A low-order mixed variational principle for the generalized Marguerre–von Kármán equations

Abstract

We propose a mixed variational principle for deducing the generalized Marguerre–von Karman equations, governing the relatively large deflections of thin elastic shallow shells. These equations account for both non-flat stress-free configurations of the shell and inelastic strains. We implement this formulation by using $$C^0$$ interior penalty methods within the UFL language provided by the FEniCS project. We present two numerical examples, with the aim to discuss the role of the shallowness and the inelastic strain, comparing the results with the fully non-linear shell model a la Naghdi and the classical displacement formulation.