Nonlinear Finite Element Analysis

Institution:
IUSS Pavia
Specialization:
EE - Earthquake Engineering
Term:
Spring 2007
Teacher(s):
FERDINANDO AURICCHIO
Credits:
6
Date (from - to):
25/06/2007 – 20/07/2007
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:

Required Reading (before the course) The Finite Element Method, by O.C. Zienkiewicz and R.L. Taylor [vol. 1: Ch. 1, 2, 3, 4, 6, 7, 8, 9, 10; vol. 2: Ch. 1, 2]. The Finite Element Method, by T.J.R. Hughes [Ch. 1, 2, 3]. Suggested Reading (before the course) Plasticity theory, by J. Lubliner (introductory parts). Mechanics of Solid Materials (introductory parts). FEAP user manual (http://www.ce.berkeley.edu/~rlt/feap/manual.pdf, http://www.ce.berkeley.edu/~rlt/feap/example.pdf, http://www.ce.berkeley.edu/~rlt/feap/) Suggested Reading (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.