Analysis of flexible elastic–plastic plates/shells behaviour under coupled mechanical/thermal fields and one-sided corrosion wear

Mathematical models of a non-linear shallow shell subjected to mechanical and temperature fields and one-sided corrosion wear are proposed. The governing equations are yielded by Hamilton’s principle. The geometric and physical non-linearity follow the Föppl–Kármán approximation and the plastic deformation theory, respectively. Dolinskii and Gutman corrosion models as well as the Duhamel–Neumann model are implemented. The governing mixed-type PDEs are derived. The algorithm to solve the PDEs is based on the method of variational iterations (MVI) and linearization. Convergence of the developed procedure is proved. Theoretical considerations are validated by numerical results. •Elastic–plastic shells under one sided corrosion are studied.•Temperature/mechanical fields are taken into account.•Governing mixed-type PDEs are derived.•Method of variational iterations is rigorously proved.•Numerous numerical results are provided.