Introduction to finite elements
Welcome to this learning project about Introduction to finite elements!
Learning Project Summary
- Project code:
- Suggested Prerequisites:
- Time investment: 6 months
- Portal:Engineering and Technology
- Department:Mechanical Engineering
- Stream:Applied Mechanics
- Level: Upper-division undergraduate/First year graduate
This course will introduce you to the topic of finite element analysis. The course will cover linear finite elements and the analysis of simple solid mechanics and heat transfer problems.
This course aims to:
- Introduce you to the finite element method
- Show you how finite element formulations are arrived at
- Show you how some engineering problems are solved numerically
Syllabus and Learning Materials
- Mathematical Preliminaries
- Tensor exercises and Physical Principles in Differential Form
- Finite element basics in one-dimension
- An example: Axially loaded bar
- More examples: Some model problems
- A time-dependent problem: the heat equation
- Homework 1 Problem set
- Homework 2 Problem set
- Homework 3 Problem set
- Homework 4 Problem set
- Homework 5 Problem set
- Homework 6 Problem set
- Homework 7 Problem set
- Homework 8 Problem set
- Homework 9 Problem set
- Homework 10 Problem set
- Homework 11 Problem set
Tests and Quizzes
Textbooks and References
- The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T. J. R. Hughes, Dover Publications, 2000.
- K-J. Bathe (1996), Finite Element Procedures, Prentice-Hall. Useful repository of information on nonlinear finite elements.
- J. N. Reddy (1993), An Introduction to the Finite Element Method, McGraw-Hill. This book is referred to a number of times in one of the texts.
- O. C. Zienkiewicz and R. L. Taylor (2000), The Finite Element Method: Volume 2 Solid Mechanics, Butterworth-Heinemann. Another excellent repository of information of nonlinear finite elements geared toward the Civil Engineers.
- R. M. Brannon (2004), Elementary Vector and Tensor Analysis for Engineers. This free online book is the best introduction I have seen for vector and tensor analysis for nonlinear mechanics.
- B. Daya Reddy (1998), Introductory Functional Analysis: With applications to boundary value problems and finite elements. , Springer-Verlag. Excellent book for engineers who want to understand the terminology used in the finite element literature and how error analysis is done.
- A.P.S. Selvadurai (2000), Partial Differential Equations in Mechanics 1,2. Springer. Excellent introductory text on partial differential equations with engineers in mind.