AN INVESTIGATION INTO GEOMETRICALLY NONLINEAR-ANALYSIS OF RECTANGULAR LAMINATED PLATES USING THE HIERARCHICAL FINITE-ELEMENT METHOD

Abstract

The geometrically nonlinear analysis of laminated composite rectangular plates is studied using the hierarchical finite element method (HFEM). The derivation of the equilibrium equations and tangential stiffness matrix are given. Symbolic computation is used to calculate the high-order polynomial integrals needed to establish the stiffness matrices. The Newton-Raphson method is used in the iterative procedure. The convergence property and the numerical stability of the method are discussed. The influence of in-plane displacements on the geometrically nonlinear deformation is also discussed. The results of static analyses indicate that the extension of HFEM to geometrically nonlinear analysis of laminated rectangular plates is very successful. It is believed that this scheme can be easily applied to geometrically nonlinear dynamic analysis of laminated plates.