Static and Vibrational Analysis of FG Graphene Origami Reinforced Joined Conical–Cylindrical Shells Using a Powerful Numerical Technique

The static and vibrational responses of joined truncated conical–cylindrical shells reinforced with functionally graded graphene origami (FG-GOri) are investigated. The reinforcement is varied through the thickness, and its influence on displacement fields, and natural frequency is evaluated. Governing equations are derived using higher-order shear deformation theory (HSDT), in which transverse shear and thickness stretching are incorporated without correction factors. The equations are discretized and solved by the Generalized Differential Quadrature (GDQ) method, a highly efficient numerical scheme for complex shell problems. The combined effects of GOri mass fraction, folding degree, and reinforcement distribution patterns (U, X, O, V) are analyzed. A non-monotonic reinforcement effect is identified, wherein the V-pattern configuration exhibits a natural frequency reduction from 345 Hz to 330 Hz as the GOri mass fraction increases from 0% to 3%, primarily due to stiffness degradation at high folding degrees. In contrast, the X-pattern configuration uniquely maintains displacement insensitivity to folding degree even at elevated mass fractions (≈3%) and is capable of achieving target displacements with significantly lower reinforcement mass, thereby demonstrating superior nanoscale efficiency and structural adaptability. Additionally, for long shells (L > 2.0 m), the influence of the small base radius on natural frequency diminished, confirming that slenderness became the dominant parameter governing the dynamic response.