Buckling analysis of functionally graded plates subjected to combined in-plane loads

The displacement field components of functionally graded plates (FGPs) couple the equilibrium equations due to the bending-extension interaction. There is no general study of FGPs buckling loads subjected to the combination of all in-plane loads in the literature. This study develops an analytical approach to finding the buckling coefficients of FGPs under combined biaxial and shear loads. The generalized integral transform technique (GITT) is simultaneously applied to the coupled buckling equations for the first time. Then, the partial differential equations are transformed into a set of linear equations, leading to the corresponding eigenvalue problem, which may be coded in Python’s programming language. The uniaxial (pure) buckling coefficients are initially obtained considering the power law and the rule of mixture approximations (including the Voigt, Modified, or Reuss models). Then, some interaction curves are developed for the biaxially and multi-axially loaded plates. The interaction curves are normalized versus the uniaxial buckling coefficient for fully clamped plates, so they only depend on the plate aspect ratio. Accordingly, a step-by-step procedure is presented for all loading states, including compression–compression–shear (CCS), compression–tension–shear (CTS or TCS), and tension–tension–shear loads (TTS).