Alleviation of parasitic slip in finite element analysis of composite beams

• The basic finite element formulation was modified by using a simple procedure.
• For the slip field, consistent interpolation is used and additional parameter is eliminated by using explicit constraint.
• The parasitic slip in basic element formulation is completely eliminated.
• A systematic solution for the differential equations of equilibrium is also provided.
• Examples illustrate the accuracy of the developed novel finite element.

In the conventional displacement-based finite element analysis of composite beams that consist of two Euler–Bernoulli beams juxtaposed with a deformable shear connection, the coupling of the transverse and longitudinal displacement fields may cause oscillations in interlayer slip field and reduction in optimal convergence rate, known as slip locking. This locking phenomenon is typical of multi-field problems of this type, and is known to produce erroneous results for the displacement based finite element analysis of composite beams based on cubic transverse and linear longitudinal interpolation fields. In this study, a very simple and novel procedure is introduced to eliminate the parasitic slip in the finite element analysis of composite beams. A systematic solution of the differential equations of equilibrium is also provided, and an exact element is developed in the paper. Numerical results presented illustrate the accuracy gained based on the proposed modification to the basic finite element formulation. Solutions based on the exact element provide benchmark results for the performance of the proposed formulation.