Locking problems in the partial interaction analysis of multi-layered composite beams

This paper presents a novel analytical formulation for the analysis of generic multi-layered composite beams formed by nn layers and interconnected by flexible interface connections between adjacent layers. Based on the principle of virtual work the weak formulation of the multi-layered partial interaction problem is presented, and its strong form is derived by integration by parts. In particular, a generic approach to derive two types of nn-layered displacement-based elements has been proposed, i.e. with (2n+42n+4) and (3n+43n+4) degrees of freedom, respectively. These elements have been used to discuss and to algebraically demonstrate the occurrence of curvature locking in nn-layered finite elements.Numerical examples are also presented for the particular cases of simply supported, propped cantilever and fixed-ended beams subjected to a uniformly distributed load to further investigate the appearance of the locking phenomenon in the case of three structural systems. For this purpose, a 10dof finite element and a 13dof one have been considered.The proposed work has demonstrated that, while the (3n+4)dof elements well describe the partial interaction behaviour, the (2n+4)dof ones suffer from curvature locking problems for high values of at least one of the n−1n−1 interface shear connection stiffnesses.Based on this study it is concluded that the use of (3n+4)dof elements is recommended while the modelling by means of the (2n+4)dof is discouraged.