Multilayered shell model with variable representation of displacements across the thickness

A multilayered zig-zag shell model is developed; it has a hierarchic representation of displacements across the thickness that a priori fulfils the interfacial stress contact conditions on interlaminar shear and normal stresses. Like for classical models, the functional d.o.f. are the mid-plane displacements and the shear rotations. Characteristic feature, the representation can vary from point to point across the thickness, in order to adapt to the variation of solutions. The coefficients of the higher-order terms are determined as functions of the d.o.f. by enforcing equilibrium conditions at discrete points across the thickness. The Lame’s coefficients are expanded up to the second order. As shown by the numerical tests, it accurately predicts the stress fields of thick laminated and sandwich shells with abruptly changing material properties with a lower overall processing time than for the fixed representation, since post-processing is unnecessary.