New 3-D zig zag theories: elastostatic assessment of strategies differently accounting for layerwise effects of laminated and sandwich composites

New physically based 3-D, fixed d.o.f., theories which enable to analyze cases with general loading and boundary conditions efficiently are proposed. Here the aim is to study the effects of an arbitrary choice of through-thickness representation of kinematic/stress variables and of zig-zag functions. The same trial functions and expansion order of analytical solutions are assumed to assess theories under the same conditions. Comparisons are carried out with exact and/or 3-D FEA solutions. Their computational burden is still comparable to that of classical plate models. The results show that whenever coefficients of representation are recalculated across the thickness by enforcing the fulfillment of all constraints prescribed by the elasticity theory, the choice of the representation form and of zig-zag functions is immaterial. In this way, a high order of generalization is allowed because the representation of one single displacement can be freely varied across the thickness and be completely different from that of other displacements. Moreover, zig-zag functions can be arbitrarily chosen or even omitted without any accuracy loss. Instead, accuracy is shown to be strongly dependent upon the assumptions made for theories only partially satisfying constraints.