Nonlinear analysis of thick plates on an elastic foundation by HT FE with p-extension capabilities

Abstract

The paper is concerned with the development of hybrid-Trefftz (HT) p-element for nonlinear analysis of Reissner-Mindlin plates resting on an elastic foundation. The foundation may be of Winkler-type or Pasternak-type. Exact solutions of the Lame-Navier equations are used for the in-plane intraelement displacement field and an incremental form of the basic equations is adopted. With the aid of incremental form of these equations, all nonlinear terms may be taken as pseudo-loads. Moreover, some modifications have been made on the nonlinear boundary equations to simplify the ensuing derivation. As a result, the in-plane and out-of-plane equations are uncoupled, and then the derivation for the HT finite element (FE) formulation becomes very simple. The practical efficiency of the new element model has been assessed through several examples.