Geometrically nonlinear quadratic solid/solid-shell element based on consistent corotational approach for structural analysis under prescribed motion

This study proposed geometrically nonlinear quadratic solid/solid-shell elements applicable for moving structures. Coordinates in the corotational (CR) formulation were established for a solid element. The proposed CR formulation was consistent with other hexahedral or tetrahedral solid type finite elements. The study involved an explicit description of relevant quantities induced during the derivation. Centrifugal and inertial terms were derived to analyze the behavior of moving structures. The formulation derived in the study was applicable for various solid type elements. Thus, an assumed-strain 18-node solid-shell element was developed based on the Hellinger–Reissner principle to avoid locking in the local element. In addition, quadratic solid elements (i.e., a 10-node tetrahedron and a 20-node hexahedron) were developed in the CR solid formulation. Finally, the results were compared with those derived by previous researches involving typical static benchmark problems and commercial software. The findings indicated a good agreement between the comparisons and validated the proposed finite elements.