Hybrid equilibrium finite element formulation for composite beams with partial interaction

Abstract

Thanks to their various benefits, composite beams have been increasingly used in various applications. This study will focus on two-layer composite beams with a flexible shear interface between layers. The finite element method, in particular its displacement-based formulation, has been recognized as the most popular method for numerical analysis of composite beams. However, when applied to Timoshenko beams with partial interaction, the displacement-based formulation may suffer from the so-called shear-locking and slip-locking phenomena, leading to erroneous solutions. Hybrid and mixed finite element formulations have been viewed as competitive alternatives, since they naturally avoid locking effects. Special types of these formulations are the so-called equilibrium-based formulations, producing statically admissible solutions. This work introduces for the first time an equilibrium-based finite element formulation for the analysis of Timoshenko composite beams with partial interaction. The formulation relies on a variational principle of complementary energy involving only force/moment-like variables as fundamental unknown fields. The approximate field variables are selected such that all equilibrium equations hold in strong form. The inter-element equilibrium is enforced by resorting to the Lagrangian multiplier method. Unlike traditional displacement-based finite element formulations, the proposed scheme is naturally free from both shearand slip-locking phenomena. The accuracy and effectiveness of the new formulation is numerically assessed through the analysis of several numerical examples. In particular, the ability of the formulation to model accurately both very flexible and very stiff shear connections is numerically shown.

A high performance flexibility-based GBT finite element

“…(27), (28), (37) inter-element equilibrium conditions. It can be easily verified that the stationary conditions of P C are the compatibility equations, Eqs.…”

“…The stationary conditions of the hybrid comple- (37) and, in addition, the inter-element equilibrium conditions on @X i . Note that in functional P HY displacement is defined only on the elements boundary (at the nodes) where it acts as a Lagrangian multiplier to enforce the Neumann boundary conditions and the inter-element equilibrium conditions.…”

“…On the other hand, it is well known that mixed/hybrid stress approaches can yield higher performance and, in particular, higher accuracy in the stress evaluation. Mixed/hybrid stress approaches have been successfully used for the analysis of beams (see, for example, [35][36][37][38]) as well as of plates (see, for example, [39][40][41][42][43]). Moreover, thanks to the high accuracy and to the mixed format, involving both displacements and stresses as independent variables, elements based on such approaches are particularly suitable to be used within corotational formulations for geometrically nonlinear analyses [44,45].…”

Structural Behaviour of Cold-Formed Steel of Double C-Lipped Channel Sections Integrated with Concrete Slabs as Composite Beams

“…Composite steel-concrete beams, conversely, are more extensively used in the construction industry. They are more economical and possess higher strength capacities than bare steel beams [12]. The use of composite principles is appropriate for promoting the widespread use of CFS sections in the construction industry [13].…”

Stability analysis of three-layer shear deformable partial composite columns

“…Komijani et al (2013) studied thermal buckling behaviour of two-layer shear deformable beams with partial interaction between the layers. Santos and Silberschmidt (2014) introduced an equilibrium-based finite element formulation for the static analysis of two-layer partial composite Timoshenko beams with uniform shear assumptions. Taig and Ranzi (2015) introduced a theoretical model and a finite element solution for analysis of two layer partial interaction composite steel-concrete beams within the framework of generalised beam theory (GBT).…”