Free Vibration Analysis of Variable-Angle Tow Composite Shells With Variable Curvature Using Carrera’s Unified Formulation

Abstract The integration of Variable-Angle Tow (VAT) composites with shell geometries offers significant potential for enhancing structural performance in aerospace engineering. This is attributed to the high stiffness-to-weight ratio of these structures and the expanded design space made possible by curvilinear fibers applied to doubly curved geometrical domains. However, the numerical analysis of such structures is often challenging due to the complexity of the governing equations and the increased computational cost associated with the higher number of unknowns. Carrera’s Unified Formulation (CUF) provides an effective approach to address these challenges, reducing computational cost while maintaining accuracy in predicting the three-dimensional (3D) stress fields characteristic of VAT composites. This study extends the application of CUF to VAT shell structures with variable curvature radii. Fibers curvature is modeled using a linear variation law. The governing equations for free vibration analysis are derived through the Principle of Virtual Displacements (PVD) within a hierarchical shell finite element framework. A two-layer ellipsoidal VAT shell is analyzed, with thickness considered as a study parameter. Validation against Abaqus 3D models demonstrates the accuracy and efficiency of the method, with strong agreement observed in fundamental frequencies and modal shapes. These findings highlight CUF as a robust and computationally efficient tool for analyzing complex VAT shells, paving the way for its implementation in practical applications.