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

Abstract This paper presents a novel analytical formulation for the analysis of generic multi-layered composite beams formed by n 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 n -layered displacement-based elements has been proposed, i.e. with ( 2 n + 4 ) and ( 3 n + 4 ) degrees of freedom, respectively. These elements have been used to discuss and to algebraically demonstrate the occurrence of curvature locking in n -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 10 dof finite element and a 13 dof one have been considered. The proposed work has demonstrated that, while the ( 3 n + 4 ) dof elements well describe the partial interaction behaviour, the ( 2 n + 4 ) dof ones suffer from curvature locking problems for high values of at least one of the n − 1 interface shear connection stiffnesses. Based on this study it is concluded that the use of ( 3 n + 4 ) dof elements is recommended while the modelling by means of the ( 2 n + 4 ) dof is discouraged.

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