Mechanical Behavior of Functionally Graded Viscoelastic composite Sandwich Panels with Graphene Platelet-Reinforced Face sheets under static pressure

This study presents a mechanical analysis of sandwich panels composed of composite facesheets reinforced with graphene platelets (GPLs) and a functionally graded viscoelastic (FGVE) core. The viscoelastic behavior of the core is characterized using Boltzmanns superposition principle and a Prony-series representation. The governing equations are derived based on threedimensional elasticity theory and reformulated within a statespace framework through the corresponding stressstrain relations. To evaluate the timedependent viscoelastic response, the Boltzmann integral is transformed into the Laplace domain and subsequently inverted to the time domain using Durbins numerical inversion technique based on Fourier series. The structural response is examined under various boundary conditions, including simply supported, clamped, and free edges. Analytical solutions are obtained for simply supported configurations via Naviers method, while general boundary conditions are treated using the differential quadrature method (DQM), providing efficient and accurate computation of static responses. The proposed formulation is validated against available benchmark solutions. Parametric studies are conducted to investigate the influence of geometry, material gradation, GPL distribution patterns, boundary conditions, and lengthtoradius ratio on the overall behavior of the sandwich structure. To the best of the authors knowledge, the mechanical behavior of sandwich panels with a functionally graded viscoelastic core has not been previously reported in the literature. This study presents the first unified theoretical framework capable of capturing the coupled effects of core viscoelasticity, functional grading, and GPL reinforcement. Moreover, the combination of Laplace-domain transformation and statespace formulation for FGVE sandwich panels offers a novel and computationally efficient approach for predicting time-dependent structural responses. The results provide useful insights for the design and optimization of advanced FG viscoelastic sandwich panels with improved mechanical performance.