Geometrically Nonlinear Analysis of Plate Bending Problems

In the previous six chapters, we have discussed the application of T-elements to various linear problems. This approach can also be used to solve both geometrically [8-10,12] and materially [1,18] nonlinear problems. The former are treated in this chapter and the latter are addressed in Chapter 8. The first application of T-elements to nonlinear plate bending problems was by Qin [8], who presented a family of hybrid-Trefftz elements based on a modified variational principle and the incremental form of field equations. In his report, exact solutions for the Lamé-Navier equations are used for the in-plane intra-element displacement field and an incremental form of the governing equations is adopted. With the aid of the incremental form of these equations, all nonlinear terms may be taken as pesudo-loads. Moreover, some modifications have been made on nonlinear boundary equations to simplify the corresponding derivation. As a result, the in-plane and out-of-plane equations are uncoupled, and then the derivation for the HT FE formulation becomes very simple. In this chapter, a family of hybrid-Trefftz elements is presented for nonlinear analysis of plate bending problems which include post-buckling problems of thin plates and large deflection of thick plates with or without elastic foundations.