Natural vibrations of variable-thickness truncated spherical shells with functionally graded bio-inspired anisotropic TPMS materials using 3D NURBS-based discretization method

In the urgency of the United Nations’ Sustainable Development Goals for sustainable infrastructures (SGD 9) and cities (SDG 11), the development of lightweight, vibration-resistant shell structures is essential for aerospace, architectural, and civil engineering applications. This study introduces a new variable-thickness truncated spherical shell composed of bio-inspired Rotating Triply Periodic Minimal Surface (RotTPMS) materials via their natural vibration characteristics. A three-dimensional isogeometric analysis (IGA) framework based on NURBS solid modeling is employed to precisely capture both complex shell geometry and graded material behavior. Unlike traditional finite element methods (FEM), Non-Uniform Rational B-Splines (NURBS) enable accurate representation of curved shells with significantly fewer elements, but still ensure accuracy. The proposed framework systematically analyzes the effects of TPMS topologies (Primitive, Gyroid, and IWP), porosity distribution patterns, crystalline orientation, and shell opening ratio ([Formula: see text]) on fundamental frequencies of these porous shells. It is observed that the porosity distribution and rotation angle of RotTPMS allow for an enhancement in natural frequency up to [Formula: see text], with only [Formula: see text] solid material, while maintaining more than [Formula: see text] of the vibration performance of fully solid isotropic structures. In addition, the study also reveals that RotTPMS, in its current fixed-rotation form, may not be optimal for curved geometries in terms of structural performance. The mismatch between globally fixed crystalline orientations and the spatially varying through-thickness directions in shells can be the key reason that limits the effectiveness of microstructural anisotropy in complex shapes. Overall, this research demonstrates the feasibility of combining RotTPMS materials with IGA modeling for vibration-sensitive shell structures, laying the foundation for future work on curvature-adaptive material orientation to unlock the full potential of programmable mechanical metamaterials.