Zig-zag theories differently accounting for layerwise effects of multilayered composites

AbstractThis paper essays the effects of the choice of through-thickness representation of variables and of zig-zag functions within a general theory by the authors from which the theories considered are particularized. Characteristic feature, coefficients are calculated using symbolic calculus, so to enable an arbitrary choice of the representation. Such choice and that of zig-zag functions is shown to be always immaterial whenever coefficients are recalculated across the thickness by enforcing the fulfillment of elasticity theory constraints. Assigning a specific role to each coefficient is shown immaterial. Moreover, the order of representation of displacements can be freely exchanged with one another and, most important, zig-zag functions can be omitted if part of coefficients are calculated enforcing the interfacial stress field compatibility. Vice versa, accuracy of theories that only partially satisfy constraints, is shown to be strongly dependent upon the assumptions made. Applications to laminated and soft-core sandwich plates and beams having different length-to-thickness ratios, different material properties and thickness of constituent layers, various boundary conditions and distributed or localized loading are presented. Solutions are found in analytic form assuming the same trial functions and expansion order for all theories. Numerical results show which simplifications are yet accurate and therefore admissible.

KeywordsComposite and sandwich plates, zig-zag theories, interlaminar transverse shear/normal stress continuity, localized and distributed loadings, FEA 3-D elastostatic solutions.

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