Matrix-tensor methods in continuum mechanics.
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Matrix-tensor methods in continuum mechanics. by Sidney F. Borg

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Published by Van Nostrand in Princeton, N.J .
Written in English

Subjects:

  • Calculus of tensors.,
  • Matrices.,
  • Continuum mechanics.

Book details:

Edition Notes

Includes bibliography.

Classifications
LC ClassificationsQA433 .B62
The Physical Object
Pagination313 p.
Number of Pages313
ID Numbers
Open LibraryOL5873309M
LC Control Number63000949

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The best book I found for my master of engineering program on this subject. It provides what a student needs to learn. It is one of the few mathematical text books that are free of the common problem of extended useless work that disturbs the reader and undermines the delivery of information. This book is right to the by:   Introduction. Definition of a Matrix. Matrix Arithmetic, Algebra, and Calculus. Introduction to Vector Analysis. A vector times a vector may equal a scalar. A vector times a vector may result in a vector. Introduction to Complex Variable Theory. CONTINUUM MECHANICS - Introduction to tensors Tensor algebra Vectors Component representation Any vector a can be uniquely de ned with the linear combination of the basis vectors (e 1, e 2 and e 3) as a = a 1e 1 + a 2e 2 + a 3e 3; (6) where the components (a 1, a 2 and a 3) are real numbers. The compo-nents of a along the bases are obtained by File Size: KB. The double dot product of two matrices produces a scalar result. It is written in matrix notation as \({\bf A}: {\bf B}\). Although rarely used outside of continuum mechanics, is in fact quite common in advanced applications of linear elasticity.

3 the Kronecker delta symbol ij, de ned by ij =1ifi= jand ij =0fori6= j,withi;jranging over the values 1,2,3, represents the 9 quantities 11 =1 21 =0 31 =0 12 =0 22 =1 32 =0 13 =0 23 =0 33 =1: The symbol ij refers to all of the components of the system simultaneously. As another example, consider the equation.   This book is a considerable outgrowth of lecture notes on Mechanics of en vironmentally related systems I, which I hold since more than ten years in the Department of Mechanics at the Darmstadt University of Technology for upper level students majoring in mechanics, mathematics, physics and the classical engineering sciences. These lectures form a canon of courses over three 5/5(1). in the current presentation is still meant to be a set of lecture notes, not a text book. It has been organized as follows: Volume I: A Brief Review of Some Mathematical Preliminaries Volume II: Continuum Mechanics Volume III: Elasticity This is Volume II. My appreciation for mechanics was nucleated by Professors Douglas Amarasekara and. Tensors have their applications to Riemannian Geometry, Mechanics, Elasticity, Theory of Relativity, Electromagnetic Theory and many other disciplines of Science and Engineering. This book has been presented in such a clear and easy way that the students will have no difficulty in understanding Size: 1MB.

Matrix-tensor methods in continuum mechanics. Matrix-tensor methods in continuum mechanics. - Full View | HathiTrust Digital Library | HathiTrust Digital Library Permanent link to this book Link to this page. Embed this book. Version. UTC About the version. About this Book. He is coeditor of the book The Complete Works of Gabrio Piola, and has served as guest coeditor for the journals Continuum Mechanics and Thermodynamics, Mathematics and Mechanics of Solids, and International Journal of Engineering by: The book is divided into twelve chapters with the following topics: Tensors, Continuum Kinematics, Stress, The Objectivity of Tensors, The Fundamental Equations of Continuum Mechanics, An Introduction to Constitutive Equations, Linear Elasticity, Hyperelasticity, Plasticity (small and large deformations), Thermoelasticity (small and large deformations), Damage Mechanics (small and large deformations), . Additional Physical Format: Online version: Borg, Sidney F. Matrix-tensor methods in continuum mechanics. Princeton, N.J., Van Nostrand [] (OCoLC)