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  • © 2013

One-Dimensional Finite Elements

An Introduction to the FE Method

  • Introduces a new educational approach using only one-dimensional elements
  • Uses intuitive mathematics and is scientifically exact
  • Describes also advanced problems like composite materials and nonlinear elasticity
  • Many examples facilitate the understanding plus solutions manual for instructors
  • Includes supplementary material: sn.pub/extras

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxiii
  2. Introduction

    • Andreas Öchsner, Markus Merkel
    Pages 1-4
  3. Motivation for the Finite Element Method

    • Andreas Öchsner, Markus Merkel
    Pages 5-32
  4. Bar Element

    • Andreas Öchsner, Markus Merkel
    Pages 33-50
  5. Torsion Bar

    • Andreas Öchsner, Markus Merkel
    Pages 51-56
  6. Bending Element

    • Andreas Öchsner, Markus Merkel
    Pages 57-110
  7. General 1D Element

    • Andreas Öchsner, Markus Merkel
    Pages 111-128
  8. Plane and Spatial Frame Structures

    • Andreas Öchsner, Markus Merkel
    Pages 129-153
  9. Beam with Shear Contribution

    • Andreas Öchsner, Markus Merkel
    Pages 155-207
  10. Beams of Composite Materials

    • Andreas Öchsner, M Merkel
    Pages 209-231
  11. Nonlinear Elasticity

    • Andreas Öchsner, Markus Merkel
    Pages 233-271
  12. Plasticity

    • Andreas Öchsner, Markus Merkel
    Pages 273-311
  13. Stability (Buckling)

    • Andreas Öchsner, Markus Merkel
    Pages 313-325
  14. Dynamics

    • Andreas Öchsner, Markus Merkel
    Pages 327-358
  15. Back Matter

    Pages 359-398

About this book

 This textbook presents finite element methods using exclusively  one-dimensional elements. The aim is to present 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 easily  understands the assumptions and limitations of mechanical modeling as well  as the underlying physics without struggling with complex mathematics. But  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 like 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.

Reviews

From the reviews:

“As its title describes, this book is about the finite element method applied to one-dimensional problems. … several problems of interest are indeed modeled using a single space variable. This book should appeal to the mechanical engineering community.” (Alexandre L. Madureira, Mathematical Reviews, January, 2014)

“This book is an excellent addition to course resources on finite elements. … Each chapter includes worked examples and a few exercise problems. Short answers for the exercises, provided at the end of the book, will be helpful to students. A valuable course resource for students in mechanical, civil, aerospace, and other engineering curricula and a useful acquisition for academic libraries. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, practicing engineers.” (R. Kolar, Choice, Vol. 51 (1), September, 2013)

Authors and Affiliations

  • Faculty of Mechanical Engineering, Department of Applied Mechanics, University of Technology Malaysia—UTM, Johor, Malaysia

    Andreas Öchsner

  • FB Maschinenbau, Hochschule Technik Wirtschaft Aalen, Aalen, Germany

    Markus Merkel

About the authors

Andreas Öchsner, born 1970, is Full Professor in the Department Solid Mechanics and Design at the University of Technology Malaysia (UTM), Malaysia and Head of the Advanced Materials and Structure Lab. Having obtained a Diploma Degree (Dipl.-Ing.) in Aeronautical Engineering at the University of Stuttgart (1997), Germany, he spent the time from 1997-2003 at the University of Erlangen-Nuremberg as a research and teaching assistant to obtain his Doctor of Engineering Sciences (Dr.-Ing.). From 2003-2006, he worked as Assistant Professor in the Department of Mechanical Engineering and Head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. His research interests are related to experimental and computational mechanics, cellular metals and thin structures and interphases. He has published over 290 scientific publications, comprising 11 research monographs, 13 book chapters and one teaching book on finite element methods. He is the general chairman of six international conferences on computational and experimental engineering (ACE-X series) and eight international conferences in the area of heat and mass transfer (DSL series). His editorial work comprises posts as Editor-in-chief of the international journal Continuum Mechanics and Thermodynamics (Springer), Editor-in-chief of the Springer book series on Advanced Structured Materials and Editor of SpringerBriefs in Applied Sciences and Technology: Computational Mechanics. His research activities were recognised in 2010 by the award of a higher doctorate degree (D.Sc.) by the University of Newcastle, Australia.

MARKUS MERKEL, born 1967, is Full Professor at Aalen University of Applied Sciences. He graduated 1993 at the University of Erlangen-Nuremberg (Germany) in Mechanical Engineering and finished his PhD-studies in 1998. Between 1999 and 2004, Markus Merkel worked at the International Technical Development Centre of Adam Opel AG. He became Professer in2004 for Engineering Design and Computational Mechanics at the Faculty of Mechanical Engineering and Materials Science. Markus Merkel is Head of the Institute of Virtual Product Development.

Bibliographic Information

  • Book Title: One-Dimensional Finite Elements

  • Book Subtitle: An Introduction to the FE Method

  • Authors: Andreas Öchsner, Markus Merkel

  • DOI: https://doi.org/10.1007/978-3-642-31797-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2013

  • Hardcover ISBN: 978-3-642-31796-5Published: 06 October 2012

  • eBook ISBN: 978-3-642-31797-2Published: 05 October 2012

  • Edition Number: 1

  • Number of Pages: XXIV, 400

  • Topics: Solid Mechanics, Computational Mathematics and Numerical Analysis, Mechanical Engineering

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access