Legendre-based node-dependent kinematics shell models for the global-local analysis of homogeneous and layered structures

The present work demonstrates the use of the node-dependent kinematics method to derive and compare several two-dimensional shell theories. The three dimensional displacement field is expressed in terms of generalized coordinates, which are subsequently expanded along the shell thickness using arbitrary functions. The in-plane unknowns, are then discretized through classical finite element approximation. Based on the Carrera Unified Formulation, the proposed method combines in a unique manner the theory of structures and the finite element method; thickness interpolation functions are defined node-wise. As a consequence, the resulting finite element model represents diverse approximation theories at each single node. In this work Taylor-based kinematics (including the Murakami Zig-Zag function) and Legendre-type nodal kinematics are incorporated at the element level without adopting mathematical artifices leading to the global-local strategy, where refined theories are selectively employed in specific areas, while maintaining acceptable computational costs. Numerical cases from the existing literature are employed to establish the effectiveness of node-dependent models in bridging a locally refined theories to global kinematics when local effects need to be considered. The analyses focus on localized loads for both homogeneous and multi-layered structures.