Flexural analysis of functionally graded sandwich plates with a novel mixed finite element formulation using quasi-3d higher order shear deformation theory

This research focuses on the modeling and analysis of Functionally Graded (FG) plates featuring a sandwich core, utilizing a generalized Higher-Order Shear Deformation Theory (HSDT) that accounts for transverse stretching effects. This framework proposed facilitates the customization of different shear functions specifically designed for functionally graded materials (FGMs), thereby ensuring the inclusion of thickness stretching considerations (εz≠0). The governing equations are derived through the application of the Hellinger-Reissner variational principle, which guarantees the stationarity of the functional. As a result, a finite element (FE) formulation is developed, incorporating two separate field variables: displacements and stress resultants. To discretize the domain of the FG plate, four-node quadrilateral elements are utilized. Initially, the functional necessitated C1 continuity; however, by employing the two-field characteristic of the mixed finite element (MFE) approach, integration by parts is utilized, which effectively reduces the C0 continuity requirement. This approach successfully captures the nonlinear and parabolic distribution of transverse shear stresses in FG sandwich plates (FGSPs). Within the use of various shear functions, the outcomes remain theoretically aligned with elasticity-based solutions and the proposed HSDT model. Furthermore, the inclusion of transverse stretching markedly improves the accuracy of bending behavior predictions for FGSPs when compared to traditional theories.