A new finite element for the analysis of functionally graded shells

Abstract

This paper presents the development of a finite element model for functionally graded shells. The formulation solves the equations of the Stress Approach Model for Functionally Graded shells (SAM-FG) developed and validated by Rubio Rascón et al. (2020). SAM-FG involves only 5 generalized displacements and its equations differ from those of classical first order shear deformation theories mainly in the expressions of the generalized stiffnesses and the approximation of stresses. A 10-node isoparametric triangular element using cubic shape functions and 5 degrees of freedom per node is proposed. The equations of the numerical method were implemented in a program called FESAM-FG. The finite element code enables to calculate and visualize generalized fields on the middle surface of the shell and stress components at a given position across the thickness of the structure. To test the accuracy and convergence of FESAM-FG results, the numerical tool is applied to the structural analysis of four families of functionally graded shells with various distributions of material properties and thickness-to-radius ratios. Results are compared to those obtained by solid finite elements, a higher order shear deformation theory developed by Viola et al. (2014) and two shell models used for laminated composite structures: an equivalent single layer model and a layerwise model, both using 30 fictitious layers.