General method of analysis for composite beams with longitudinal and transverse partial interaction

This paper presents an analytical formulation for the analysis of two-layered composite beams with longitudinal and vertical partial interaction. The particularity of this model is its ability to incorporate an interface connection deforming both longitudinally, i.e., along the beam length, and vertically, i.e., transverse to the connection interface, which is modelled by means of a uniformly distributed spring. The novel formulation is based on the principle of virtual work expressed in terms of the displacement field consisting of the vertical and axial displacements of the two layers; for completeness, the proposed model is presented in both its weak and strong forms. The partial interaction problem is then solved by means of the finite element method. A parametric study is presented to investigate the effects of different combinations of longitudinal and transverse connection rigidities on the overall structural response. For the purpose of these simulations, a bi-linear constitutive model has been specified for the transverse interface connection to reflect the more realistic case in which two different responses are observed in the transverse interaction, one in which one layer is bearing against the other one, one when the two layers are separating. An iterative procedure has been proposed to obtain the convergence to the final solution.