On mechanical behavior of two-layer functionally graded sandwich curved beams resting on elastic foundations using an analytical solution and refined Timoshenko beam theory

For the first time, static bending, free vibration, and buckling studies of the two-layer functionally graded sandwich (TFGS) curved beams resting on Pasternak’s foundation utilizing the analytical precise solution and the refined Timoshenko beam theory (RTBT) are carried out in this study. The curved beam system is composed of two layers of single curved beams that are connected together by shear connectors. Each single curved beam layer is constructed entirely of FG sandwich material, including the bottom surface, core, and top surface. With the introduction of the new distribution shape function, it is possible to get a parabolic distribution of the transverse shear strain and shear stress throughout the whole thickness of the beam, with zero values at the beam's surfaces. The Navier solution is used to investigate the static bending, free vibration, and buckling of simply supported TFGS curved beams. The modified beam theory has been shown to be effective for analyzing the static bending, free vibration, and buckling responses of the beam system. The comparison of the deflection, normal and transverse shear stresses, natural frequency, and mechanical buckling load of curved beams computed using this proposed theory and other methodologies illustrates the new theory's correctness and effectiveness. Additionally, the influence of parameters such as the upper and lower layers' material volume exponents, the material ratio, the open angle, the thickness ratio, and the elastic foundation stiffness is explored. The study finding of this paper are really significant in terms of calculation and application in engineering practice. Contributing to the advancement of numerical computational mechanics by enhancing its development. Moreover, this is a critical and credible resource for future research on this sort of construction.