Calculating 3D Stresses in Layered Composite Plates and Shells

Advanced failure criteria for fibre composites must take into account all the six components of the stress tensor. This is an important requirement especially in the case of compression transversally to the fibre direction. Failure then will appear in a transsverse shearing mode which may cause severe damage in adjacent layers. Transverse normal stress plays an important role in the initiation of delamination. Plate and shell analysis, however, is duly performed by assuming a plane state of stress. This results in global displacements as well as cross sectional forces and moments which depict the reality with suitable accuracy. Starting from these results, equilibrium conditions can be applied to determine the local stress components in transverse direction. Therewith, the transverse shear stresses require that the first derivatives and transverse normal stress, even the second derivatives of the membrane stresses should be known that demand higher order approximations of the global solution. For plate problems, this deficiency can be eased up. Under the assumption of two cylindrical bending modes, the shear stress distribution over the thickness can be obtained from equilibrium conditions. With a linear distribution of the membrane displacements, the shear stresses turn out to be layerwise quadratic. Thus, a direct dependency is established between the transverse shear stresses and forces. This procedure reduces the order of differentiation by one, so that standard finite plate elements with quadratic displacement approximations are sufficient to determine the transverse shear and normal stresses in layered composites. For shell problims, the influence of membrane forces on the transverse stresses is essential and cannot be negleceted. In order to demonstrate applicability of the procedure, the stress distributions will be presented for layered composite structures of different geometric dimensions and various stacking orders under mechanical as well as thermal loads. A compatison with results obtained from 3D analyses as well as from the numerical solutions shows excellent accuracy and efficiency of the procedure proposed