Download or read book Mathematical Models of Solids and Fluids a Short Introduction written by Pascal Grange and published by Oxford University Press. This book was released on 2021 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to continuum mechanics, which models the behaviour of elastic solids and viscous fluids. It assumes only a working knowledge of classical mechanics, linear algebra and multivariable calculus. Every chapter contains exercises, with detailed solutions. The book is aimed at undergraduate students from scientific disciplines. Mathematics students will find examples of applications involving techniques from different branches of mathematics, such as geometry and differential equations. Physics students will find a gentle introduction to the notions of stress and material laws. Engineering students will find examples of classic exactly-solvable problems. The emphasis is on the thorough derivation of exact solutions, but estimates of the relevant orders of magnitude are provided.
Download or read book Mathematical Models of Solids and Fluids a short introduction written by Pascal Grange and published by Liverpool University Press. This book was released on 2021-09-15 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to continuum mechanics, which models the behaviour of elastic solids and viscous fluids. It assumes only a working knowledge of classical mechanics, linear algebra and multivariable calculus. Every chapter contains exercises, with detailed solutions. The book is aimed at undergraduate students from scientific disciplines. Mathematics students will find examples of applications involving techniques from different branches of mathematics, such as geometry and differential equations. Physics students will find a gentle introduction to the notions of stress and material laws. Engineering students will find examples of classic exactly-solvable problems. The emphasis is on the thorough derivation of exact solutions, but estimates of the relevant orders of magnitude are provided.
Download or read book Mathematical Models of Fluid Dynamics written by Rainer Ansorge and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Without sacrificing scientific strictness, this introduction to the field guides readers through mathematical modeling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behavior of the dynamics of physical flow. The book is carefully divided into three main parts: - The design of mathematical models of physical fluid flow; - A theoretical treatment of the equations representing the model, as Navier-Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as quantitative insights into the processes of flow events; - The construction and effective use of numerical procedures in order to find quantitative descriptions of concrete physical or technical fluid flow situations. Both students and experts wanting to control or predict the behavior of fluid flows by theoretical and computational fluid dynamics will benefit from this combination of all relevant aspects in one handy volume.
Download or read book Computational Multiscale Modeling of Fluids and Solids written by Martin Oliver Steinhauser and published by Springer Science & Business Media. This book was released on 2007-10-28 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devastatingly simple, yet hugely effective, the concept of this timely text is to provide a comprehensive overview of computational physics methods and techniques used for materials modeling on different length and time scales. Each chapter first provides an overview of the physical basic principles which are the basis for the numerical and mathematical modeling on the respective length scale. The book includes the micro scale, the meso-scale and the macro scale.
Download or read book Mathematical Modeling for Complex Fluids and Flows written by Michel Deville and published by Springer Science & Business Media. This book was released on 2012-01-13 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics. In doing so it supplies the means to design mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non-Newtonian fluids such as those required in food processing and polymeric flows. The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian, viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory, especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomial representations and accounting for non-inertial and curvature effects. Ranging from fundamental concepts to practical methodology, and including discussion of emerging technologies, this book is ideal for those requiring a single-source assessment of current practice in this intricate yet vital field.
Download or read book Mathematical Modelling of Solids with Nonregular Boundaries written by A.B. Movchan and published by CRC Press. This book was released on 2020-07-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling of Solids with Nonregular Boundaries demonstrates the use of asymptotic methods and other analytical techniques for investigating problems in solid mechanics. Applications to solids with nonregular boundaries are described in detail, providing precise and rigorous treatment of current methods and techniques. The book addresses problems in fracture mechanics of inhomogeneous media and illustrates applications in strength analysis and in geophysics. The rigorous approach allows the reader to explicitly analyze the stress-strain state in continuous media with cavities or inclusions, in composite materials with small defects, and in elastic solids with sharp inclusions. Effective asymptotic procedures for eigenvalue problems in domains with small defects are clearly outlined, and methods for analyzing singularly perturbed boundary value problems are examined. Introductory material is provided in the first chapter of Mathematical Modelling of Solids with Nonregular Boundaries, which presents a survey of relevant and necessary information, including equations of linear elasticity and formulations of the boundary value problems. Background information - in the form of definitions and general solutions - is also provided on elasticity problems in various bounded and unbounded domains. This book is an excellent resource for students, applied scientists, and engineers.
Download or read book Fluid Mechanics a Very Short Introduction written by Eric Lauga and published by Oxford University Press. This book was released on 2022-06-02 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Short Introductionsb: Brilliant, Sharp, InspiringFluid mechanics is an important branch of physics concerned with the way in which fluids, such as liquids and gases, behave when in motion and at rest. A quintessential interdisciplinary field of science, it interacts with many other scientific disciplines, from chemistry and biology to mathematicsand engineering.This Very Short Introduction introduces readers to the field of fluid mechanics by focusing on the fundamental physical ideas underlying it, and using everyday phenomena from daily life to demonstrate them, from dripping taps to swimming ducks. Following this set of core physical concepts, it showshow these underlying principles can be applied to a wide range of flow behaviours. Eric Lauga also highlights the role of fluid motion in both the natural and industrial world, and considers future applications of fluid mechanics in science.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.
Download or read book Computational Multiscale Modeling of Fluids and Solids written by Martin Steinhauser and published by Springer. This book was released on 2009-09-02 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devastatingly simple, yet hugely effective, the concept of this timely text is to provide a comprehensive overview of computational physics methods and techniques used for materials modeling on different length and time scales. Each chapter first provides an overview of the physical basic principles which are the basis for the numerical and mathematical modeling on the respective length scale. The book includes the micro scale, the meso-scale and the macro scale.
Download or read book Introduction to Mathematical Fluid Dynamics written by Richard E. Meyer and published by Courier Corporation. This book was released on 2012-03-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, and more. Geared toward advanced undergraduate and graduate students of mathematics and science; prerequisites include calculus and vector analysis. 1971 edition.
Download or read book Theoretical Fluid Mechanics written by Richard Fitzpatrick and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Theoretical Fluid Mechanics' has been written to aid physics students who wish to pursue a course of self-study in fluid mechanics. It is a comprehensive, completely self-contained text with equations of fluid mechanics derived from first principles, and any required advanced mathematics is either fully explained in the text, or in an appendix. It is accompanied by about 180 exercises with completely worked out solutions. It also includes extensive sections on the application of fluid mechanics to topics of importance in astrophysics and geophysics. These topics include the equilibrium of rotating, self-gravitating, fluid masses; tidal bores; terrestrial ocean tides; and the Eddington solar model."--Prové de l'editor.
Download or read book Mathematical Models of Fluiddynamics written by Rainer Ansorge and published by Wiley-VCH Verlag GmbH. This book was released on 2003-01 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the field contains a careful selection of topics and examples without sacrificing scientific strictness. The author guides readers through mathematical modelling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behaviour of the dynamics of physical flow. Both students and experts intending to control or predict the behavior of fluid flows by theoretical and computational fluid dynamics will benefit from the combination of all relevant aspects in one handy volume. The book consists of three main parts: The design of mathematical models of physical fluid flow; A theoretical treatment of the equations representing the model, as Navier-Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as quantitative insights into the processes of flow events; The construction and effective use of numerical procedures in order to find quantitative descriptions of concrete physical or technical fluid flow situations. This is the first text of its kind to merge all these subjects so thoroughly.
Download or read book Mathematical Fluid Mechanics written by Jiri Neustupa and published by Birkhäuser. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.
Download or read book Mathematical Theory in Fluid Mechanics written by G P Galdi and published by CRC Press. This book was released on 1996-08-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of four contributions that are based on a series of lectures delivered by Jens Frehse. Konstantin Pikeckas, K.R. Rajagopal and Wolf von Wahl t the Fourth Winter School in Mathematical Theory in Fluid Mechanics, held in Paseky, Czech Republic, from December 3-9, 1995. In these papers the authors present the latest research and updated surveys of relevant topics in the various areas of theoretical fluid mechanics. Specifically, Frehse and Ruzicka study the question of the existence of a regular solution to Navier-Stokes equations in five dimensions by means of weighted estimates. Pileckas surveys recent results regarding the solvability of the Stokes and Navier-Stokes system in domains with outlets at infinity. K.R. Rajagopal presents an introduction to a continuum approach to mixture theory with the emphasis on the constitutive equation, boundary conditions and moving singular surface. Finally, Kaiser and von Wahl bring new results on stability of basic flow for the Taylor-Couette problem in the small-gap limit. This volume would be indicated for those in the fields of applied mathematicians, researchers in fluid mechanics and theoretical mechanics, and mechanical engineers.
Download or read book Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids written by Laura De Lorenzis and published by Springer. This book was released on 2021-02-09 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book examines innovative numerical methods for computational solid and fluid mechanics that can be used to model complex problems in engineering. It also presents innovative and promising simulation methods, including the fundamentals of these methods, as well as advanced topics and complex applications. Further, the book explores how numerical simulations can significantly reduce the number of time-consuming and expensive experiments required, and can support engineering decisions by providing data that would be very difficult, if not impossible, to obtain experimentally. It also includes chapters covering topics such as particle methods addressing particle-based materials and numerical methods that are based on discrete element formulations; fictitious domain methods; phase field models; computational fluid dynamics based on modern finite volume schemes; hybridizable discontinuous Galerkin methods; and non-intrusive coupling methods for structural models.
Download or read book Mathematical Modeling for Complex Fluids and Flows written by Michel Deville and published by Springer. This book was released on 2012-01-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics. In doing so it supplies the means to design mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non-Newtonian fluids such as those required in food processing and polymeric flows. The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian, viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory, especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomial representations and accounting for non-inertial and curvature effects. Ranging from fundamental concepts to practical methodology, and including discussion of emerging technologies, this book is ideal for those requiring a single-source assessment of current practice in this intricate yet vital field.
Download or read book Fundamentals of the Mechanics of Solids written by Paolo Maria Mariano and published by Birkhäuser. This book was released on 2015-11-30 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This distinctive textbook aims to introduce readers to the basic structures of the mechanics of deformable bodies, with a special emphasis on the description of the elastic behavior of simple materials and structures composed by elastic beams. The authors take a deductive rather than inductive approach and start from a few first, foundational principles. A wide selection of exercises, many with hints and solutions, are provided throughout and organized in a way that will allow readers to form a link between abstract mathematical concepts and real-world applications. The text begins with the definition of bodies and deformations, keeping the kinematics of rigid bodies as a special case; the authors also distinguish between material and spatial metrics, defining each one in the pertinent space. Subsequent chapters cover observers and classes of possible changes; forces, torques, and related balances, which are derived from the invariance under classical changes in observers of the power of the external actions over a body, rather than postulated a priori; constitutive structures; variational principles in linear elasticity; the de Saint-Venant problem; yield criteria and a discussion of their role in the representation of material behavior; and an overview of some bifurcation phenomena, focusing on the Euler rod. An appendix on tensor algebra and tensor calculus is included for readers who need a brief refresher on these topics. Fundamentals of the Mechanics of Solids is primarily intended for graduate and advanced undergraduate students in various fields of engineering and applied mathematics. Prerequisites include basic courses in calculus, mathematical analysis, and classical mechanics.
Download or read book Numerical Modeling in Materials Science and Engineering written by Michel Rappaz and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies related to the modeling of the complex phenomena occurring in materials processing. It is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics, and for engineering professionals or researchers.
