The (3,2)-Mixed Refined Zigzag Theory for generally laminated beams: Theoretical development and C0 finite element formulation

A third-order Refined Zigzag Theory for multilayered composite and sandwich beams is developed based on the Reissner Mixed Variational Theorem. The assumed kinematics enriches the Timoshenko’s beam Theory: a second- and a third-order smeared polynomial terms along with a piece-wise linear contributions are added to the axial displacement, whereas the transverse displacement is approximated with a power-series expansion up to the second-order term. Transverse shear and normal stress, continuous and able to satisfy the boundary stress conditions on the outer beam surfaces, are assumed by the model: the transverse shear stress is derived with the aid of the Elasticity equations, whereas a third-order power-series expansion is adopted for the transverse normal stress. Based on the proposed model, an efficient C0-continuous beam element is formulated by adopting the anisoparametric interpolation strategy to avoid the shear locking phenomenon. The accuracy of the proposed model and the finite element implementation is assessed by solving problems concerning the elasto-static behavior of generally laminated beams, both simply supported and clamped at the ends. Comparison with reference solution (Elasticity or high-fidelity FE model) demonstrates the remarkable accuracy of the proposed model, both in terms of displacements and stresses distributions, as well as the finite element implementation efficiency.