A mixed method for investigating free vibrations in fiber-reinforced shells with non-uniform curvature

Abstract

The main goal of this work involves conducting numerical simulations to determine the vibrational behavior of composite shell structures. The introduction of doubly-curved laminated shells plays a pivotal role in diverse engineering applications, offering an expanded design space and the potential to enhance mechanical performance. However, the analysis of this kind of structures poses significant challenges due to the need to account for the curvature of the shell mid-surface. Moreover, the aspect ratio strongly influences the structural response in terms of free vibrations, also affecting the accuracy of the numerical solution. To address these complexities, this work employs the Carrera’s unified formulation, a well-established methodology for evaluating composites structural behavior which allows to set the expansion order of through-the-thickness polynomials as a free parameter of the simulation. In this context, the governing equations of the problem are derived through pure displacement and mixed formulations, within a finite element framework, ensuring a robust and adaptable analysis approach. This study extends the application of the unified formulation to complex shell geometries featuring non-uniform curvatures along the mid-surface principal directions. Free vibration analyses are performed to determine fundamental frequencies and mode shapes, with results benchmarked against 3D models from Abaqus and classical theoretical predictions. The comparison demonstrates the effectiveness of the proposed approach, establishing its efficacy for advanced structural investigation of fiber-reinforced shells with spatially varying curvatures, regardless of the considered slenderness ratio.