Introduction to Tensor Calculus and Continuum Mechanics

Introduction to Tensor Calculus and Continuum Mechanics
Title Introduction to Tensor Calculus and Continuum Mechanics PDF eBook
Author John Henry Heinbockel
Publisher
Pages 367
Release 1996
Genre
ISBN

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Tensor Algebra and Tensor Analysis for Engineers

Tensor Algebra and Tensor Analysis for Engineers
Title Tensor Algebra and Tensor Analysis for Engineers PDF eBook
Author Mikhail Itskov
Publisher Springer Science & Business Media
Pages 253
Release 2009-04-30
Genre Technology & Engineering
ISBN 3540939075

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There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.

Tensor Analysis and Continuum Mechanics

Tensor Analysis and Continuum Mechanics
Title Tensor Analysis and Continuum Mechanics PDF eBook
Author Wilhelm Flügge
Publisher Springer Science & Business Media
Pages 215
Release 2013-11-11
Genre Science
ISBN 3642883826

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Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.

A Brief on Tensor Analysis

A Brief on Tensor Analysis
Title A Brief on Tensor Analysis PDF eBook
Author James G. Simmonds
Publisher Springer Science & Business Media
Pages 124
Release 2012-10-31
Genre Mathematics
ISBN 1441985220

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In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.

Introduction to Continuum Mechanics

Introduction to Continuum Mechanics
Title Introduction to Continuum Mechanics PDF eBook
Author David Rubin
Publisher Newnes
Pages 571
Release 2012-12-02
Genre Science
ISBN 0080983871

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Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors is introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples and problems, many with solutions. Through the addition of more advanced material (solution of classical elasticity problems, constitutive equations for viscoelastic fluids, and finite deformation theory), this popular introduction to modern continuum mechanics has been fully revised to serve a dual purpose: for introductory courses in undergraduate engineering curricula, and for beginning graduate courses.

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials
Title Continuum Mechanics and Theory of Materials PDF eBook
Author Peter Haupt
Publisher Springer Science & Business Media
Pages 666
Release 2013-03-14
Genre Technology & Engineering
ISBN 3662047756

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The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

Continuum Mechanics and Linear Elasticity

Continuum Mechanics and Linear Elasticity
Title Continuum Mechanics and Linear Elasticity PDF eBook
Author Ciprian D. Coman
Publisher Springer Nature
Pages 528
Release 2019-11-02
Genre Technology & Engineering
ISBN 9402417710

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This is an intermediate book for beginning postgraduate students and junior researchers, and offers up-to-date content on both continuum mechanics and elasticity. The material is self-contained and should provide readers sufficient working knowledge in both areas. Though the focus is primarily on vector and tensor calculus (the so-called coordinate-free approach), the more traditional index notation is used whenever it is deemed more sensible. With the increasing demand for continuum modeling in such diverse areas as mathematical biology and geology, it is imperative to have various approaches to continuum mechanics and elasticity. This book presents these subjects from an applied mathematics perspective. In particular, it extensively uses linear algebra and vector calculus to develop the fundamentals of both subjects in a way that requires minimal use of coordinates (so that beginning graduate students and junior researchers come to appreciate the power of the tensor notation).