Improved finite element analysis of multilayered, doubly curved composite shells

An improved finite element model for the bending and free vibration analysis of doubly curved, laminated composite shells having spherical and ellipsoidal shapes is presented. The present formulation is based on the stress resultant-type Koiter's shell theory and no restriction is imposed on the magnitude of curvature components to capture the deep and shallow shell cases. The twist curvature component is incorporated along with the normal curvatures to keep the strain equations complete. Transverse shear deformation is also considered according to Mindlin's hypotheses. Both the Lagrangian and Serendipity families of isoparametric elements are incorporated in the analysis code to study their performance in different problems. The present five-DOF shell formulation is kept sufficiently general to capture both the bending- and membrane-dominated problems. The accuracy and efficiency of the proposed finite element are illustrated by examples and are compared with those existing in the open literature. The comparison shows that the present analysis yields accurate results with a relatively small number of elements.