ME593

ME 563 - Nonlinear Finite Elements
Spring 2011
MWF: 12:20-01:10 am 110 Walker

Instructor:         Professor Pan Michaleris
                              232 Reber Bldg
                              863-7273
                              pxm32@psu.edu
                              Office hours: Monday 1:20-2:00pm, Wednesday: 11:05-12:00noon

Text:

Class notes (password given to registred students)

Supplementary text:

T. Belytscho, W.K. Liu, and B. Moran. Nonlinear Finite Elements for Continua and Structures. Wiley, NY 2000.

K.-J. Bathe. Finite Element Procedures. Prentice Hall, NJ 1996. ISBN: 0133014584

M.A. Crisfield. Non-linear Finite Element Analysis of Solids and Structures . Volume 1, Wiley, NY 1991.

R.D. Cook, D.S. Malkus, and M.E. Plesha. Concepts and Applications of Finite Element Analysis. Wiley, NY 1989.

T.R. Chandrupatla and A.D. Belegundu. Introduction to Finite Elements in Engineering. Prentice Hall, NJ 1997.

References on Matlab:

Amos Gilat. Matlab. An introduction with applications. John Wiley. 2004. ISBN: 0-471-43997-5.

D. M. Etter, D. C. Kuncicky, D. Hull. Introduction to MATLAB 6, Prentice Hall 2001. ISBN:0-13-032845-5.

D. Hanselman, B. Littlefield. Mastering MATLAB 6, A comprehensive tutorial and reference, Prentice Hall 2001. ISBN:0-13-019468-9.

E. B.Magrab, S. Azarm, B. Balachandran, J. Duncan, K. Herold, G. Walsh. An engineer's guide to MATLAB,
Prentice Hall 2000. ISBN : 0-13-011335-2.

Prerequisites: ME/EMCH 461 or EMCH 560 or AGE 513

Announcements , Grading Policy , Class Objectives , Tentative Schedule , Projects , Links

Announcements:

The following dates we meet at 316 Hammond:

Grading Policy:

Biweekly (computer) projects (70%)
Final computer project (30%)
No exams.

Class Objectives:

The objective of this course is to introduce the theory and application of the finite element method for non-linear systems. Non-linearities arising from both material behavior and large deformations will be discussed.

Applications of non-linear finite element methods include:

Modeling of structures with non-linear material properties
Modeling of structures with large deformations
Buckling and post buckling deformation
Elastodynamics and crash, impact, explossive modeling
Material processing
Bioengineering
Nanotechnology

The course will involve both code development in either Matlab, C or Fortran to demonstrate the finite element formulation. Commercial software such as Ansys and Abaqus will be used to demonstrate the method in case studies.

The course is suited to graduate students in Architectural, Bio-, Civil, Mechanical, Industrial, and Manufacturing Engineering and Material Science.

Tentative Outline

Introduction to iterative and incremental solution procedures
Material nonlinearity:

nonlinear heat transfer
nonlinear elasticity
elasto-plasticity
visco-elasticity

Geometric nonlinearity:

continoum mechanics review
total and updated Lagrangian formulations
coupled material-geometry nonlinearity

Explicit methods
Contact analysis

Friction less contact

Dynamic structural analysis

Implicit and explicit methods of solution

Fluid Dynamics

Projects

P1, due Jan 21 (solution soln: 2dof.pdf, sp2.m)
problems 3.1 (Full NR only) and 3.2 from notes, due Feb 11
problem 3.4, due Feb 25
P4, due March 18

Final project, due in class the week of April 24.

Links

Dflux umat
Abaqus Heat Transfer tutorial

Elastic umat.f, Elasto-plastic umat2.f

2D elasticity codes: el2d2.m, qua4b.m, qua4b1.m

selectivelly reduced integration qua4 element: qua4b2.m

2D plasticity codes (HW5): el2de.m, qua4b1.m, plastt2d.m

1D explicit elastodynamics explicit1d.m, bar1dex.m

Unix Systems Group
Quick Summary of Unix Commands
Unix Intro
Linear FEA