singularities in elliptic boundary value problems and elasticity and their connection with failure initiation 37 interdisciplinary applied mathematics

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Singularities In Elliptic Boundary Value Problems And Elasticity And Their Connection With Failure Initiation

Author : Zohar Yosibash
ISBN : 9781461415084
Genre : Mathematics
File Size : 39. 13 MB
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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.

The Trigonometry Tryst

Author : J. A. Bailey
ISBN : 1539695352
Genre :
File Size : 27. 2 MB
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The Trigonometry Tryst is a revolutionary story that will fascinate both students and teachers. By bringing complex math terms to life, this story creates relationships that unfold easily for readers who once perceived trigonometry as challenging. Csc, a smart but troubled computer engineering major at Unit University, is confused and shocked to discover that Tan is moving out of their shared apartment and in with someone in a better quadrant. Tan and Cot work together on an architecture project and endure many heated debates before their relationship grows, and they begin working with each other's drastic personality differences. Cos, seeking her perfect match, is intrigued by the thoughtful and mysterious Sin, but she's never dared approach him. She continues her search by using the university's matchmaking system. One profile seizes her attention, but there are very few details about this person. Meanwhile, Sec, a basketball star with a bruised ego, hears that Cos is trying to find this mysterious match and becomes angry as Cos never desired to date him when he pursued her in the past. He teams up with Csc to detour Cos's efforts, so she may never find out who this mysterious match is and if he's right for her.

New Trends In Analysis And Interdisciplinary Applications

Author : Pei Dang
ISBN : 9783319488127
Genre : Mathematics
File Size : 23. 4 MB
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This book presents a collection of papers from the 10th ISAAC Congress 2015, held in Macau, China. The papers, prepared by respected international experts, address recent results in Mathematics, with a special focus on Analysis. By structuring the content according to the various mathematical topics, the volume offers specialists and non-specialists alike an excellent source of information on the state-of-the-art in Mathematical Analysis and its interdisciplinary applications.

Numerical Solution Of Partial Differential Equations Theory Algorithms And Their Applications

Author : Oleg P. Iliev
ISBN : 9781461471721
Genre : Mathematics
File Size : 42. 25 MB
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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.

Shapes And Geometries

Author : M. C. Delfour
ISBN : 9780898719369
Genre : Mathematics
File Size : 25. 67 MB
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Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

Centrifugal Pump Design

Author : John Tuzson
ISBN : 0471361003
Genre : Technology & Engineering
File Size : 49. 4 MB
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A hands-on, applications-based approach to the design and analysis of commonly used centrifugal pumps Centrifugal Pump Design presents a clear, practical design procedure that is solidly based on theoretical fluid dynamics fundamentals, without requiring higher math beyond algebra. Intended for use on the factory floor, this book offers a short, easy-to-read description of the fluid mechanic phenomena that occur in pumps, including those revealed by the most recent research. The design procedure incorporates a simple computer program that allows designs to be checked immediately and corrected as needed; readers learn to calibrate the performance calculation program based on their own test data. Other important features of this book include: * Up-to-date coverage of detailed design data * Guidance on selection, troubleshooting, and modification of existing pumps * A numerical example illustrating the design of a pump as readers move through the book * Manual calculations-including worked examples-and personal computer program listings critical to pump design * Ample references to all subjects for further study This unique handbook closes the gap between research and application and puts the fundamentals of advanced fluid mechanics where they will do the most good: in the hands of engineers, teachers, and designers who create industrial pumps.

Mathematical Analysis Of Evolution Information And Complexity

Author : Wolfgang Arendt
ISBN : 9783527628032
Genre : Science
File Size : 51. 2 MB
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Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.

Encyclopedia Of Thermal Stresses

Author : Richard B. Hetnarski
ISBN : 9400727380
Genre : Technology & Engineering
File Size : 74. 37 MB
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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.

Numerical Matrix Analysis

Author : Ilse C. F. Ipsen
ISBN : 9780898716764
Genre : Mathematics
File Size : 45. 63 MB
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Matrix analysis presented in the context of numerical computation at a basic level.

Variational Analysis And Aerospace Engineering

Author : Giuseppe Buttazzo
ISBN : 9780387958576
Genre : Mathematics
File Size : 39. 31 MB
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