Free vibration analysis of functionally graded shells using an edge-based smoothed finite element method

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the stiffness matrices are obtained by using the strain-smoothing technique over the smoothing domains that are formed by two adjacent MITC3 triangular shell elements sharing an edge. The strain-smoothing technique can improve significantly the accuracy and convergence of the original MITC3. The material properties of functionally graded shells are assumed to vary through the thickness direction by a power-rule distribution of volume fractions of the constituents. The numerical examples demonstrated that the present ES-MITC3method is free of shear locking and achieves the high accuracy compared to the reference solutions in the literature. © 2019 by the authors.