Elastic Model for Polyethylene Terephthalate Fibre Reinforcement Structures: Application in Free Vibration Analysis of FG-TPMS Shell Panels in Concrete (PET-FG-TPMS)

Abstract This paper investigates new frameworks for Polyethylene Terephthalate fiber-reinforced functionally graded triply periodic minimal surface shells (PET-FG-TPMS) with concrete material. We propose one functional classification framework focused on controlling mass density, elastic modulus, and shear modulus, with an average porosity of 0.35. The study examines three plate-based TPMS structures: Primitive, Gyroid, and I-Wrapped Package-graph. Free vibration analyses of the plates and shell are performed using a theoretical model with three-dimensional isogeometric analysis (3D IGA). Critical parameters like porosity coefficient, TPMS type, inclusion types, and volumes of the two material phases are thoroughly explored. Their effects on the plate response are presented for different thicknesses. The mass density framework is particularly promising for comparing different TPMS structures, with the TPMS compensating for the stiffness deficit of PET reinforcement, as assessed through fundamental vibration frequencies. Each type of TPMS has its advantages with different PET reinforcement ratios. This study aims to advance the development of concrete PET-FG-TPMS plates and shells, highlight the impact of various functional classification frameworks, and guide the design of lightweight, mechanically efficient structures.