Fundamental frequency optimization of variable stiffness Multi-Region composite panels in Presence of geometrical nonlinearity

Multi-region laminate optimization offers a comprehensive approach to enhance aerospace structures, making them efficient, safe, and cost-effective. Similarly, Automated Fiber Placement (AFP) processes optimize toolpaths and fiber deposition, reducing waste, saving time, and improving composite quality. Strategically placing fibers where needed, it boosts structural performance and allows for innovative composite designs. This study, first, focuses on optimizing the Fundamental Natural Frequency (FNF) of composite panels, which feature various Curvilinear Fiber Paths (CFP) mathematically modeled using bilinear interpolation distributed across different regions of the panel with comparisons drawn against the conventional Unidirectional (UD) fiber layup. Secondly, a study is conducted to explore the Fundamental Amplitude-dependent Nonlinear Frequencies (FANF) within the context of the optimized configuration featuring curved fiber layup. The modulation of stiffness in composite laminates is achieved through continuous adjustments of fiber angles, governed by the CFP function. A nonlinear structural model, grounded in the principles of virtual work, is employed for this analysis. The formulation incorporates Green's nonlinear kinematic strain relations to accommodate geometric nonlinearities, and First-order Shear Deformation Theory (FSDT) is applied to extend the analysis to moderately thick cylindrical panels, including transverse shear deformations. The principal aim of this investigation is to evaluate the impact of Variable Stiffness (VS) parameters across multiple regions on the linear and nonlinear free vibration characteristics of the panel. This research examines symmetric eight-layered composite panel incorporating three distinct design regions and two boundary condition sets. The Generalized Differential Quadrature (GDQ) method is employed to solve the nonlinear equations of motion governing these structures. The numerical findings show the impact of fiber angle paths and boundary conditions on the FNF of cylindrical panels.