The finite element method is a numerical technique for solving differential equations (which include heat transfer, fluid mechanics, and solid mechanics). The course is intended to provide engineers and scientists with the formulation and implementation of the finite element method. Formulations and applications will be drawn from heat transfer, fluid mechanics, solid mechanics, and general fluid problems. Emphasis in this course will be placed on methodologies for linear, and steady-state and time-dependent problems.Â
All students taking this course must have a graduate standing in engineering, and have taken a course equivalent to Matrix Structural Analysis or Numerical Methods. The students of the course must have background in (ordinary and partial) differential equations, and working knowledge of a computer programming language (preferably MATLAB).
It is necessary that students have to know a computer programming language as there will be programming assignments in the course. Some popular programming language for scientific computing include MATLAB, C/C++, Fortran 90/95/00, Python. If you do not know any programming language, I recommend you to learn MATLAB as it is easy to learn. In addition, I will write pseudocode in the class, which will be similar to MATLAB's syntax. No class time will be spent on teaching any specific programming language. It is, therefore, the responsibility of the students to learn their favorite programming language. Several resources on computer programming languages (including MATLAB) are provided on the course website.
The finite element method is a powerful numerical technique of solving differential equations in the analytical description of physical phenomena such as solid mechanics, fluid mechanics and heat transfer. The objectives of the course include:
The formulation of the finite element method as applied to representative problems of solid mechanics, fluid mechanics, and heat transfer.
Obtain numerical solutions of simple (but representative) problems of solid mechanics, fluid mechanics and heat transfer using the finite element method.
Computer implementation of the finite element analysis steps for the model problems discussed in the course.
The final grade in this course will be based on the following weighting:
Machine Problems (30%)
Course Project (30%)
Final Exam (40%)
Your letter grade will be assigned based on
F < 60 <= D <= 70 < C <= 80 < B <= 90 < A <= 100
Assignments in the form of Homework and Machine Problems will be assigned regularly. Late work will NOT be accepted for any reason. Assignments done on papers taken out of spiral binding book will not be accepted. Unstapled submission will not be graded. For Machine Problems, students should submit a hard copy of the computer code. Significant points will be assigned for modularity of the code, logic, and comments in the code.
There will be a three-hour comprehensive final exam, which will be closed book. Only pen/pencil, eraser, and calculator will be allowed.
Students must make arrangements in advance if they expect to miss an exam. Exam absences due to recognized University-related activities, religious holidays, verifiable illness, and family/medical emergencies will be dealt with on an individual basis. In all cases of absence from exams a written excuse is required. Ignorance of the time and place of an exam will not be accepted as an excuse for absence.
It shall be the general policy for this course that homework, machine problems, project, and exams shall be graded on the basis of the answers only -- partial credit (if given) is given solely on the discretion of the instructor. All work requiring calculations shall be properly and completely documented for credit. All grading shall be done by the instructor, or under his discretion and supervision, and the decision of the instructor is final.
Only in very rare cases will exams be considered for re-grading, e.g., when the total number of points deducted is not consistent with the assigned grade. Partial credit (if any) is not subject to appeal. Work which, while possibly correct, but cannot be followed, will be considered incorrect -- and will not be considered for a grade change. Grade assigned to homework problems will not be considered for re-grading. If re-grading is necessary, the student is to submit a signed formal letter to the instructor explaining the situation that requires consideration for re-grading, the material to be re-graded must be attached to this letter. The letter and attached material must be received within one week from the date returned by the instructor.
I strongly encourage students to ask questions and expect them to actively participate in the proceeding of the class. I will assign reading assignments and initiate discussion sessions about the assigned topics.
Always re-work your lecture notes before the next class, checking every step and filling in missing details.
Read the text as you re-work your notes. This will help you get the big picture.
Ask me before each class about the points you did not follow in the last class.