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Finite Elements for Truss and Frame Structures

An Introduction Based on the Computer Algebra System Maxima

  • Andreas Öchsner
  • Resam Makvandi

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the SpringerBriefs in Computational Mechanics book sub series (BRIEFSCOMPUTAT)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Andreas Öchsner, Resam Makvandi
    Pages 1-2
  3. Andreas Öchsner, Resam Makvandi
    Pages 3-7
  4. Andreas Öchsner, Resam Makvandi
    Pages 9-42
  5. Andreas Öchsner, Resam Makvandi
    Pages 43-72
  6. Andreas Öchsner, Resam Makvandi
    Pages 73-91
  7. Andreas Öchsner, Resam Makvandi
    Pages 93-119

About this book

Introduction

This book is intended as an essential study aid for the finite element method. Based on the free computer algebra system Maxima, the authors offer routines for symbolically or numerically solving problems in the context of plane truss and frame structures, allowing readers to check classical ‘hand calculations’ on the one hand and to understand the computer implementation of the method on the other. The mechanical theories focus on the classical one-dimensional structural elements, i.e. bars, Euler–Bernoulli and Timoshenko beams, and their combination to generalized beam elements. Focusing on one-dimensional elements reduces the complexity of the mathematical framework, and the resulting matrix equations can be displayed with all components and not merely in the form of a symbolic representation. In addition, the use of a computer algebra system and the incorporated functions, e.g. for equation solving, allows readers to focus more on the methodology of the finite element method and not on standard procedures. 

Keywords

Finite element numerical methods one-dimensional elements Maxima Euler-Bernoulli Beams Timoshenko Beams Finite element method computer algebra system

Authors and affiliations

  • Andreas Öchsner
    • 1
  • Resam Makvandi
    • 2
  1. 1.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingen am NeckarGermany
  2. 2.Institute of MechanicsOtto von Guericke University MagdeburgMagdeburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-94941-3
  • Copyright Information The Author(s), under exclusive license to Springer International Publishing AG, part of Springer Nature 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-94940-6
  • Online ISBN 978-3-319-94941-3
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site