Geometrically nonlinear analysis of functionally graded shells using an edge-based smoothed MITC3 (ES-MITC3) finite elements

Abstract

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of shells. In this study, the ES-MITC3 is extended to the geometrically nonlinear analysis of functionally graded shells. In the ES-MITC3, the stiffness matrices are obtained using the strain smoothing technique over the smoothing domains that formed by two adjacent MITC3 triangular shell elements sharing an edge. The material properties of functionally graded (FG) shells are assumed to vary through the thickness direction by a power rule distribution of volume fractions of the constituents. The nonlinear finite element formulation based on the first-order shear deformation theory with the von Karman’s large deflection assumption is used to describe the large deformations of the FG shells. Several numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods.