Bending and vibrations analyses of laminated beams by using a zig-zag-layer-wise theory

This paper proposes one-dimensional layer-wise theories that make use of higher-order zig-zag functions defined over fictitious/mathematical layers of the cross-sectional area. These advanced kinematics enable the computational costs to be reduced while the accuracy of the classical layer-wise theories in which the number of physical and numerical layers coincide, is maintained. Variable kinematics theories have been obtained using piecewise continuous power series expansions of an arbitrary order defined over the whole cross-section of the structure. As in the classical layer-wise approach, the cross-section can be divided into a variable number of mathematical subdomains. The expansion order of each subdomain is therefore an input parameter of the analysis. This feature enables the solution to be refined locally as the kinematics expansion can be enriched over generic regions of the cross-section. The governing equations have been obtained by applying the Principle of Virtual Displacements, along with the Carrera Unified Formulation, and have been solved using the Finite Element method. Numerical simulations have been performed considering laminated and sandwich beams with very low length-to-depth ratio values. Comparisons between the present results and solutions available in the literature have pointed out the advantages of this approach, in terms of accuracy of the displacements, of the stress distributions over the beam cross-section and of the natural frequencies with respect to the classical layer-wise theories.