One of the defining properties of thin shell problems is that the solution can be viewed as a linear combination of local features, each with its own characteristic thickness-dependent length scale. For perforated shells it is thus possible that for the given dimensionless thickness, the local features dominate, and the problem of deriving effective material parameters becomes ill-posed. In the general case, one has to account for many different aspects of the problem that directly affect the effective material parameters. Through a computational study we derive a conjecture for the admissible thickness-ranges. The effective material parameters are derived with a minimisation process over a set of feasible instances. The efficacy of the conjecture and the minimisation process is demonstrated with an extensive set of numerical experiments.
Giani, S., & Hakula, H. (2020). On Effective Material Parameters of Thin Perforated Shells under Static Loading. Computer Methods in Applied Mechanics and Engineering, 367, Article 113094. https://doi.org/10.1016/j.cma.2020.113094