A Theory for Multilayered Composite Beams

Composite laminates are nowadays widely employed as lightweight components in civil engineering, automotive and aerospace applications due to their excellent mechanical properties, such as, the high strength and stiffness per unit weight, the path loads management capability. Moreover by using composite laminated materials it is possible to manufacture large size structures with less riveted joints, which leads to a reduction of the overall structural complexity and of the manufacturing and inspection times and costs. A drawback of layered composites is represented by the the low values of throughthe-thickness tensile and shear strengths, with respect to the in-plane ones, that affect the overall performances of the composite elements particularly in the case of highly loaded structures, near geometric discontinuities as cut-outs and free-edges and crossing different plies interfaces, where an elastic mismatch occurs. It follows that the proper modillization of the composite laminated configurations represents a crucial point in the composite structures design step even for beam-like structures. Of course, analytical or numerical 3-D solutions are the most accurate but they present very high computational costs. For such reason, 1-D laminated beam theories are used to reduce the analysis effort preserving a suitable level of accuracy. The 1-D approaches can be mainly classified according to the assumed kinematical model; in particular, one has the Layerwise (LW) theories, which are accurate for thin to thick beams but their computational costs increases with the number of plies, and the so-called Equivalent Single Layer (ESL) theories, characterized by a computational effort independent of the number of plies but the solution accuracy decreases as the beam thickens. Alternatives are represented by the zigzag approaches where the kinematical model is enriched by a layerwise discontinuous a-priori selected function such that the continuity condition of the transverse stress components is enforced. In this work, a theory for multilayered composite beams is presented. A {m-n} layer-wise kinematical model is developed in such a way the point-wise balance equations are fulfilled. Then, the interface continuity conditions written in terms of displacements and stress components are invoked allowing for a reduction of the model degrees of fredom. In particular, the involved layer-wise kinematical quantities are written in terms of the primary variables of one layer only. Thus, the computational effectiveness of the equivalent single layer theories is obtained preserving the solution accuracy of the layer-wise model, avoiding any a-priori selection of enriching functions. To obtain a beam kinematical model which take full advantage of an equivalent single-layer approach, a set of generalized kinematical variables is introduced in such a way to rewrite the layers kinematics in terms of variables representative of the beam as a whole. Stress resultants are then obtained in terms of the generalized variables derivatives by integrating the stress tensor components along the thickness directions and allow to define the stiffnes properties of the equivalent single-layer beam. Anlytical solutions are last computed and presented to show the effectiveness of the proposed model by comparing the results obtained with literature analytic solutions and finite element simulations