Overview
- 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
Part of the book series: Lecture Notes in Applied and Computational Mechanics (LNACM, volume 67)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
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.
Authors and Affiliations
Bibliographic Information
Book Title: Computational Contact Mechanics
Book Subtitle: Geometrically Exact Theory for Arbitrary Shaped Bodies
Authors: Alexander Konyukhov, Karl Schweizerhof
Series Title: Lecture Notes in Applied and Computational Mechanics
DOI: https://doi.org/10.1007/978-3-642-31531-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
Hardcover ISBN: 978-3-642-31530-5Published: 15 August 2012
Softcover ISBN: 978-3-642-44541-5Published: 20 September 2014
eBook ISBN: 978-3-642-31531-2Published: 14 August 2012
Series ISSN: 1613-7736
Series E-ISSN: 1860-0816
Edition Number: 1
Number of Pages: XXII, 446
Topics: Solid Mechanics, Theoretical and Applied Mechanics, Classical Mechanics