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Finite Elements Using Maxima

Theory and Routines for Rods and Beams

  • Andreas Öchsner
  • Resam Makvandi
Book

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Andreas Öchsner, Resam Makvandi
    Pages 1-1
  3. Andreas Öchsner, Resam Makvandi
    Pages 3-12
  4. Andreas Öchsner, Resam Makvandi
    Pages 13-78
  5. Andreas Öchsner, Resam Makvandi
    Pages 79-161
  6. Andreas Öchsner, Resam Makvandi
    Pages 163-204
  7. Andreas Öchsner, Resam Makvandi
    Pages 205-247
  8. Back Matter
    Pages 249-256

About this book

Introduction

This book provides a study aid on the finite element method. Based on the free computer algebra system “Maxima”, it presents routines to symbolically or numerically solve problems in the context of plane truss and frame structures. This allows readers to not only check classical “hand calculations” but also understand the computer implementation of the method. The mechanical theories focus on the classical one-dimensional structural elements, i.e. bars, Euler–Bernoulli and Timoshenko beams as well as their combination to generalized beam elements. Focusing on one-dimensional elements reduces the complexity of the mathematical framework and the resulting matrix equations can still be displayed with all components, and not only in a symbolic representation. The use of a computer algebra system and the incorporated functions, e.g. for equation solving, highlights the methodology of the finite element method rather than standard procedures.

The book is based on the Springer Brief “Finite Elements for Truss and Frame Structures” (978-3-319-94940-6) by the same authors.

Keywords

Euler-Bernoulli beam Timoshenko beams free computer algebra system Mathematica Maxima one-dimensional elements

Authors and affiliations

  • Andreas Öchsner
    • 1
  • Resam Makvandi
    • 2
  1. 1.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingenGermany
  2. 2.Institute of Mechanics (IFME)Otto von Guericke University MagdeburgMagdeburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-17199-5
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-17198-8
  • Online ISBN 978-3-030-17199-5
  • Buy this book on publisher's site