Large deflections of functionally graded sandwich beams with influence of homogenization schemes

Functionally graded materials (FGMs) are increasingly used in sandwich construction to improve mechanical performance of structures. The effective material properties used in modelling FGM structures, however, are dependent on a chosen homogenization scheme. For the first time, the influence of different homogenization schemes on large deflections of dual-phase FGM sandwich beams is studied in this paper by using a nonlinear finite element procedure. The material properties of the sandwich beams are considered to vary in the thickness direction by a power function. Four homogenization schemes, namely the schemes due to Voigt, Mori–Tanaka, Hashin–Shtrikman and Tamura–Tomota–Ozawa, are employed to estimate the effective elastic moduli of the beams. Based on the total Lagrange formulation, a first-order shear deformable nonlinear beam element is formulated and employed in the study. Newton–Raphson iterative method is used in combination with the arc-length technique to obtain the large deflection curves and stress distribution of the beams. Numerical results reveal that the material distribution indicated by the material grading index and the homogenization scheme have play an important role on the behaviour of the beams, and the influence of the material grading index on the large deflection response is dependent on the homogenization scheme. Among the four homogenization schemes studied, it is shown that the large deflection response obtained by the Voigt model is more conservative than that using the other schemes.