The History of Theoretical, Material and Computational Mechanics - Mathematics Meets Mechanics and Engineering, 1st Edition

  • Published By:
  • ISBN-10: 3642399053
  • ISBN-13: 9783642399053
  • DDC: 620.1
  • Grade Level Range: College Freshman - College Senior
  • 490 Pages | eBook
  • Original Copyright 2014 | Published/Released May 2014
  • This publication's content originally published in print form: 2014

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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. 

Table of Contents

Front Cover.
Half Title Page.
Other Frontmatter.
Title Page.
Copyright Page.
1: Mechanical Conservation Principles, Variational Calculus and Engineering Applications from the 17th to the 20th Century.
2: The Origins of Mechanical Conservation Principles and Variational Calculus in the 17th Century.
3: Principles of Least Action and of Least Constraint.
4: Lagrange’s “Récherches Sur La Libration De La Lune” – From the Principle of Least Action to Lagrange’s Principle.
5: The Development of Analytical Mechanics by Euler, Lagrange and Hamilton – From a Student’s Point of View.
6: Heun and Hamel – Representatives of Mechanics around 1900.
7: The Machine of Bohnenberger.
8: On the Historical Development of Human Walking Dynamics.
9: Material Theories of Solid Continua and Solutions of Engineering Problems.
10: On the History of Material Theory – A Critical Review.
11: Some Remarks on the History of Plasticity – Heinrich Hencky, a Pioneer of the Early Years.
12: Prandtl-Tomlinson Model: A Simple Model Which Made History.
13: A Historical View on Shakedown Theory.
14: Some Remarks on the History of Fracture Mechanics.
15: Porous Media in the Light of History.
16: Parameter Identification in Continuum Mechanics: From Hand-Fitting to Stochastic Modelling.
17: Historical Development of the Knowledge of Shock and Blast Waves.
18: The Historical Development of the Strength of Ships.
19: Theories.
20: The Development of Fluid Mechanics from Archimedes to Stokes and Reynolds*.
21: The Millennium-Problem of Fluid Mechanics – the Solution of the Navier-Stokes Equations.
22: On Non-uniqueness Issues Associated with Fröhlich's Solution for Boussinesq’s Concentrated Force Problem for an Isotropic Elastic Halfspace.
23: Essential Contributions of Austria to Fluid Dynamics Prior to the End of World War II.
24: Numerical Methods in Solid Mechanics from Engineering Intuition and Variational Calculus.
25: From Newton’s Principia via Lord Rayleigh’s Theory of Sound to Finite Elements.
26: History of the Finite Element Method – Mathematics Meets Mechanics –Part I: Engineering Developments.
27: History of the Finite Element Method – Mathematics Meets Mechanics –Part II: Mathematical Foundation of Primal Fem for Elastic Deformations.
Author Index.
Subject Index.