Geometry-consistent strain energy-based modelling, optimization, and dynamic response analysis of structures composed of re-entrant honeycomb cellular solids

In the present work, a geometry-consistent decoupled strain energy-based analytical framework is developed to derive closed-form expressions for the effective mechanical properties of re-entrant honeycomb (REH) cellular structures. To facilitate this, an independent deformation behavior of inclined and straight ligaments constituting the complete unit-cell architecture, is evaluated. Unlike conventional homogenized formulations based on uniform ligament behavior, the proposed framework enables member-wise identification of stiffness contribution and load transfer mechanisms governing the effective elastic response of the cellular structure. The decoupled formulation further facilitates selective geometric tailoring of mechanically dominant ligaments, thereby enabling simultaneous enhancement of stiffness, lightweight Ness and load-carrying capability without uniformly increasing ligament thickness throughout the structure. A geometry-consistent multi-objective optimization framework is subsequently developed to maximize stiffness-to-weight efficiency through selective ligament-wise thickness redistribution under density-based constraints. The optimized configurations demonstrate approximately 30% to 60% improvement in relative stiffness while preserving lightweight structural characteristics. Finally, the practical applicability of the optimized REH cellular architecture is investigated through finite element-based dynamic analysis of robotic manipulator links modeled using equivalent homogenized properties. The obtained displacement--time decay and frequency response analyses demonstrate improved vibration attenuation capability, enhanced dynamic stability, and reduced resonance sensitivity of the optimized configurations. Overall, the proposed framework provides a computationally efficient methodology for designing lightweight cellular structures with tunable mechanical properties suitable for advanced robotic and lightweight structural engineering applications.