Simple Polynomial Reissner–Mindlin Shell Model and Its Application in Efficient Analysis of Complex Underground Structures

Abstract

The isogeometric (IG) Reissner–Mindlin (R–M) shell model solves the problem of shear and membrane locking that besets the finite element (FE) R–M shell model of nonthick underground structures, but still faces complicated modeling and computation, especially for the multijoint structures. In order to change such situation, a simple polynomial (SP) R–M shell model is proposed. Similar to the IG displacement, the SP displacement has the advantage of easy locking reduction due to its convenience in degree elevation. The definition of the SP displacement is independent of the shape and the control points, so the elements can be divided with no new degrees of freedom created, which lays a foundation for the simplified modeling strategy of “joint definition after block description.” Micro-width connectors are introduced to unify the modeling of interblock links, interblock joints, and intrablock joints, and to quantitatively determine the actual state of each joint through incremental iteration. A program with parameterized preprocessing and postprocessing is written based on the SP R–M shell model to realize the one-key analysis of complex underground structures. As verification, three engineering cases are modeled and computed. The errors of typical displacements and bending moments from the SP R–M shell model and the IG R–M shell model are no more than 3%, while the errors of the results from the FE R–M shell model and the IG R–M shell model are around 20%, which reveals the feasibility and advantages of the SP R–M shell model.