Finite Element Analysis of Nonlinear Structures

The principle of virtual work is employed to derive general relations governing geometrically nonlinear structural behavior. From these basic relations, three general finite-element analysis models, namely, potential energy, direct and incremental, are formulated for nonlinear pre- and post-buckling analyses. In addition, a quadratic eigenvalue model is developed for the prediction of critical load levels. The analysis models are expressed in matrix notation within the framework of the finite-element technology and an inter-consistency is observed among the component matrices. These matrices are given geometrical interpretation and a hierarchy of nonlinearity is developed. Specific representative finite elements are considered and alternative computational procedures are associated with the several levels in the hierarchy of nonlinearity. Recommendations are made concerning the conduct of geometrically nonlinear finite-element analysis.