Non-linear analysis of laminated composite and sigmoid functionally graded anisotropic structures using a higher-order shear deformable natural Lagrangian shell element

Finite element solutions based on the higher-order shear deformation theory are presented for the geometrical non-linear analysis of through-thickness functionally graded plates and shells. Natural co-ordinate-based higher-order transverse shear strains are used in present shell element. The fiber orientation of plates and shells is assumed to vary according to a sigmoid distribution in terms of the volume fractions of the constituents. The formulation of a non-linear 9-node Element-based Lagrangian shell element is presented and natural co-ordinate-based strains are used in present shell element. Using the assumed natural strain method the present shell element generates neither membrane nor shear locking behavior. Numerical results of the linear and non-linear analysis are presented to show the combined effect of the fiber orientation, loading conditions, aspect ratios and side-to-thickness ratios on the mechanical behaviors. Besides, a comparison of the non-linear results of isotropic and anisotropic functionally graded structures is investigated.