A hybrid discontinuous Galerkin semi-discrete finite element method for skewed and curved laminated beams/plates/shells based on Delta function

Abstract

A hybrid discontinuous finite element method based on Delta function is developed for skewed and curved laminated beams/plates. Equal-order interpolations for displacement field and interface stress field are obtained without numerical oscillations. For the displacement field, the Consistent Orthogonal Basis Function Space is applied. For the interface stress field, the Delta function is used as basis functions. Two types of Delta functions are discussed. For the first type, the Delta function is defined uniformly on the interface. For the second type, the Delta function is defined on the Gauss points. It is observed that the numerical oscillation occurs in the first type for a large deformation analysis. For the second type, it is always numerical stable. The effect domain of the Delta function is discussed such that the stress on the interface is able to be calculated.The laminated plate and beam with clamped boundary conditions are studied. The interface shear stress is compared with ANSYS. Numerical oscillation is not observed for the second type Delta function with equal-order interpolations of displacement and interface stress. Skewed and curved laminated plates are also analyzed. The accuracy is still good for various angles between adjacent edges and various curvatures.