Finite Element Method I
Spring Semester, 2017
Finite Element Method I
First Graduate level course in Finite Element
Method
Closely follows the Graduate level FEM
course taught at the University of Michigan,
USA by Prof. Greg Hulbert (Winter, 2006)
Lectures based on the text book The Finite
Element Method: Linear Static and Dynamic
Finite Element by Thomas J. R. Hughes,
Dover Publications, 2000.
Text Books
The Finite Element Method: Linear Static
and Dynamic Finite Element Analysis, by
Thomas J. R. Hughes, Dover Publications,
ISBN: 0486411818; (Soft copy is available
online and with the instructor)
An Introduction to the Finite Element
Method, by J. N. Reddy, 2nd Edition,
McGraw Hill, NY, 1993 (Soft copy is
available online and with the instructor)
Finite Element Procedures by K. A. J.
Bathe, Elsevier Science, 1982
Assignments and Grading
There are four homework assignments, each worth
15% of the total grade.
One in-class midterm examination will be given
(15% of total grade). The exam is scheduled on ---?
(8th 9th week)
One take-home exam / project (25% of total grade)
The homework assignments comprise a
combination of theoretical exercises, programming
assignments and use of commercial software
(optional)
While the programming assignments can be
completed in any computing language by a student,
examples and skeleton code will be presented
using MATLAB
Group assignments are not permitted
Perspective and Objectives
First Graduate level course in Linear Finite
Element Method
Emphasis on Finite Element theory,
supplemented with commercial FE software
All of the physics may not be fully understood
all of the time
Audience: Across all engineering disciplines
Perspective and Objectives
The course teaches
FE fundamentals (feel good )
FE implementation (coding)
Skills needed for further study and research
in the field of FE
The course does not teach
FE software like ANSYS, ABAQUS,
LSDYNA etc
Computing languages like C++, Python,
Matlab etc
Development of field equations (physics)
Calculus of Variation
Perspective and Objectives
Upon completion of the course:
Systematically evolve a physical (well
posed) problem of interest given in
differential equation form into finite element
based set of algebraic equations for
numerical solution
Modify or add (informatively) relevant FE
routines / elements to an existing research
or commercial code
Realize and understand the accuracy and
limitations of FE methods, both
theoretically and practically
Perspective and Objectives
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Tools and Software
Modern coding environment
MATLAB is the tool of convenience (this
course)
Other environments can be used like,
Mathematica, MAPLE, C++, etc
Introduction and optional use of commercial
software
Pre / Post processing (Hypermesh)
FE Solvers (ANSYS, ABAQUS, MSC
NASTRAN etc)
FE code architecture and theory best learnt
and understood by implementation (coding)
Course Syllabus
Week 1:
Course introduction
From differential equations to code: 1D
elasticity (truss problem)
Analytic solution
Approximate solution
Week 2:
From differential equations to code: 1D
elasticity (truss problem)
Strong form
Weak form
Galerkin form
Introduction to finite elements
Course Syllabus
Week 3:
From differential equations to code: 1D
elasticity (truss problem)
Finite element formulation
Code structure
Accuracy and error analysis
Week 4:
From differential equations to code: 1D
elasticity (truss problem)
Accuracy and error analysis
Multidimensional problems: Heat Conduction
(Steady State)
Problem formulation
Course Syllabus
Week 5:
Multidimensional problems: Heat Conduction
(Steady State)
Problem formulation
Strong form
Weak form
Galerkin form
Matrix form
Finite element formulation
Course Syllabus
Week 6:
Multidimensional problems: Heat Conduction
(Steady State)
Finite element data structures
2D and 3D finite elements
Week 7:
Multidimensional problems: Linear Elasticity
From Strong form to code
Week 8:
Multidimensional problems: Linear Elasticity
Mixed finite element formulation
2D and 3D finite elements
Course Syllabus
Week 9:
Review and midterm exam
Week 10:
Introduction to plates and shells
Week 11:
Vibration problems: Modal Analysis
Problem formulation
Treatment of mass terms
Accuracy of mode shape and natural
frequencies
Course Syllabus
Week 12:
Introduction to Buckling Analysis / Fracture
Analysis
From strong from to code
Week 13:
Introduction to Nonlinear Finite Element
Analysis
Course review / Additional Topics
Project / Take Home
Thank You
