A single-variable approach for layered beams with imperfect interfaces

The first-order shear deformable laminated beam problem is reformulated in terms of a fictitious bending displacement as primal variable. A fourth-order differential equation governs the problem with two additional unknown constants coming from the integration of the longitudinal displacement. With the classical six boundary conditions, the problem is complete and well posed. An isogeometric collocation scheme is developed to solve the problem numerically. The formulation is completely locking-free and satisfies high continuity requirements for the approximation functions. The results for an exemplary structure confirm the validity and the good performance of the method, which is preliminary to the single variable reformulation of a more accurate zig-zag model for laminates with perfect and imperfect interfaces.