The Characterization Of Finite Elasticities

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The Characterization Of Finite Elasticities

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Author : David J. Grynkiewicz
language : en
Publisher: Springer Nature
Release Date : 2022-10-26

The Characterization Of Finite Elasticities written by David J. Grynkiewicz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-26 with Mathematics categories.

This book develops a new theory in convex geometry, generalizing positive bases and related to Carathéordory’s Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra) This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids. This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.

Finite Elasticity And Viscoelasticity A Course In The Nonlinear Mechanics Of Solids

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Author : Aleksey Drozdov
language : en
Publisher: World Scientific
Release Date : 1996-01-11

Finite Elasticity And Viscoelasticity A Course In The Nonlinear Mechanics Of Solids written by Aleksey Drozdov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-11 with Mathematics categories.

This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory. The objective is to expose the most intriguing aspects of elasticity and viscoelasticity with finite strains in such a way as to ensure mathematical correctness, on the one hand, and to demonstrate a wide spectrum of physical phenomena typical only of nonlinear mechanics, on the other.A novel aspect of the book is that it contains a number of examples illustrating surprising behaviour in materials with finite strains, as well as comparisons between theoretical predictions and experimental data for rubber-like polymers and elastomers.The book aims to fill a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics. The book has been developed from a graduate course in applied mathematics which the author has given for a number of years.

Nasa Technical Memorandum

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Author :
language : en
Publisher:
Release Date : 1988

Nasa Technical Memorandum written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Aeronautics categories.

Algorithmic Learning Theory

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Author : Yoav Freund
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-29

Algorithmic Learning Theory written by Yoav Freund and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-29 with Computers categories.

This book constitutes the refereed proceedings of the 19th International Conference on Algorithmic Learning Theory, ALT 2008, held in Budapest, Hungary, in October 2008, co-located with the 11th International Conference on Discovery Science, DS 2008. The 31 revised full papers presented together with the abstracts of 5 invited talks were carefully reviewed and selected from 46 submissions. The papers are dedicated to the theoretical foundations of machine learning; they address topics such as statistical learning; probability and stochastic processes; boosting and experts; active and query learning; and inductive inference.

Collected Papers Of R S Rivlin

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Author : Grigory I. Barenblatt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14

Collected Papers Of R S Rivlin written by Grigory I. Barenblatt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-14 with Technology & Engineering categories.

R.S. Rivlin is one of the principal architects of nonlinear continuum mechanics: His work on the mechanics of rubber (in the 1940s and 50s) established the basis of finite elasticity theory. These volumes make most of his scientific papers available again and show the full scope and significance of his contributions.

Defects And Anelasticity In The Characterization Of Crystalline Solids

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Author : American Society of Mechanical Engineers. Winter Annual Meeting
language : en
Publisher: American Society of Mechanical Engineers
Release Date : 1992

Defects And Anelasticity In The Characterization Of Crystalline Solids written by American Society of Mechanical Engineers. Winter Annual Meeting and has been published by American Society of Mechanical Engineers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.

Catalog Of National Bureau Of Standards Publications 1966 1976

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Author : United States. National Bureau of Standards. Technical Information and Publications Division
language : en
Publisher:
Release Date : 1978

Catalog Of National Bureau Of Standards Publications 1966 1976 written by United States. National Bureau of Standards. Technical Information and Publications Division and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Government publications categories.

Nonlinear Problems Of Elasticity

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Author : Stuart Antman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Nonlinear Problems Of Elasticity written by Stuart Antman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.

Constitutive Models For Rubber Viii

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Author : Nere Gil-Negrete
language : en
Publisher: CRC Press
Release Date : 2013-06-03

Constitutive Models For Rubber Viii written by Nere Gil-Negrete and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-03 with Technology & Engineering categories.

Due to their unique properties, rubber materials are found in multiple engineering applications such as tires, engine mounts, shock absorbers, flexible joints, seals, etc. Nevertheless, the complex nature of the behavior of such material makes it difficult to accurately model and predict the performance of these units.The challenge to correctly rep

Scientific And Technical Aerospace Reports

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Author :
language : en
Publisher:
Release Date : 1995

Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.