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Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation

Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation Author Zohar Yosibash
ISBN-10 9781461415084
Release 2011-12-02
Pages 462
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This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.



Numerical Solution of Partial Differential Equations Theory Algorithms and Their Applications

Numerical Solution of Partial Differential Equations  Theory  Algorithms  and Their Applications Author Oleg P. Iliev
ISBN-10 9781461471721
Release 2013-06-04
Pages 327
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One of the current main challenges in the area of scientific computing​ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.



Encyclopedia of Thermal Stresses

Encyclopedia of Thermal Stresses Author Richard B. Hetnarski
ISBN-10 9400727380
Release 2013-12-04
Pages 6643
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The Encyclopedia of Thermal Stresses is an important interdisciplinary reference work. In addition to topics on thermal stresses, it contains entries on related topics, such as the theory of elasticity, heat conduction, thermodynamics, appropriate topics on applied mathematics, and topics on numerical methods. The Encyclopedia is aimed at undergraduate and graduate students, researchers and engineers. It brings together well established knowledge and recently received results. All entries were prepared by leading experts from all over the world, and are presented in an easily accessible format. The work is lavishly illustrated, examples and applications are given where appropriate, ideas for further development abound, and the work will challenge many students and researchers to pursue new results of their own. This work can also serve as a one-stop resource for all who need succinct, concise, reliable and up to date information in short encyclopedic entries, while the extensive references will be of interest to those who need further information. For the coming decade, this is likely to remain the most extensive and authoritative work on Thermal Stresses.



Applied Mathematics

Applied Mathematics Author Susmita Sarkar
ISBN-10 9788132225478
Release 2015-10-13
Pages 313
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The book is based on research presentations at the international conference, “Emerging Trends in Applied Mathematics: In the Memory of Sir Asutosh Mookerjee, S.N. Bose, M.N. Saha and N.R. Sen”, held at the Department of Applied Mathematics, University of Calcutta, during 12–14 February 2014. It focuses on various emerging and challenging topics in the field of applied mathematics and theoretical physics. The book will be a valuable resource for postgraduate students at higher levels and researchers in applied mathematics and theoretical physics. Researchers presented a wide variety of themes in applied mathematics and theoretical physics—such as emergent periodicity in a field of chaos; Ricci flow equation and Poincare conjecture; Bose–Einstein condensation; geometry of local scale invariance and turbulence; statistical mechanics of human resource allocation: mathematical modelling of job-matching in labour markets; contact problem in elasticity; the Saha equation; computational fluid dynamics with applications in aerospace problems; an introduction to data assimilation, stochastic analysis and bounds on noise for Holling type-II model, graph theoretical invariants of chemical and biological systems; strongly correlated phases and quantum phase transitions of ultra cold bosons; and the mathematical modelling of breast cancer treatment.



THE SINGULARITY EXPANSION METHOD IN ELECTROMAGNETICS A SUMMARY SURVEY AND OPEN QUESTIONS

THE SINGULARITY EXPANSION METHOD IN ELECTROMAGNETICS  A SUMMARY SURVEY AND OPEN QUESTIONS Author Carl E. Baum
ISBN-10 9781105424045
Release
Pages
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THE SINGULARITY EXPANSION METHOD IN ELECTROMAGNETICS A SUMMARY SURVEY AND OPEN QUESTIONS has been writing in one form or another for most of life. You can find so many inspiration from THE SINGULARITY EXPANSION METHOD IN ELECTROMAGNETICS A SUMMARY SURVEY AND OPEN QUESTIONS also informative, and entertaining. Click DOWNLOAD or Read Online button to get full THE SINGULARITY EXPANSION METHOD IN ELECTROMAGNETICS A SUMMARY SURVEY AND OPEN QUESTIONS book for free.



Nonlinear Effects in Fluids and Solids

Nonlinear Effects in Fluids and Solids Author Michael M. Carroll
ISBN-10 9781461303299
Release 2012-12-06
Pages 384
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This volume of scientific papers is dedicated with gratitude and esteem to Ronald Rivlin and is offered as a token of appreciation by former students, col laborators, and friends. Ronald Rivlin's name is synonymous with modem developments in contin uum mechanics. His outstanding pioneering theoretical and experimental re ·search in finite elasticity is a landmark. From his work there has followed a spate of developments in which he played the leading role-the theory of fiber-rein forced materials, the developments of the theory of constitutive equations, the theory of materials with memory, the theory of the fracture of elastomers, the theory of viscoelastic fluids and solids, the development of nonlinear crystal physics, the theory of small deformations superimposed on large, and the effect of large initial strain on wave propagation. It is in Rivlin's work that universal relations were first recognized. Here also are to be found lucid explanations of physical phenomena such as the Poynting effect for elastic rods in torsion. Addi tionally, he and his co-workers predicted the presence of secondary flows for viscoelastic fluids in straight pipes of noncircular cross section under a uniform pressure head. While some others may have displayed a cavalier lack of concern for physical reality and an intoxication with mathematical idiom, Rivlin has al ways been concerned with genuine mathematical and physical content. All of his papers contain interesting and illuminating material-and may be read with profit by anyone interested in continuum mechanics.



Variational Analysis and Aerospace Engineering

Variational Analysis and Aerospace Engineering Author Giuseppe Buttazzo
ISBN-10 9780387958576
Release 2009-08-21
Pages 518
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Variational Analysis and Aerospace Engineering has been writing in one form or another for most of life. You can find so many inspiration from Variational Analysis and Aerospace Engineering also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Variational Analysis and Aerospace Engineering book for free.



Elliptic Operators and Compact Groups

Elliptic Operators and Compact Groups Author M.F. Atiyah
ISBN-10 9783540378112
Release 2006-08-01
Pages 100
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Elliptic Operators and Compact Groups has been writing in one form or another for most of life. You can find so many inspiration from Elliptic Operators and Compact Groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Elliptic Operators and Compact Groups book for free.



Hyperbolic Problems

Hyperbolic Problems Author American Institute of Mathematical Sciences
ISBN-10 1601330170
Release 2014
Pages 1069
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Hyperbolic Problems has been writing in one form or another for most of life. You can find so many inspiration from Hyperbolic Problems also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Hyperbolic Problems book for free.



Physical and Mathematical Modeling of Earth and Environment Processes

Physical and Mathematical Modeling of Earth and Environment Processes Author Vladimir Karev
ISBN-10 9783319777887
Release 2018-03-24
Pages 382
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This book is the result of collaboration within the framework of the Third International Scientific School for Young Scientists held at the Ishlinskii Institute for Problems in Mechanics of Russian Academy of Sciences, 2017, November. The papers included describe studies on the dynamics of natural system – geosphere, hydrosphere, atmosphere—and their interactions, the human contribution to naturally occurring processes, laboratory modeling of earth and environment processes, and testing of new developed physical and mathematical models. The book particularly focuses on modeling in the field of oil and gas production as well as new alternative energy sources.



Iris Runge

Iris Runge Author Renate Tobies
ISBN-10 9783034802512
Release 2012-01-05
Pages 442
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This book concerns the origins of mathematical problem solving at the internationally active Osram and Telefunken Corporations during the golden years of broadcasting and electron tube research. The woman scientist Iris Runge, who received an interdisciplinary education at the University of Göttingen, was long employed as the sole mathematical authority at these companies in Berlin. It will be shown how mathematical connections were made between statistics and quality control, and between physical-chemical models and the actual problems of mass production. The organization of industrial laboratories, the relationship between theoretical and experimental work, and the role of mathematicians in these settings will also be explained. By investigating the social, economic, and political conditions that unfolded from the time of the German Empire until the end of the Second World War, the book hopes to build a bridge between specialized fields – mathematics and engineering – and the general culture of a particular era. It hopes, furthermore, to build a bridge between the history of science and industry, on the one hand, and the fields of Gender and Women’s Studies on the other. Finally, by examining the life and work of numerous industrial researchers, insight will be offered into the conditions that enabled a woman to achieve a prominent professional position during a time when women were typically excluded from the scientific workforce.



Modern Mathematical Methods and High Performance Computing in Science and Technology

Modern Mathematical Methods and High Performance Computing in Science and Technology Author Vinai K. Singh
ISBN-10 9789811014543
Release 2016-08-06
Pages 285
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The book discusses important results in modern mathematical models and high performance computing, such as applied operations research, simulation of operations, statistical modeling and applications, invisibility regions and regular meta-materials, unmanned vehicles, modern radar techniques/SAR imaging, satellite remote sensing, coding, and robotic systems. Furthermore, it is valuable as a reference work and as a basis for further study and research. All contributing authors are respected academicians, scientists and researchers from around the globe. All the papers were presented at the international conference on Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST 2015), held at Raj Kumar Goel Institute of Technology, Ghaziabad, India, from 27–29 December 2015, and peer-reviewed by international experts. The conference provided an exceptional platform for leading researchers, academicians, developers, engineers and technocrats from a broad range of disciplines to meet and discuss state-of-the-art mathematical methods and high performance computing in science & technology solutions. This has brought new prospects for collaboration across disciplines and ideas that facilitate novel breakthroughs.



Mechanics of Poroelastic Media

Mechanics of Poroelastic Media Author A.P.S. Selvadurai
ISBN-10 0792333292
Release 1996-01-31
Pages 398
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Mechanics of Poroelastic Media has been writing in one form or another for most of life. You can find so many inspiration from Mechanics of Poroelastic Media also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mechanics of Poroelastic Media book for free.



An Introduction to Continuum Mechanics

An Introduction to Continuum Mechanics Author J. N. Reddy
ISBN-10 9781107025431
Release 2013-07-29
Pages 470
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This best-selling textbook presents the concepts of continuum mechanics, and the second edition includes additional explanations, examples and exercises.



Partial Differential Equations

Partial Differential Equations Author Roland Glowinski
ISBN-10 9781402087585
Release 2008-06-26
Pages 292
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For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.



ICCS20 20th International Conference on Composite Structures

ICCS20   20th International Conference on Composite Structures Author Nicholas Fantuzzi
ISBN-10 9788893850414
Release 2017-07-24
Pages 352
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Composite materials have aroused a great interest over the last few decades, as proven by the huge number of scientific papers and industrial progress. The increase in the use of composite structures in different engineering practices justify the present international meeting where researches from every part of the globe can share and discuss the recent advancements regarding the use of structural components within advanced applications such as buckling, vibrations, repair, reinforcements, concrete, composite laminated materials and more recent metamaterials. Studies about composite structures are truly multidisciplinary and the given contributions can help other researches and professional engineers in their own field. This Conference is suitable as a reference for engineers and scientists working in the professional field, in the industry and the academia and it gives the possibility to share recent advancements in different engineering practices to the outside world. This book aims to collect selected plenary and key-note lectures of this International Conference. For this reason, the establishment of this 20th edition of International Conference on Composite Structures has appeared appropriate to continue what has been begun during the previous editions. ICCS wants to be an occasion for many researchers from each part of the globe to meet and discuss about the recent advancements regarding the use of composite structures, sandwich panels, nanotechnology, bio-composites, delamination and fracture, experimental methods, manufacturing and other countless topics that have filled many sessions during this conference. As a proof of this event, which has taken place in Paris (France), selected plenary and key-note lectures have been collected in the present book.



Production Factor Mathematics

Production Factor Mathematics Author Martin Grötschel
ISBN-10 364211248X
Release 2010-08-05
Pages 402
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Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like How can mathematics improve to the improvement of technological processes and products? What is happening already? Where are the deficits? What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering.