Considerations about the choice of layerwise and through-thickness global functions of 3-D physically-based zig-zag theories

A generalization of physically-based fixed degrees of freedom 3-D zig-zag theories is developed, which allows for any arbitrary choice of layerwise and representation functions. Thereby users can choose arbitrarily the representation case-by-case. This paper aims to prove that the choice of global and layerwise functions is immaterial whenever coefficients are recalculated exactly (via symbolic calculus) by the enforcement of interfacial stress continuity, boundary conditions and equilibrium in point form, as prescribed by the elasticity theory. Vice versa, accuracy of theories partially fulfilling constraints will prove to largely depend on the assumptions made and to be inadequate when strong layerwise effects rise, under distributed/localized step loading and boundary conditions other than simply supported edges (tests carried out in closed-form). The present and previous authors’ theories are tested with the aim to understand in which cases an adequate level of accuracy is still achieved by lower-order theories that are derived as particularizations.