Finite Element Plate Formulation Including Transverse Shear Effects for Representing Composite Shell Structures

Abstract

A finite element formulation for the analysis of thin to moderately thick laminated composite shell structures is presented. A plate type element is developed with shear effects included by relaxing the Kirchhoff-Love hypothesis and prescribing the neu tral surface displacements independently from the rotations. The in-plane layer stresses are calculated using the constitutive equations. Once the in-plane stress variation has been obtained, the equilibrium equations are integrated to obtain the transverse shear and nor mal stresses. Two example problems are considered herein. For symmetric angle-plied or unidirectional winding it has been found that a pressurized cylinder, in addition to expand ing radially, also rotates about its axis. This contradicts the assumption that a symmetri cally wound cylinder under pressure exhibits axisymmetric deformation; thus a full cylin der model must be analyzed to produce the actual deformation. Laminated circular cylindrical shells are also analyzed with both clamped and simply supported ends in order to observe the action of transverse interlaminar shear and normal stresses. It is confirmed that near a load or structural discontinuity (restrained end), interlaminar stresses of con siderable magnitude occur and thus must be taken into account if delamination is to be avoided.