# Finite elements

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Welcome to this learning project about **Finite elements**!

## Learning Project Summary[edit | edit source]

**Project code:****Suggested Prerequisites:****Time investment:**6 months**Portal:Engineering and Technology****School:Engineering****Department:Mechanical Engineering****Stream:Applied Mechanics****Level:**Upper-division undergraduate/First year graduate

## Content summary[edit | edit source]

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.

## Goals[edit | edit source]

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

## Contents[edit | edit source]

### Syllabus and Learning Materials[edit | edit source]

- Mathematical Preliminaries
- Tensor exercises and Physical Principles in Differential Form
- Finite element basics in one-dimension

### Assignments[edit | edit source]

- 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[edit | edit source]

### Textbooks and References[edit | edit source]

** Textbooks**

- 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.*

**References**

**Mathematics**:- 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.*

- R. M. Brannon (2004), Elementary Vector and Tensor Analysis for Engineers.