Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory

The paper presents the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter being the drilling degree of freedom. The material law is derived by through-the-thickness integration of the Cosserat plane stress equations. The constitutive equations are formulated with respect to the neutral physical surface. The influence of the power-law exponent, micropolar characteristic length is evaluated in geometrically nonlinear FEM analyses. The results obtained with the neutral physical surface approach are compared with those computed with the middle surface approach. The influence of choice of the reference surface is observed especially in nonlinear stability analysis.