Geometrically nonlinear analysis of laminated composite thin shells using a modified first-order shear deformable element-based Lagrangian shell element

The formulation of a nonlinear composite 9-node modified first-order shear deformable element-based Lagrangian shell element is presented for the solution of geometrically nonlinear analysis of laminated composite thin plates and shells. The application limit of modified shear deformation theory is presented for the correct analysis of composite laminates. However, it is evident that it results in a parabolic distribution of the transverse shear strains and satisfies the zero transverse shear stresses requirements at the shell surfaces. It also requires insignificant modifications to be implemented in existing displacement-based first-order shell elements. Natural co-ordinate-based higher-order transverse shear strains are used in present shell element. Using the assumed natural strain method the present shell element generates neither membrane nor shear locking behavior. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear analysis of plates and shells or for the geometrically nonlinear analysis of laminated composite thin plates and shells with large displacement but small strain.