A hierarchical global-local shell finite element analysis of variable stiffness composite structures

The present talk addresses the extension of hierarchical shell finite elements based on Carrera’s Unified Formulation (CUF) to a global-local approach for the investigation of Variable-Angle Tow (VAT) composite structures. VAT laminates are characterized by curvilinear fibres laid along predefined paths, enabling enhanced mechanical performance and a wider structural design space. Nevertheless, their analysis typically requires high computational effort to accurately capture the complex displacement and stress fields resulting from the variable in-plane fibre distribution. In the proposed strategy, a global analysis is first performed over the entire structural domain using low-order Abaqus shell elements with a reduced number of degrees of freedom. A subsequent local analysis employs a refined CUF model with higher-order through-the-thickness approximations in a layer-wise manner, enabling accurate and efficient capture of the high stress gradients that typically arise near geometric singularities and discontinuities. The governing equations are derived within the CUF framework using both the Principle of Virtual Displacements (PVD) and the Reissner’s Mixed Variational Theorem (RMVT). Validation against full three-dimensional finite element simulations in Abaqus demonstrates the accuracy of the proposed methodology. Comparisons in terms of degrees of freedom confirm that the global–local CUF-based approach achieves high accuracy near discontinuities at a significantly reduced computational cost relative to full 3D models. Furthermore, the differences observed between the PVD and RMVT formulations highlight the critical role of transverse stress prediction in the analysis of VAT composites.