Comparison of dual-mixed h- and p-version finite element models for axisymmetric problems of cylindrical shells

Dimensionally reduced cylindrical shell models using complementary energy-based variational formulations of a priori non-symmetric stresses are compared. One of them is based on the three-field dual-mixed Hellinger–Reissner variational principle, the fundamental variables of which are the stress tensor, the rotation and displacement vectors. The other one is derived from the two-field dual-mixed Fraeijs de Veubeke variational principle in terms of the self-equilibrated stress field and rotations. The most characteristic properties of the shell models are that the kinematical hypotheses used in the classical shell theories are not applied and the unmodified three-dimensional constitutive equations are employed. Our investigations are restricted to the axisymmetric case. The developed dual-mixed hp finite element models with C0 continuous tractions and with discontinuous rotations and displacements are presented for bending–shearing (including tension–compression) problems. The computational performance of the constructed shell elements is compared through two representative model problems. It is numerically proven that no significant differences can be experienced between the two well-performing shell elements in the convergence rates.

► Two cylindrical shell models using complementary energy-based variational principles are compared.
► One of them is based on the dual-mixed Hellinger–Reissner principle of stresses, rotations and displacements.
► The other one is deduced from the Fraeijs de Veubeke principle of the self-equilibrated stress field and rotations.
► The kinematical hypotheses used in the classical shell theories are not applied.
► hp finite elements with C0 continuous surface tractions and discontinuous rotations and displacements are presented and compared.