Nonlinear Finite Element Analysis

IUSS Pavia
EE - Earthquake Engineering
Fall 2004
Date (from - to):
09/11/2004 – 10/12/2004

The goal of the course is to present theory and applications of the finite element method for linear and non-linear problems. After some preliminaries, the course will focus on mixed and/or enhanced approaches for the solution of linear problems and on possible numerical treatments for the solution of non-linear material problems. Finally, the course will briefly address coupled thermo-mechanical problems and non-linear geometrical problems.
Emphasis will be on the theoretical developments as well as on the implementation and coding of three-dimensional finite elements together with the relative numerical algorithms within the research-oriented finite element code FEAP.
Contents. Preliminaries: strong and weak forms for linear thermal and mechanical problem. Mixed Hellinger-Reissner and Hu-Washizu formulations. Enhanced formulations. Viscoelasticity, plasticity and visco-plasticity with corresponding return-map integration algorithms. Solution of coupled problems. Treatment of finite deformation mechanical problems

Suggested readings:

Before the course:

  • Plasticity theory, by J. Lubliner (introductory parts).
  • Mechanics of Solid Materials (introductory parts).
  • FEAP user manual (, ,

During the course:

  • The Finite Element Method, by O.C. Zienkiewicz and R.L. Taylor [vol. 1: Ch. 11, 12, 19; vol. 2: Ch. 3, 10].
  • The Finite Element Method, by T.J.R. Hughes [Ch. 4].
  • Computational Inelasticity, by J.C. Simo and T.J.R. Hughes.