actively pursues economic multi-functionality through precise control of pore size and density. This approach draws inspiration from bio-inspired functionally graded materials, which prioritises gradual transitions, observed in the intriguing instances of squid beaks and varying bone porosity. Consequently, this paradigm has given rise to novel continuously graded porous (CGP) metal foam structures. Building upon these concepts, this paper introduces an innovative numerical model to analyse the buckling behaviour of bio-inspired CGP nanocomposite cylindrical shells. An effective constitutive law for an elastic isotropic metal matrix containing distributed elastic carbon-nanotubes (CNTs) is estimated, considering CNTs agglomeration through an Eshelby-Mori-Tanaka (EMT) approach. Unlike conventional methods, Euler-Bernoulli beams model stiffeners within CGP shells for a more realistic representation of stiffener effects. Equilibrium equations based on Reddy’s higher-order shell theory are derived using the Euler equation, and stability equations are obtained through the variational method. The stability equations were solved employing the generalised differential quadrature and Levy techniques. The intricate interplay between CNTs and porosity distributions significantly affects the stability behaviour of CGP shells. These findings offer valuable insights for designing closed-cell cellular stiffened shells with optimal porosity to improve buckling stability