Layerwise zig-zag model with selective refinement across the thickness

In this paper a multilayered model with a hierarchic representation of displacements is developed. The representation, which is based on Jacobi polynomials, can be different for any computational layer, from point to point across the thickness and for any functional d.o.f., aimed at adapting the model to the local variations of solutions. This refinement is obtained by keeping the number of d.o.f. unchanged. The displacements are described through a zig-zag representation in any computational layer, in order to fulfil the stress contact conditions at the inner interfaces. A displacement-based version of the model with the six displacement components at the upper and lower faces as functional d.o.f. and a mixed version with the six interlayer stress components are developed. The numerical results mainly concern simply supported thick sandwich beams under sinusoidal loading, but results are also presented for thin cantilevered sandwich beams and laminated plates. The model accurately predicts displacements and stress fields using a single computational layer, even when material properties abruptly change. The computational effort for the adaptive representation is advantageous by the viewpoint with respect to a fixed representation or with the use of post-processing methods.