On the formulation of a high-order discontinuous finite element method based on orthogonal polynomials for laminated plate structures

Abstract

Laminated plate structures are analyzed by a discontinuous finite element method with emphasis on determining the transverse shear and normal stress components at the interface of adjacent layers accurately. A Consistent Orthogonal Basis Function Space is used for the interpolation of the displacement field and the traction field between two adjacent layers. The mass matrix of the laminated plate becomes diagonal. Moreover, it is observed that the basis functions are very similar to the vibration mode shapes, even through we do not solve any eigenvalue problem in their generation. These basis functions are uniquely determined by the structure's configuration and associated boundary conditions. The stress field between the layers can be accurately calculated, even for the region near the boundaries that might have sharp stress gradients. Several numerical examples are studied with different boundary conditions. The results for both the deformation and the stress components are compared with the traditional finite element method, especially in terms of the number of degrees-of-freedom (DOF) used in the proposed method and the classic FEM. It is observed that the proposed method is able to use a much fewer number of DOF than that of commercial FEM software (ANSYS etc) to obtain accurate solutions to both the deformation of the plate and the stress field between adjacent layers.