# One-Dimensional Finite Elements

## An Introduction to the FE Method

• Andreas Öchsner
• Markus Merkel
Book

1. Front Matter
Pages i-xxiii
2. Andreas Öchsner, Markus Merkel
Pages 1-4
3. Andreas Öchsner, Markus Merkel
Pages 5-30
4. Andreas Öchsner, Markus Merkel
Pages 31-49
5. Andreas Öchsner, Markus Merkel
Pages 51-61
6. Andreas Öchsner, Markus Merkel
Pages 63-110
7. Andreas Öchsner, Markus Merkel
Pages 111-128
8. Andreas Öchsner, Markus Merkel
Pages 129-152
9. Andreas Öchsner, Markus Merkel
Pages 153-204
10. Andreas Öchsner, Markus Merkel
Pages 205-227
11. Andreas Öchsner, Markus Merkel
Pages 229-267
12. Andreas Öchsner, Markus Merkel
Pages 269-306
13. Andreas Öchsner, Markus Merkel
Pages 307-318
14. Andreas Öchsner, Markus Merkel
Pages 319-350
15. Andreas Öchsner, Markus Merkel
Pages 351-364
16. Back Matter
Pages 365-418

### Introduction

This textbook presents finite element methods using exclusively one-dimensional elements. It presents the complex methodology in an easily understandable but mathematically correct fashion. The approach of one-dimensional elements enables the reader to focus on the understanding of the principles of basic and advanced mechanical problems. The reader will easily understand the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. Although the description is easy, it remains scientifically correct.

The approach using only one-dimensional elements covers not only standard problems but allows also for advanced topics such as plasticity or the mechanics of composite materials. Many examples illustrate the concepts and problems at the end of every chapter help to familiarize with the topics. Each chapter also includes a few exercise problems, with short answers provided at the end of the book.

The second edition appears with a complete revision of all figures. It also presents a complete new chapter special elements and added the thermal conduction into the analysis of rod elements. The principle of virtual work has also been introduced for the derivation of the finite-element principal equation.

### Keywords

FEM textbook Backward-Euler algorithm Bending Plasticity Composite Materials Finite Elements Method FEM Nonlinear Elasticity Shear Forces Structural Mechanics Timoshenko Beams Torsion

#### Authors and affiliations

• Andreas Öchsner
• 1
• Markus Merkel
• 2
1. 1.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingenGermany
2. 2.Institute for Virtual Product DevelopmentAalen University of Applied SciencesAalenGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-75145-0
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Engineering
• Print ISBN 978-3-319-75144-3
• Online ISBN 978-3-319-75145-0