Geometrically and materially non-linear analysis of planar composite structures with an interlayer slip

We have proposed the governing equations of a composite planar beam which fully take into account the exact geometrical and material non-linearities as well as finite slip between the layers. The present equations also exactly account for the equilibrium between the contact surfaces of the layers in the deformed state as well as for the tangential separation of layers at the edges. The equations of the model are then cast into the discretized weak form by the modified principle of virtual work using the unconventional finite element technique, where strains and the interlayer normal contact traction represent the interpolated quantities. The computational efficiency and accuracy of the formulation has been validated by comparing the results with the experimental ones on the steel–concrete beam using the results of an experiment of Chapman and Balakrishnan [Chapman JC, Balakrishnan S. Experiments on composite beams, Struct Eng 1964; 42(11):369–383]. Of a particular importance in assessing the present formulation are also the results for the buckling load of a composite timber column. The results, incorporating the non-linear stress–strain law of timber and a large range of slendernesses of the column, clearly show a substantial effect of slip modulus on the buckling load. Thus the present formulation is also well suited for the buckling investigations of composite beams.

► The governing equations of a composite planar beam with interlayer slip are derived.
► Geometrical and material nonlinearity are taken into account.
► The tangent stiffness matrix is derived and implemented in an exact analytical form.
► The finite-element formulation results in a superb convergence and accuracy.
► Formulation is also well suited for the buckling investigations of composite beams.