Finite Element Analysis of Composite Plates and Shells

In this chapter, an overview of recent developments on finite element analysis of composite plates and shells are presented. Two major developments in the last decade by the author and his colleagues have been in the formulation of (1) least–squares finite element models of plates and (2) the weak-form Galerkin finite element formulations of first-order and third-order shell theories. The least–squares formulations are based on the first-order shear deformation theory, while the weak-form Galerkin is based on the first-order as well as the third-order shear deformation theories. Results using the weak-form Galerkin finite element model based on improved 7-parameter first-order theory are also included for geometrically nonlinear cases. The least–squares finite element models of plates are based on mixed formulations in which displacements as well as stress resultants are treated as the unknown field variables. The weak-form Galerkin finite element models are displacement-based. In the latter, a family of high-order Lagrange interpolation functions (with equally spaced nodes and Gauss–Lobatto–Legendre nodes) is used to prevent shear locking. Numerical results are presented for a number of benchmark problems involving isotropic, laminated composite, as well as functionally graded plates and shells.