Advanced Applications of Finite Element Method
ME 55200/ 3 Cr.
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.
- Available Online: No
- Credit by Exam: No
- Laptop Required: No
P: ME 55100 or equivalent.
- 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:
- Apply variational principles to develop advanced finite element models for various problems in solids, fluids, and heat transfer areas.
- Develop and solve finite models in nonlinear mechanics including geometric and material nonlinearities.
- Solve advanced problems in solid mechanics using general-purpose finite element codes for two- and three-dimensional solid elasticity and plate bending problems.
- Solve advanced problems in fluid mechanics using general-purpose finite element codes for incompressible and compressible fluids.
- Solve advanced problems in heat transfer using general-purpose finite element codes for problems with convection and radiation.
- Use various structured and unstructured mesh generation techniques for complex geometries.
- Analyze and evaluate the solution of finite element codes.
- Code advanced finite element programs with minimum extra training.
- Apply the method to advanced problems in their specific field of study.
- Mathematical preliminaries (2 classes)
- Finite element preliminaries (2 classes)
- Nonlinear heat transfer and other field problems in one-dimension (2 classes)
- Nonlinear bending of beams (2 classes)
- Solution procedures for linear and nonlinear algebraic equations (2 classes)
- Nonlinear heat transfer and other field problems in two-dimensions (2 classes)
- Nonlinear bending of elastic plates (2 classes)
- Flow of viscous incompressible fluids (2 classes)
- Nonlinear analysis of transient problems (2 classes)
- Compressible flows (2 classes)
- Finite element formulations of solid continua (2 classes)
- Material nonlinearities (2 classes)
- Solid-fluid interactions (2 classes)
- Parallel computing (2 classes)
- Tests (2 classes)
Note: one class = 75 minutes