An adaptable refinement approach for shell finite element models based on node-dependent kinematics

Towards improving the numerical efficiency in the analysis of multi-layered shell structures with the finite element (FE) method, an adaptable two-level mathematical refinement approach is proposed for refined curvilinear shell elements. Based on Carrera Unified Formulation (CUF), the approximation of displacement functions of shell elements can be improved by refining the through-the-thickness assumptions and enriching the shape functions. By using the hierarchical Legendre polynomial expansions (HLE) as shape functions, the element capabilities can be enhanced conveniently without re-meshing. To further increase the numerical efficiency of shell FE models, Node-Dependent Kinematics (NDK) is utilized to implement local kinematic refinements on the selected FE nodes within the domain of interest. The conjunction of NDK with the two-level refinements of the shell FE models leads to an adaptable refinement approach in the analysis of shell structures, which can be used to build FE models with optimal efficiency and high fidelity. The competence of the proposed approach is investigated through numerical studies on laminated shells.