Differential Geometry and Kinematics of Continua by John D Clayton

Differential Geometry and Kinematics of Continua

byJohn D Clayton

Kobo ebook | July 31, 2014

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This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided.

Contents:

  • Introduction
  • Geometric Fundamentals
  • Kinematics of Integrable Deformation
  • Geometry of Anholonomic Deformation
  • Kinematics of Anholonomic Deformation
  • List of Symbols
  • Bibliography
  • Index

Readership: Researchers in mathematical physics and engineering mechanics.
Key Features:

  • Presentation of mathematical operations and examples in anholonomic space associated with a multiplicative decomposition (e.g., of the gradient of motion) is more general and comprehensive than any given elsewhere and contains original ideas and new results
  • Line-by-line derivations are frequent and exhaustive, to facilitate practice and enable verification of final results
  • General analysis is given in generic curvilinear coordinates; particular sections deal with applications and examples in Cartesian, cylindrical, spherical, and convected coordinates. Indicial and direct notations of tensor calculus enable connections with historic and modern literature, respectively
Title:Differential Geometry and Kinematics of ContinuaFormat:Kobo ebookPublished:July 31, 2014Publisher:World Scientific Publishing CompanyLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9814616052

ISBN - 13:9789814616058

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