Novel Sandwich Composite Shell Structures in Nonlinear Geometric and Dynamic Analyses

This research introduces a novel structure for a doubly curved shallow shell, termed the “single-variable-edge and variable-thickness doubly curved shallow shell” (SVEVT-DCSS). The shell is constructed from a functionally graded carbon nanotube/fiber/polymer multiscale laminated composite with three distinct carbon nanotube distribution patterns: uniform distribution (UD), FG-O, and FG-X. These distributions are modeled using the Halpin–Tsai micromechanical approach and an orthotropic micromechanical model. Employing the theory of elasticity and the Von Karman–Donnell geometrical nonlinearity assumption, the governing equations for the mechanical behavior of the shell, which rests on a Winkler–Pasternak elastic foundation and is subjected to a thermomechanical environment, are formulated. By applying Galerkin’s method to these equations, the dynamic characteristics of the shell are determined. The nonlinear dynamic responses of the SVEVT-DCSS are analyzed with a focus on both periodic and chaotic behavior. Furthermore, the accuracy and reliability of the results are validated through comparisons with existing literature and finite element method simulations. The findings, presented through numerical tables and graphical figures, demonstrate the significant potential of this novel shell structure for practical engineering applications, contributing to advancements in aerospace, civil, and mechanical engineering.