Functionally Graded Beams Resting on Foundations: A Review of Modelling, Analysis and Future Research Directions

The analysis of beams resting on elastic foundations has attracted significant attention in structural and mechanical engineering due to its extensive applications in different domains. Beams on elastic foundations interact continuously with deformable media. To represent this interaction mathematically, researchers have developed a variety of single-parameter, two-parameter and three-parameter models as well as continuous models. Among the structural elements employed to investigate these models, functionally graded material (FGM) beams have emerged as an attractive platform due to their continuously varying material properties and extensive use in modern engineering applications. Over the past two decades, extensive research has been conducted on the behavior of graded beams resting on elastic foundations using various beam theories, foundation models and analytical as well as numerical solution techniques. The present paper puts forward a detailed review of the existing literature concerning static bending, buckling, free and forced vibration analyses of FG beams supported by elastic foundations. Various material gradation schemes, including power law, exponential, sigmoid, porous and carbon nanotube-reinforced FGMs, are discussed. The review further examines the application of different foundation models such as Winkler, Pasternak, Kerr, Vlasov and nonlinear elastic foundations. A comparative evaluation of the available studies is provided to identify current trends and limitations. Finally, potential future research directions involving multi-physics coupling, advanced foundation modelling, machine-learning-assisted prediction and micro/nano-scale applications are highlighted. The review aims to serve as a valuable reference for researchers and engineers working in the field of FG beams interacting with elastic foundations.