Lecture Notes in Applied and Computational Mechanics

Computational Contact Mechanics

Geometrically Exact Theory for Arbitrary Shaped Bodies

Authors: Konyukhov, Alexander, Schweizerhof, Karl

  • Fuses differential geometry into computational contact mechanics
  • Research monograph on computational contact mechanics formulated in a covariant form
  • Gives the necessary introductory treatment of differential geometry for curves and surfaces
  • Contains new analytical results for the verification of contact algorithms
  • Gives the reader a closed form algorithms for finite element implementations independently of the type of approximation  involved in the discretization process as well as for any isogeometric analysis
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  • ISBN 978-3-642-44541-5
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About this book

This book contains a systematical analysis of geometrical situations  leading to  contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface.  Each contact pair  is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system.  The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a  certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others  are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are  then ready-for-implementation numerical algorithms within the finite element method including any arbitrary discretization techniques such as high order and isogeometric finite elements, which are most convenient for the considered geometrical situation.

The book proposes a consistent study of geometry and kinematics, variational formulations, constitutive relations for surfaces and discretization techniques for all considered geometrical pairs and  contains the associated  numerical analysis as well as some new analytical results in contact mechanics.

Table of contents (14 chapters)

  • Introduction

    Konyukhov, Alexander (et al.)

    Pages 1-24

  • Differential Geometry of Surfaces and Curves

    Konyukhov, Alexander (et al.)

    Pages 25-34

  • Closest Point Projection Procedure and Corresponding Curvilinear Coordinate System

    Konyukhov, Alexander (et al.)

    Pages 35-62

  • Geometry and Kinematics of Contact

    Konyukhov, Alexander (et al.)

    Pages 63-118

  • Weak Formulation of Contact Conditions

    Konyukhov, Alexander (et al.)

    Pages 119-133

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-3-642-31531-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-3-642-31530-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $209.00
price for USA
  • ISBN 978-3-642-44541-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Computational Contact Mechanics
Book Subtitle
Geometrically Exact Theory for Arbitrary Shaped Bodies
Authors
Series Title
Lecture Notes in Applied and Computational Mechanics
Series Volume
67
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-31531-2
DOI
10.1007/978-3-642-31531-2
Hardcover ISBN
978-3-642-31530-5
Softcover ISBN
978-3-642-44541-5
Series ISSN
1613-7736
Edition Number
1
Number of Pages
XXII, 446
Topics