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Öchsner Andreas. - Computational Plasticity for Finite Elements: a Fortran-Based Introduction

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Öchsner Andreas. Computational Plasticity for Finite Elements: a Fortran-Based Introduction
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Computational Plasticity for Finite Elements: a Fortran-Based Introduction: summary, description and annotation

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This volume demonstrates the use of FORTRAN for numerical computing in the context of the finite element method. FORTRAN is still an important programming language for computational mechanics and all classical finite element codes are written in this language, some of them even offer an interface to link user-code to the main program. This feature is especially important for the development and investigation of new engineering structures or materials. Thus, this volume gives a simple introduction to programming of elasto-plastic material behavior, which is, for example, the prerequisite for implementing new constitutive laws into a commercial finite element program.

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Contents
Landmarks
SpringerBriefs in Applied Sciences and Technology SpringerBriefs in - photo 1
SpringerBriefs in Applied Sciences and Technology SpringerBriefs in Computational Mechanics
Series Editors
Holm Altenbach
Lehrstuhl Technische Mechanik, Institut fr Mechanik, Otto-von-Guericke-Universitt Magdeburg, Magdeburg, Germany
Andreas chsner
Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen am Neckar, Germany
Lucas F. M. da Silva
Department of Mechanical Engineering, University of Porto, Porto, Portugal

More information about this series at http://www.springer.com/series/8886

Michael Trapp and Andreas chsner
Computational Plasticity for Finite Elements A Fortran-Based Introduction
Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 2
Michael Trapp
TU Munich, Munich, Germany
Andreas chsner
Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen am Neckar, Germany
ISSN 2191-530X e-ISSN 2191-5318
SpringerBriefs in Applied Sciences and Technology
ISBN 978-3-319-77205-9 e-ISBN 978-3-319-77206-6
https://doi.org/10.1007/978-3-319-77206-6
Library of Congress Control Number: 2018933499
The Author(s) 2018
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Printed on acid-free paper

This Springer imprint is published by Springer Nature

The registered company is Springer International Publishing AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

In this book, we want to demonstrate the use of the classic programming language FORTRAN for numerical computing in the context of the finite element method. For this purpose, we are focusing specifically on the subject of computational plasticity.

FORTRAN is a programming language, specifically designed for scientific and engineering applications. Since its initial release in the 1950s, many upgrade features have been added.

FORTRAN has asserted itself due to its practical use. Unlike earlier programs with machine or assembly code, FORTRAN uses higher language with abstract words and syntax, which automize computation instructions. This makes the code easy to read and write, and much less prone to bugs.

A decided advantage of FORTRAN is its flexibility. As it does not depend on a particular computing system, a transfer is very simple. In this context, it should be noted that all classical finite element packages are written in this language. Some even offer an interface to link ones own code to the commercial package. As a general-purpose tool, FORTRAN is a modern alternative for numerical computing and scientific programming. As opposed to many numerical software, FORTRAN is always transparent and easy to work with.

We look forward to receiving some comments and suggestions for the next edition of this textbook.

Michael Trapp

Andreas chsner

Griffith University

Gold Coast, Australia

January 2018

Acknowledgements

It is important to highlight the contribution of the students which helped to finalize the content of this book. Their questions, comments and struggle during different lectures, assignments and final examinations helped us to structure this book. Furthermore, we would like to express our sincere appreciation to the Springer Publisher, especially to Dr. Christoph Baumann, for giving us the opportunity to realize this book.

Symbols and Abbreviations
Latin Symbols (Capital Letters)
Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 3

Area, cross-sectional area

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 4

Elasticity matrix

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 5

Youngs modulus

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 6

Intermediate modulus

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 7

Plastic modulus

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 8

Elasto-plastic modulus

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 9

(Approximated) tangent modulus

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 10

Yield condition

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 11

(Applied (total)) force

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 12

Internal force

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 13

Identity matrix

First invariant Second invariant Th - photo 14

First invariant

Computational Plasticity for Finite Elements a Fortran-Based Introduction - image 15
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