Advanced modeling of nonlinear bending behavior in functionally graded graphene nanoplatelet reinforced composite structures

Abstract

This study investigates the applicability of nanomaterial-based structural components in earthquake engineering and proposes a high-accuracy analytical model for their nonlinear mechanical performance. The research focuses on the nonlinear bending response of functionally graded composite beams reinforced with graphene nanoplatelets (FG-GPLRCs), where material properties vary continuously along the thickness of the section. To accurately describe the complex deformation mechanisms under different loading conditions, an energy-based analytical framework is adopted using the Higher Order Shear Deformation Theory (HSDT) proposed by Touratier. Traditional beam theories provide reasonable accuracy for small deflections but fail to capture the coupled effects of geometric and material nonlinearities that become significant at higher deformation levels. This limitation is critical for structures subjected to dynamic and cyclic loads such as seismic actions. The model developed in this study formulates a generalized equilibrium system incorporating higher order displacement components, shear deformations, and off-axis stresses to represent nonlinear bending behavior with high precision. By applying the total potential energy principle, the governing equations and boundary conditions are derived from the stationary condition of energy, yielding a unified formulation applicable to both thin and thick beams under various boundary and loading conditions. The main objective of the research is to develop a theoretical model that can represent the complex deformation of functionally graded graphene nanoplatelet reinforced composite beams under different loads while accounting for both geometric and material nonlinearities. The originality of the study lies in integrating geometric nonlinearity and functional material gradation within a single analytical framework, providing a more accurate understanding of how high-stiffness and high-energy-absorption composites behave under extreme conditions without causing irreversible damage. Functionally graded materials (FGMs) are advanced composite systems in which two or more constituent materials are continuously distributed through the thickness of the structural element, thereby eliminating interfacial stresses and delamination issues. This continuous gradation enhances the mechanical and thermal properties, leading to improved structural integrity and energy absorption capacity. In FG-GPLRC systems, graphene nanoplatelets are embedded in a polymer matrix with specified weight fractions and thickness-dependent distributions. Due to their outstanding elastic modulus and tensile strength, even a small amount of graphene reinforcement significantly increases stiffness and strength. Literature studies have shown that a one percent weight fraction of graphene can yield mechanical properties comparable to those of carbon nanotube reinforced composites. The analyses in this research demonstrate that the distribution function, concentration ratio, and thickness profile of graphene nanoplatelets considerably affect structural performance. Parametric studies were performed for different GPL distribution types, including bottom-concentrated, top-concentrated, and symmetric configurations, as well as for various boundary conditions such as simply supported and clamped beams. The results indicate that functionally graded distributions produce more balanced deformation profiles and improved energy dissipation capacities compared to homogeneous distributions. From an earthquake engineering perspective, the outcomes of this study are particularly significant. Conventional reinforced concrete and steel structures dissipate seismic energy through plastic deformation, which leads to residual damage and costly repairs. In contrast, FG-GPLRC structures can provide superior strength and damping capacity within the elastic range, allowing for the development of lightweight, sustainable, and damage-resistant structural systems. The results further show that Touratier's HSDT-based model delivers more accurate predictions than classical beam theories, especially in representing through-thickness shear behavior without requiring correction factors. The literature review reveals that while FG-GPLRC materials have been extensively studied in mechanical and aerospace contexts, their potential applications in earthquake engineering have received limited attention. Yee et al. (2022) demonstrated the efficiency of an energy-based nonlinear bending analysis for graphene reinforced composites, validating the relevance of HSDT formulations. Building upon this foundation, the present research extends the method to boundary and loading conditions representative of seismic actions. This provides a theoretical and analytical bridge between nanoscale material innovation and macroscale structural resilience. The findings of the study indicate that functionally graded graphene nanoplatelet reinforced composites can be effectively utilized in components such as bridge girders, base isolation systems, and energy dissipative connectors. These materials offer enhanced energy storage and recovery capability, enabling structures to withstand large deformations elastically. Consequently, this study contributes to the development of performance-based earthquake engineering by integrating nanomaterial advancements into the design of high-efficiency, low-maintenance, and sustainable structural systems.