# Nonlinear finite elements

Welcome to this learning project about nonlinear finite elements!

## Introduction

Finite element analysis (FEA) is a computer simulation technique used in engineering analysis. It uses a numerical technique called the finite element method (FEM) to solve partial differential equations. There are many finite element software packages, both free and proprietary. Development of the finite element method in structural mechanics is usually based on an energy principle such as the virtual work principle or the minimum total potential energy principle. * Completion status: this resource has reached a high level of completion.

### Content summary

This is an introductory course on nonlinear finite element analysis of solid mechanics and heat transfer problems. Nonlinearities can be caused by changes in geometry or be due to nonlinear material behavior. Both types of nonlinearities are covered in this course.

### Goals

This learning project aims to.

• provide the mathematical foundations of the finite element formulation for engineering applications (solids, heat, fluids).
• expose students to some of the recent trends and research areas in finite elements.

Here's a short quiz to help you find out what you need to brush up on before you dig into the course:

## Contents

Syllabus and Learning Materials

### Syllabus and Learning Materials

1. Mathematical Preliminaries
2. Linear finite element basics
3. Nonlinear finite element basics
4. Nonlinear deformation of beams
5. Nonlinear deformation of plates and shells
1. Basic linear plate and shell elements
2. Nonlinear plates and shells
3. Time-dependent deformation of shells
6. Basic continuum mechanics
7. Finite element formulation in three dimensions.
1. Updated Lagrangian formulation
8. Verification and Validation.
Assignments, tests and quizzes

## Textbooks and References

### Textbooks

• An Introduction to Nonlinear Finite Element Analysis by J. N. Reddy, Oxford University Press, 2004, ISBN 019852529X.
• Nonlinear Finite Elements for Continua and Structures by T. Belytschko, W. K. Liu, and B. Moran, John Wiley and Sons, 2000.
• Computational Inelasticity by J. C. Simo and T. J. R. Hughes, Springer, 1998.
• The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T. J. R. Hughes, Dover Publications, 2000.