An algorithm of a family of 3D-based, solid-to-shell transition, hpq/hp-adaptive finite elements

The basic information on an algorithm of a family of new triangular-prism, 3D-based, hpq/hp-adaptive, solid-to-shell transition finite elements has been presented in the paper, where h, p and q denote an averaged size as well as longitudinal and transverse orders of approximation of the elements, respectively. Novelty of the elements consists in application of hpq- and hp-approximations in solid and shell parts of the elements, respectively. In that context, crucial parts of the algorithm such as: hierarchical shape functions, modification of the stiffness and nodal forces of the shell part of the elements, and constrained $hpq/hp$-approximation are elucidated. Usefulness of the elements for modelling and analysis of complex structures is proved by a numerical example.