Partially Layer Wise advanced Zig Zag and HSDT models based on the Generalized Unified Formulation

The Generalized Unified Formulation (GUF) for composites and sandwich structures is a computational multi-theory architecture which can generate a large variety of types of theories with any combination of the orders of expansion for the different primary variables. All the theories are generated from the expansion of six theory-invariant 1 × 1 arrays (kernels). For the first time, an extension and further generalization of the GUF is proposed: each displacement unknown is independently described (in an axiomatic sense) with respect the other primary variables. In particular, each displacement can present a Layer Wise or an Equivalent Single Layer types of discretizations with or without the Zig Zag enhancement which takes into account the displacements’ thickness derivative interlaminar discontinuity.The Partially Zig Zag Advanced Higher Order Shear Deformation Theories (PZZAHSDTs), Partially Layer Wise Higher Order Shear Deformation Theories (PLHSDTs), Partially Layer Wise Advanced Higher Order Shear Deformation Theories (PLAHSDTs), Partially Layer Wise Advanced Zig Zag and Higher Order Shear Deformation Theories (PLAZZHSDTs) are introduced and discussed for the first time. These types of theories are compared with the advanced Equivalent Single Layer, Zig Zag, and Layer Wise approaches. In the framework of displacement-based models, a Finite Element implementation of the Generalized Unified Formulation is presented for the first time and numerical evaluations of sandwich structures subjected to various boundary conditions are discussed. A challenging high Face-to-Core Stiffness Ratio (FCSR) is also adopted to asses the performances of this large set of new approaches. It is demonstrated that the Partially Layer Wise Theories provide a computationally efficient alternative to standard Layer Wise models.

► Partially Layer Wise and Partially Zig Zag Theories are presented for the first time. ► The Generalized Unified Formulation is further generalized to cover these theories. ► FEM implementation of the Generalized Unified Formulation is presented for the time. ► Zig Zag enhancement or Layer Wise description for the in-plane displacements greatly improves the accuracy of the model. ► Layer Wise axiomatic description is recommended for sandwich structures with high face-to-core stiffness ratio.