EGM6352: Advanced Finite Element Methods

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

Instructor: Dr. Nam-Ho Kim, Department of Mechanical and Aerospace Engineering, Office: 210 MAE-A, Phone: 352-575-0665, Email: nkim@ufl.edu, Web: http://wwws.mae.ufl.edu/nkim/

Class time and location: E118 CSE, MWF 7^th period (1:50 - 2:40 PM)

Office hours: MWF 4^th period (10:40 - 11:30 AM)

Text books:

1. "Lecture Note: Introduction to Nonlinear Finite Element Analysis" by N. H. Kim (Required). Springer, 2014, ISBN-10: 1441917454. Available at Amazon.com
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

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 spring 2017 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 minimum potential energy, and Principle of virtual work, Finite element formulation
2. Introduction to nonlinear FEA procedures
   • Linear vs. nonlinear problems, Solution procedure, Newton-Raphson method, Incremental N-R method, Incremental secant method
3. 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
4. FEA for elastoplasticity
   • Behavior of ductile material, 1D elastoplasticity, Work hardening (isotropic and kinematic), FEA procedure for 1D elastoplasticity, Multi-dimensional elastoplasticity, Failure criteria, Equivalent stress and effective strain, Hardening model, Rate-independent elastoplasticity, Numerical integration for elastoplasticity, Return-mapping algorithm, Consistent tangent operator, Elastoplasticity with finite rotation, Objective stress rate, Finite deformation elastoplasticity with hyperelasticity, Multiplicative decomposition, Principle of maximum dissipation, Spectral decomposition and time integration, Return mapping in principal stress space, consistent tangent operator
5. FEA of contact problem
   • Contact problem -- boundary nonlinearity, General contact formulation, Variational inequality and constrained optimization, Variational equation, Linearization of contact form, Friction model
6. 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 consistency; 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 on Canvas at https://ufl.instructure.com/courses/335300. Homework needs to be submitted by midnight on Canvas. Late homework will not be accepted.

   Examination: There will be two mid-term exams and no final exam. Tentative exam dates are February 27th and April 12th. EDGE students will have 3 days of window before/after on-campus students' exam schedule.

   Class participation: Students can get small extra credits if s/he finds an error in the textbook and report to the instructor first time. Students who asked questions or answered questions in the class should send an email to the instructor to get class participation points. To get full credits (5%), students need to ask/answer 5 times throughout the semester.

   Projects: There will be two term projects. One project is related to computer implementation of hyperelasticity, and the other is solving nonlinear structural problems using Abaqus. 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 by midnight on Canvas. Late projects submitted by the next day 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: 15%, Class participation: 5% (A=93~100, A-=90~92.9, B+=87~89.9, B=83~86.9, B-=80~82.9, C+=77~79.9, C=73~76.9, C-=70~72.9, D+=67~69.9, D=63~66.9, D-=60~62.9, E=0~59.9)

   Software: All students are required to install Abaqus SE on their personal computer. It is not allowed to use lab computer for class assignments. Use the following link to download Abaqus: http://academy.3ds.com/software/abaqus-student-edition/. You will need the software for homeworks and projects. If you are familiar to other FE software (ANSYS, Nastran, etc), you can use it, but class will follow with Abaqus.

   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.