Prerequisites:

ME 551 or equivalent (an introductory finite element course)

Textbooks:

J.N. Reddy, "An Introduction to Nonlinear Finite Element Analysis", Oxford University Press, 2004
H.U. Akay, "Supplementary Notes for ME 551," IUPUI, 2006

Description:

Various algorithms for nonlinear and time-dependent problems in two and three dimensions. Emphasis on advanced applications with problems chosen from fluid dynamics, heat transfer, and solid mechanics areas. Independent project required.

Goals:

To introduce to students several advanced topics which are not covered in sufficient detail in an introductory course. Solution of nonlinear and time- dependent problems in two-and three-dimensions are studied. Aims at giving the students a chance to investigate practical problems of their interest in detail.

Topics:

1. Mathematical preliminaries (2 classes)
2) Finite element preliminaries (2 classes)
3. Nonlinear heat transfer and other field problems in one-dimension (2 classes)
4. Nonlinear bending of beams (2 classes)
5. Solution procedures for linear and nonlinear algebraic equations (2 classes)
6. Nonlinear heat transfer and other field problems in two-dimensions (2 classes)
7. Nonlinear bending of elastic plates (2 classes)
8. Flow of viscous incompressible fluids (2 classes)
9. Nonlinear analysis of transient problems (2 classes)
10. Compressible flows (2 classes)
11. Finite element formulations of solid continua (2 classes)
12. Material nonlinearities (2 classes)
13. Solid-fluid interactions (2 classes)
14. Parallel computing (2 classes)
15. Tests (2 classes)

Note: one class = 75 minutes