Partially Zig-Zag Advanced Higher Order Shear Deformation Theories Based on the Generalized Unified Formulation

The Generalized Unified Formulation (GUF) is a multi-theory and a multi-fidelity architecture for the generation of a virtually infinite class of Advanced Higher Order Shear Deformation Theories (AHSDT) or Zig-Zag theories or Layer-Wise (LW) theories with any order of expansion for each of the primary variables. This work will present, for the first time in the literature, an extension of GUF to address problems in which every single variable can have either an Equivalent Single Layer (ESL) or a Zig-Zag-enhanced ESL description [Partially Zig-Zag Advanced Higher Order Shear Deformation Theories (PZZAHSDT)]. Applications to the case of thick sandwich structures are presented: starting from a baseline fourth-order AHSDT which also includes the transverse strain effects, all the possible types of PZZAHSDT are generated and compared with the baseline and with a fourth-order fully Zig-Zag theories.

► The Generalized Unified Formulation is extended to cover partially Zig-Zag theories.
► Each primary variable may have any order of expansion and Zig-Zag description.
► The Zig-Zag form for the displacements is important only for thick plates.
► The transverse shear stresses present a Zig-Zag form even for thin plates.
► Including the Zig-Zag effects of the in-plane displacements improves the accuracy.