A beam theory for layered composites subjected to uniformly distributed load

A theory for multilayered composite beams undergoing transverse uniformly distributed loads is presented. The formulation starts by assuming a layer-wise kinematical model characterized by third order approximation of the axial displacements and fourth order approximation of the transverse displacements. By enforcing the point-wise balance equations as well as the interface continuity conditions, the layer-wise kinematical model is rewritten in terms of a set of generalized kinematical variables associated with the beam as a whole. Stress resultants are then obtained in terms of the generalized variables derivatives and of the normal stresses applied to the top and bottom surfaces of the laminate. The stiffness properties of the beam are also explicitly obtained. The beam stress resultant equilibrium equations allow to write the boundary value governing problem. Once the problem is solved in terms of the generalized variables, the layer-wise kinematical and stress fields are recovered by a simple post-processing step. The proposed theory allows to ensure the accuracy level of the layer-wise formulations preserving the computational efficiency of the equivalent-single-layer theories.