IUPUI School of Engineering and Technology

IUPUI School of Engineering and Technology

Advanced Applications of Finite Element Method

ME 55200 / 3 Cr. (3 Class)

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.


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


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.


After completion of this course, the students should be able to:

  1. Apply variational principles to develop advanced finite element models for various problems in solids, fluids, and heat transfer areas.
  2. Develop and solve finite models in nonlinear mechanics including geometric and material nonlinearities.
  3. Solve advanced problems in solid mechanics using general-purpose finite element codes for two- and three-dimensional solid elasticity and plate bending problems.
  4. Solve advanced problems in fluid mechanics using general-purpose finite element codes for incompressible and compressible fluids.
  5. Solve advanced problems in heat transfer using general-purpose finite element codes for problems with convection and radiation.
  6. Use various structured and unstructured mesh generation techniques for complex geometries.
  7. Analyze and evaluate the solution of finite element codes.
  8. Code advanced finite element programs with minimum extra training.
  9. Apply the method to advanced problems in their specific field of study.
  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