EGM 6352 - ADVANCED FINITE ELEMENT METHODS - Fall 2006

• Instructor : Dr. L. Vu-Quoc, Tel: 392-6227, E-mail: vu-quoc AT ufl.edu.
• Office: 135 NEB (New Engineering Building)
• Classroom: MAE-B 229
• Class time: MWF, period 5 (11:45am - 12:35pm)
• Office hours: MWF, period 9 (4:05pm - 4:55pm)

Course objectives:

• To provide a solid mechanics and mathematical foundations of the finite-element formulation for various engineering applications (heat, fluids, solids, electromagnetics).
• Beyond the basic material for the finite element methods (FEM), among possible topics to be covered are computational singularity / fracture mechanics, X-FEM (extended FEM), geometric and material nonlinearities, homogenization methods, immersed FEM, etc., depending on mutual interests of students and instructor.
• Ultimately, a goal of the course is to introduce students to some of the recent research interests related to the FEM (as exemplified in the list of articles below), and to help provide the necessary (mechanics and mathematics) background for students to read the recent literature in the field. Strategy:
  • Select a representative paper for each field of application (heat, fluids, solids, electromagnetics).
  • Identify the "obscure" mathematical expressions (i.e., "Greek", "Latin", "Sanskrit", etc. :-)) in these papers.
  • Go back to the basics to develop an understanding of these expressions.
  • Read and survey some more of the recent papers in each field; additional suggestions from students are welcomed.
• The course will be taught as a seminar; here, (moderate) "Russian-style seminar" is preferred and highly encouraged.
  NOTE on the "Russian-style seminar": "It encourages listeners to aggressively ask questions right from the start of a talk. At times the main speaker is pushed aside, and things can get downright abrasive." (for more details, see Settling In on Campus, Yudhijit Bhattacharjee, Science, Vol 304, Issue 5675, 1282-1284 , 28 May 2004). The speaker could be the instructor, and the listeners could be the students (but we can do away with being abrasive; in other words, be moderate).
• Projects and in-class presentations (TBA). A possible team project: Install, test, modify some open-source finite element codes. There will be no exams. At the end of the semester, it is possible to have in-class team presentations of papers selected by students.
• This course should be of interest to engineering students in all areas of engineering (computer science, chemical, civil, electrical, mechanical and aerospace, nuclear, etc.).

Prerequisites: Having had a course on FEM would be an advantage, but not necessary, since this course is intended for a wider audience and will be taught from the basics with a bend toward a more rigorous presentation of the FEM and its general applications, and particularly to develop skills in FE formulation.

Textbook: None required.

References:

Books:
addall.com, bestbookbuys.com, bookfinder.com.
• Malvern, L.E. [1969], Introduction to the Mechanics of a Continuous Medium , Prentice-Hall. New = $110.67; Used = $60. Library call No. 531 M 262i. A good reference for continuum mechanics, which is a basic foundation for the finite element method. See also the course EGM 6611 Continuum Mechanics, Fall 2003. Thu, 23 Sep 2004.
• T.J.R. Hughes [2000], The Finite Element Method: Linear Static and Dynamic Finite Element Analysis.
  Format: Paperback ISBN: 0486411818 List Price: $ 26.95 Publisher: Dover Publications; (September 1, 2000).
  Written by an engineer for engineers with a more mathematical bend than the average. Thu, 01 Jul 2004.
• M. Asghar Bhatti, Advanced Topics in Finite Element Analysis of Structures: With Mathematica and MATLAB Computations Wiley (January 3, 2006) ISBN: 0471648078. Fri, 07 Jul 2006.
• Body & Soul: Applied Mathematics Education Reform Project, Books, Software, Software, Education material, Fri, 19 May 2006.
  • Computational Turbulent Incompressible Flow, by J. Hoffman and C. Johnson, Springer 2006. (Preliminary version in pdf file). Including discussions on General Galerkin (G2) method, turbulence modeling, Boltzmann's Statistical Mechanics, etc. Fri, 19 May 2006.
  • Computer code TO BE COMPLETED Thu, 10 Aug 2006.
• J.C. Simo and T.J.R. Hughes, Computational inelasticity TO BE COMPLETED Thu, 10 Aug 2006.
• G. Allaire [2001], Shape Optimization by the Homogenization Method.
  Format: Hardcover ISBN: 0387952985 List Price: $ 79.95 Publisher: Springer-Verlag; 1st edition (October 19, 2001).
  Mathematical aspects of the homogenization theory; application to composite materials, shape optimization for conductivity and elasticity problems; numerical algorithms. The homogenization theory part provides background materials for several multiscale methods. Wed, 14 Jul 2004.
• See my course web page in Fall 2004 for other books of interest on the FEM.

Articles:
• Numerical analysis (essay) by N. Trefethen to appear in Princeton Companion to Mathematics. Mon, 27 Mar 2006.
Fracture mechanics, singularity computation
• Vu-Quoc, L., and Tran, V.X., ``Singularity analysis and fracture energy release rate for composites: Piecewise homogeneous-anisotropic materials'', Computer Methods in Applied Mechanics and Engineering, John H. Argyris Memorial Issue, Vol.195, No.37-40, pp.5162-5197, 15 July 2006. (html, pdf) (toc, Part I, Part II )
Ferroelectric materials and FEM formulation Wed, 20 Sep 2006.
• Y. Su and C.M. Landis, Continuum thermodyanmics of ferroelectric domain evolution: Theory, finite element implementation and application to domain wall pinning preprint, (2006).
• C.M. Landis, Non-linear Constitutive Modeling of Ferroelectrics Current Opinion in Solid State and Materials Science, 8, pp. 59-69, (2004).
• More applications of ferroelectric materials: Electroceramics National Physical Laboratory, UK.
• papers on XFEM
• Simo and Taylor 1985 paper on consistent tangent
Structural mechanics, structural dynamics
• Vu-Quoc, L., and Tan, X.G., `` Optimal solid shells for nonlinear analyses of multilayer composites. Part I: Statics, '' Computer Methods in Applied Mechanics and Engineering, Vol.192, No.9-10, pp.975-1016, Feb 2003. (pdf) (toc)
• Vu-Quoc, L., and Tan, X.G., `` Optimal solid shells for nonlinear analyses of multilayer composites. Part II: Dynamics, '' Computer Methods in Applied Mechanics and Engineering, Vol.192, No.9-10, pp.1017-1059, Feb 2003. (pdf) (toc)
• See my course web page in Fall 2004 for articles on multiscale analysis.
• Is Gauss quadrature better than Clenshaw-Curtis? by N. Trefethen submitted. Mon, 15 May 2006.

Open-source software: Possible team projects (install, test, apply/modify)
• CAE Linux Courtesy of Aaron Franzen.
• Calculix
• FEniCS
• Getfem++

Other interesting links:

• Continuum mechanics of two-phase porous media by R. Larsson.
• Theory manual of LS-DYNA (pdf) Courtesy of Aaron Franzen. Wed, 25 Oct 2006.
• The Neumann boundary condition
  Carl Neumann Courtesy of Charlie Barker. Wed, 25 Oct 2006.
• See also my teaching schedule for more info on this course as taught in previous years.
• The hunger site: Click to donate food with no cost to you. Mon, 26 Jul 2004.

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Home page: Loc Vu-Quoc E-mail: vu-quoc AT ufl.edu MAE Department