EGM6352: Advanced Finite Element Methods (Sec 6316)

Catalog information: Credit 3, Prerequisite: EML 4500, EML 5526

Instructor: Dr. Nam-Ho Kim, Associate professor, Department of Mechanical and Aerospace Engineering, Office: 210 MAE-A, Phone: 846-0665, Email: nkim@ufl.edu, Web: http://www.mae.ufl.edu/nkim/

Class time and location: 102 NEB, MW 8^th period (3:00 - 4:15 PM)

Office hours: MW 9^th period (4:15 - 5:00 PM)

Text books:

1. "Lecture Note: Nonlinear Finite Element Analysis" by N. H. Kim (Required). Available at Target Copy (University Ave, EDGE students can call 352-376-3826 and ask for remote purchasing.)
2. "Computational Inelasticity", by J.C. Simo and T.J.R. Hughes, Springer, NY. (Recommended). Available at Amazon.com
3. "Nonlinear Finite Elements for Continua and Structures", by T. Belytschko, W. K. Liu, and B. Moran, Wiley, NY. (Recommended). Available at Amazon.com
4. "Finite Element Method Volume 2: Solid Mechanics" 5^th ed., by O. C. Zienkiewicz and R. L. Taylor, Butterworth Heinemann, Oxford (Recommended), Amazon.com.

Course Objectives and Outcomes

Catalog description: Advanced topics in finite element analysis, emphasized on nonlinear problems including nonlinear elasticity, hyperelasticity, elastoplasticity (small and large deformation), and contact problems

The objective of this course is to learn advanced topics in finite element methods so that this tool can be used for analysis, design, and optimization of engineering systems. Due to the variety of topics, specific topic will be emphasized in each year. The course offered in fall 2008 will focus on nonlinear structural analysis. Various nonlinearities in structural problems will be studied in the mathematical and numerical aspects. Students will also be exposed in computer programming and use of commercial finite element programs. The main topics covered in the course, in general, are outlined below.

1. Preliminary concepts
   • Index notation and summation rule, Vector and tensor calculus, Mechanics of continuous bodies, Boundary-value problem, Principle of virtual work, Linear operator and energy method
2. Finite element analysis procedure - linear problems
   • Bar element, Beam element (Euler and Timoshenko), Plate element (Kirchhoff and Mindlin-Reissner), Solid element
3. Introduction to nonlinear FEA procedures
   • Linear vs. nonlinear problems, Solution procedure, Newton-Raphson method, Incremental N-R method, Incremental secant method
4. FEA for nonlinear elastic problems
   • Nonlinear elastic problems, Mapping and deformation gradient, Nonlinear strains, Polar decomposition, Deformation of volume and surface, Stress measures, Total Lagrangian formulation, Linearization (Tangent stiffness), Updated Lagrangian formulation, FE implementation of nonlinear elasticity, Hyperelasticity, strain energy density, Nearly incompressibility, Mooney-Rivline material, Mixed formulation
5. FEA for elastoplasticity
   • Behavior of ductile material, 1D elastoplasticity, Work hardening (isotropic and kinematic), FEA procedure for 1D elastoplasticity, State determination, Ramberg-Osgood model, Multi-dimensional elastoplasticity, Failure criteria, Equivalent stress and effective strain, Hardening model, Rate-independent elastoplasticity, Classical elastoplasticity, Numerical integration for elastoplasticity, Return-mapping algorithm, Consistent tagent operator, Implementation, Elastoplasticity with finite rotation, Objective stress rate, Finite rotation with objective rate, Variational principle for finite rotation, Linearization and implementation, Finite deformation elastoplasticity with hyperelasticity, Multiplicative decomposition and intermediate configuration, Principle of maximum dissipation, Spectral decomposition and time integration, Return mapping in principal stress space, consistent tagent operator
6. FEA of contact problem
   • Contact problem -- boundary nonlinearity, General contact formulation, Variational inequality and constrained optimization, Variational equation, Linearization of contact form, Friction model
7. FEA of dynamic problem (Depending on course progress)
   • Temporal discretization; Parabolic system (heat transfer problem); Consistent mass and lumped mass, mass lumping technique; Time integration methods: explicit and implicit methods; Stability, convergence and consystency; Hyperbolic system (structural dynamics and wave propagation); Numerical dissipation and dispersion

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   Other Information

   Homework is an essential part of this course. Various programming and formulation problems will be assigned through the class website at http://www.mae.ufl.edu/nkim/egm6352.html. Students are responsible to check the class website for homework and project assignments. Late homework will not be accepted without medical or other valid reasons.

   Examination: There will be one mid-term exam and one final exam.

   Projects: There will be two projects. One project is related to computer implementation of plasticity, and the other is solving nonlinear structural problems using commercial programs. Here the students are encouraged to learn certain aspects of the software on their own as an exercise in self-education and life long learning. Projects must be submitted on time in class. Late projects submitted by the next class will receive 90% credit. Projects received later than that will not be accepted without medical or other valid reasons.

   Grading: Exam: 40%, Projects: 40%, Homeworks: 20%

   Academic honesty: All students admitted to the University of Florida have signed a statement of academic honesty committing themselves to be honest in all academic work and understanding that failure to comply with this commitment will result in disciplinary action. This statement is reminder to uphold your obligation as a student at the University of Florida and to be honest in all work submitted and exams taken in this class and all others.