Non-polynomial zig-zag unified shear deformation formulation solved via boundary discontinuous method for laminated sandwich plates

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Analytical solutions of mechanical problems with refined theories and challenge boundary conditions are still a topic of research due to intrinsic complexity. In this paper, a generalized refined theory is formulated to obtain analytical solutions for the static problem of cross-ply laminated and sandwich plates with several boundary conditions. These theories are implemented in the framework of the Carrera unified formulation (CUF) based on the equivalent-single-layer (ESL) approach. The displacement field of ESL-based models are expanded over the thickness direction by using non-polynomial terms, e.g. trigonometric, hyperbolic and the so-called zig-zag (ZZ) Murakami’s functions. The principle of virtual displacements (PVD) statement is used to derive the strong form of the governing equations in terms of displacements variables. These equations are solved by the boundary-discontinuous double Fourier series approach which provides highly accurate analytical solutions. This work gives a detailed comparison of results obtained using the presented ZZ models highlighting the differences with 3D FEM results. Furthermore, the influence of non-polynomial and ZZ terms in each ESL model is investigated. The superior robustness of the presented methodology compared to past works is demonstrated, making the proposed results suitable as a benchmark for validating new theories and finite elements. The findings can be also useful to train artificial intelligence (AI) models that can allow to the development of faster digital twin structure technology.