Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method

A layerwise shear deformation theory for functionally graded (FGM) sandwich shells and laminated composite shells is discretized using a differential quadrature finite element method (DQFEM). The DQFEM is a weak-form differential quadrature method that can provide highly accurate results using only a few sampling points. The layerwise theory proposed by Ferreira is based on an expansion of Mindlin's first-order shear deformation theory in each layer. The combination of the DQFEM with Ferreira's layerwise theory allows a very accurate prediction of the field variables. Effective material properties of the FGM are estimated according to both Voigt's rule of mixture (ROM) and Mori-Tanaka (MT) scheme. The DQFEM solutions were compared with various models in literature and especially showed very good agreements with results based on layerwise theories. The analysis of FGM sandwich and laminated composite shells based on Ferreira's layerwise theory indicates that the DQFEM is an effective method for high accuracy analysis of large-scale problems.