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

Abstract

Summary 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. Copyright © 2017 John Wiley & Sons, Ltd.

A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures

“…This goal is reached, for instance, through the use of efficient solution algorithms, like in Koiter, 4‐6 Koiter–Newton approaches, 7,8 and in generalized path following methods 9,10 . Conversely, the reduction of the discrete variables is pursued, among the others, by the isogeometric formulations 11,12 that take advantage from the high continuity of interpolation functions, and by high‐performing finite elements (FE) 13,14 . Within this last group of FE, interesting results have been obtained by mixed formulations that assume both displacement and stresses fields as primary variables 15,16 .…”

“…Due to its attractive features, the CR formulation has been extensively employed through the years. Recently, it has been applied to 3D beams, 25 generalized beam theory (GBT), 26,27 plate/shell models, 28‐30 and solid‐shell formulations 13,14 …”