Displacement-based finite element formulations for material-nonlinear analysis of composite beams and treatment of locking behaviour

In this paper a numerical procedure is developed for the material-nonlinear analysis of composite beams composed of two Euler–Bernoulli beams juxtaposed with a deformable shear connection. In the displacement-based finite element analysis of composite beams, however, the coupling of the transverse and longitudinal displacement fields may cause oscillations in the interlayer slip field and reduction in optimal convergence rate, known as slip-locking. A very simple and novel procedure is introduced to develop an assumed strain formulation, which alleviates slip-locking in the numerical analysis of composite beams and provides superconvergent points for slip values. It is also shown that by changing the primary variable fields of Newmark's mathematical model, to interpolate the slip field directly, slip-locking can be completely eliminated. Numerical examples are presented to illustrate the performances and the numerical characteristics of the proposed methods.

► The basic finite element formulation was modified using a simple assumed strain formulation.
► The slip values based on different assumed strain formulations coincide at a point.
► By changing the primary variables an efficient finite element was developed.
► By changing the primary variables curvature-locking can be alleviated.
► A procedure was developed for material-nonlinear analysis of composite beams.