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The History of Theoretical, Material and Computational Mechanics - Mathematics Meets Mechanics and Engineering

  • Book
  • © 2014

Overview

Editors:
  1. Erwin Stein

    1. Institute of Mechanics and Computational Mechanics (IBNM), Gottfried Wilhelm Leibniz Universität Hannover, Hannover, Germany

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  • Comprehensive presentation of the History of Theoretical, Material and Computational Mechanics
  • Presents the edited results of the sessions on History of Mechanics held at the last GAMM meetings at Karlsruhe, Germany (2010), Graz, Austria (2011) and Darmstadt, Germany (2012)
  • Written by leading experts in the field

Part of the book series: Lecture Notes in Applied Mathematics and Mechanics (LAMM, volume 1)

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Table of contents (23 chapters)

  1. Front Matter

    Pages 1-11
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  2. Mechanical Conservation Principles, Variational Calculus and Engineering Applications from the 17th to the 20th Century

    1. Front Matter

      Pages 1-1
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    2. The Origins of Mechanical Conservation Principles and Variational Calculus in the 17th Century

      • Erwin Stein
      Pages 3-22

    3. Principles of Least Action and of Least Constraint

      • Ekkehard Ramm
      Pages 23-43

    4. Lagrange’s “Récherches sur la libration de la lune”

      • Hartmut Bremer
      Pages 45-59

    5. The Development of Analytical Mechanics by Euler, Lagrange and Hamilton – From a Student’s Point of View

      • Maximilian Gerstner, Patrick R. Schmitt, Paul Steinmann
      Pages 61-72

    6. Heun and Hamel – Representatives of Mechanics around 1900

      • Hartmut Bremer
      Pages 73-80

    7. The Machine of Bohnenberger

      • Jörg F. Wagner, Andor Trierenberg
      Pages 81-100

    8. On the Historical Development of Human Walking Dynamics

      • Werner Schiehlen
      Pages 101-116

  3. Material Theories of Solid Continua and Solutions of Engineering Problems

    1. Front Matter

      Pages 117-117
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    2. On the History of Material Theory – A Critical Review

      • Albrecht Bertram
      Pages 119-131

    3. Some Remarks on the History of Plasticity – Heinrich Hencky, a Pioneer of the Early Years

      • Otto T. Bruhns
      Pages 133-152

    4. Prandtl-Tomlinson Model: A Simple Model Which Made History

      • Valentin L. Popov, J. A. T. Gray
      Pages 153-168

    5. A Historical View on Shakedown Theory

      • Dieter Weichert, Alan Ponter
      Pages 169-193

    6. Some Remarks on the History of Fracture Mechanics

      • Dietmar Gross
      Pages 195-209

    7. Porous Media in the Light of History

      • Wolfgang Ehlers
      Pages 211-227

    8. Parameter Identification in Continuum Mechanics: From Hand-Fitting to Stochastic Modelling

      • Rolf Mahnken
      Pages 229-247

    9. Historical Development of the Knowledge of Shock and Blast Waves

      • Torsten Döge, Norbert Gebbeken
      Pages 249-265

    10. The Historical Development of the Strength of Ships

      • Eike Lehmann
      Pages 267-295

  4. Theories, Engineering Solutions and Applications in Fluid Dynamics

    1. Front Matter

      Pages 297-297
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Keywords

About this book

This collection of 23 articles is the output of lectures in special sessions on “The History of Theoretical, Material and Computational Mechanics” within the yearly conferences of the GAMM in the years 2010 in Karlsruhe, Germany, 2011 in Graz, Austria, and in 2012 in Darmstadt, Germany; GAMM is the “Association for Applied Mathematics and Mechanics”, founded in 1922 by Ludwig Prandtl and Richard von Mises. The contributions in this volume discuss different aspects of mechanics. They are related to solid and fluid mechanics in general and to specific problems in these areas including the development of numerical solution techniques. In the first part the origins and developments of conservation principles in mechanics and related variational methods are treated together with challenging applications from the 17th to the 20th century. Part II treats general and more specific aspects of material theories of deforming solid continua and porous soils. and Part III presents important theoretical and engineering developments in fluid mechanics, beginning with remarkable inventions in old Egypt, the still dominating role of the Navier-Stokes PDEs for fluid flows and their complex solutions for a wide field of parameters as well as the invention of pumps and turbines in the 19th and 20th century. The last part gives a survey on the development of direct variational methods – the Finite Element Method – in the 20th century with many extensions and generalizations.

 

Editors and Affiliations

  • Institute of Mechanics and Computational Mechanics (IBNM), Gottfried Wilhelm Leibniz Universität Hannover, Hannover, Germany

    Erwin Stein

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