Finite beam elements based on Legendre polynomial expansions and node-dependent kinematics for the global-local analysis of composite structures

This article presents an approach to obtain refined beam models with optimal numerical efficiency. Hierarchical Legendre Expansions (HLE) and Node-dependent Kinematics (NDK) are used in combination to build efficient global-local FE models. By relating the kinematic assumptions to the selected FE nodes, kinematic refinement local to the nodes can be realized, and global-local models can be conveniently constructed. Without using any coupling approach or superposition of displacement field, beam models with NDK have compact and coherent formulations. Meanwhile, HLE is used in the local zone for the enrichment of the beam cross-sections to satisfy the requirement for high solution accuracy, leaving the global model with lower-order kinematic assumptions. Through the numerical investigation on slender laminated structures, it is demonstrated that the computational costs can be reduced significantly without losing numerical accuracy.