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8126 results in Fluid dynamics and solid mechanics

Page 170 of 407

  • 7 - Elastic Material Models

  • Franco M. Capaldi, Merrimack College, Massachusetts
  • Book:
    Continuum Mechanics
    Published online:
    05 August 2012
    Print publication:
    18 June 2012, pp 183-213

  • Summary

    In this chapter, we discuss constitutive model development for elastic materials. A material is considered purely elastic if it lacks the means to internally dissipate energy during deformation. Thus, a purely elastic material will not exhibit hysteresis or rate dependence. In addition, the deformation of an elastic material is reversible. Removal of load will allow the material to regain its original shape. A thermoelastic material model was used to introduce the concepts of constitutive modeling in Chapter 4. While many of the results from the analysis in Chapter 4 will be restated here, the reader may refer back to Chapter 4 for the detailed derivations.

    While first developing the general framework for finite thermoelasticity, we will also discuss specialization of the model for isothermal finite elasticity, which assumes constant uniform temperature fields, hyperelastic materials for which there exists a strain energy function, and linear thermoelastic materials for which stress and strain are proportional. While the linear dependence between stress and strain works well for some materials, many engineering materials such as natural and synthetic polymers exhibit strong nonlinearity of the stress-strain curve even before yielding. This leads to a material nonlinearity in the constitutive response functions. In addition, subjecting any material model to large strains leads to a geometric nonlinearity. Large strain deformation is referred to as finite deformation. Interestingly, some of these polymers may be deformed to very large strains and recover their original shape when released.

  • A MODIFIED PÓLYA URN PROCESS AND AN INDEX FOR SPATIAL DISTRIBUTIONS WITH VOLUME EXCLUSION

  • Part of
  • BENJAMIN J. BINDER, EMILY J. HACKETT-JONES, JONATHAN TUKE, KERRY A. LANDMAN
  • Journal:
    The ANZIAM Journal / Volume 53 / Issue 2 / October 2011
    Published online by Cambridge University Press:
    12 June 2012, pp. 122-133
    • Article
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  • Spatial data sets can be analysed by counting the number of objects in equally sized bins. The bin counts are related to the Pólya urn process, where coloured balls (for example, white or black) are removed from the urn at random. If there are insufficient white or black balls for the prescribed number of trials, the Pólya urn process becomes untenable. In this case, we modify the Pólya urn process so that it continues to describe the removal of volume within a spatial distribution of objects. We determine when the standard formula for the variance of the standard Pólya distribution gives a good approximation to the true variance. The variance quantifies an index for assessing whether a spatial point data set is at its most randomly distributed state, called the complete spatial randomness (CSR) state. If the bin size is an order of magnitude larger than the size of the objects, then the standard formula for the CSR limit is indicative of when the CSR state has been attained. For the special case when the object size divides the bin size, the standard formula is in fact exact.

Principles of Seismology
  • Agustin Udías
  • Published online:
    05 June 2012
    Print publication:
    13 January 2000
  • This book, first published in 2000, is an introductory text on seismology intended for upper division undergraduates and graduate students. It emphasises fundamental concepts and basic mathematical developments, and is intended to be 'student friendly'. The author explains the fundamental concepts in full detail with step-by-step development of the mathematics, although the book does assume a knowledge of vector and tensor analysis, calculus and ordinary and partial differential equations, as well as of fundamental physics, especially mechanics and elasticity theory. Simple examples, such as one-dimensional problems and liquid media are used as introductory topics. The book covers most of the fundamental topics in seismology, including seismic wave propagation, normal mode theory, ray theory approximation, body and surface waves, source mechanisms, kinematic and dynamic models and applications to the understanding of the structure of the Earth and seismotectonics. The book also contains appendices on useful mathematical tools and includes extensive problems.

Viscous Flow
  • H. Ockendon, J. R. Ockendon
  • Published online:
    05 June 2012
    Print publication:
    27 January 1995
  • Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of alternative methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.

Engineering Fluid Dynamics
  • An Interdisciplinary Systems Approach
  • Clement Kleinstreuer
  • Published online:
    05 June 2012
    Print publication:
    28 February 1997
  • This text provides a thorough treatment of the fundamental principles of fluid mechanics and convection heat transfer and shows how to apply the principles to a wide variety of fluid flow problems. The book is intended for use by final year undergraduate and beginning graduate students in engineering. The focus is on incompressible viscous flows with special applications to non-Newtonian fluid flows, turbulent flows, and free-forced convection flows. A special feature of the text is its coverage of generalised mass, momentum, and heat transfer equations, cartesian tensor manipulations, scale analyses, mathematical modelling techniques and practical solution methods. The final chapter is unique in its case-study approach, applying general modelling principles to analyse non-isothermal flow systems found in a wide range of engineering disciplines. Numerous end-of-chapter sample problem solutions, homework assignments, and mathematical aids are provided to enhance the reader's understanding and problem-solving skills.

Scaling
  • Grigory Isaakovich Barenblatt
  • Published online:
    05 June 2012
    Print publication:
    13 November 2003
  • Many phenomena in nature, engineering or society when seen at an intermediate distance, in space or time, exhibit the remarkable property of self-similarity: they reproduce themselves as scales change, subject to so-called scaling laws. It's crucial to know the details of these laws, so that mathematical models can be properly formulated and analysed, and the phenomena in question can be more deeply understood. In this 2003 book, the author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural attributes of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.

Fluid Mechanics
  • A Short Course for Physicists
  • Gregory Falkovich
  • Published online:
    05 June 2012
    Print publication:
    14 April 2011
  • The multidisciplinary field of fluid mechanics is one of the most actively developing fields of physics, mathematics and engineering. In this book, the fundamental ideas of fluid mechanics are presented from a physics perspective. Using examples taken from everyday life, from hydraulic jumps in a kitchen sink to Kelvin–Helmholtz instabilities in clouds, the book provides readers with a better understanding of the world around them. It teaches the art of fluid-mechanical estimates and shows how the ideas and methods developed to study the mechanics of fluids are used to analyze other systems with many degrees of freedom in statistical physics and field theory. Aimed at undergraduate and graduate students, the book assumes no prior knowledge of the subject and only a basic understanding of vector calculus and analysis. It contains 32 exercises of varying difficulties, from simple estimates to elaborate calculations, with detailed solutions to help readers understand fluid mechanics.

Introduction to Computational Fluid Dynamics
  • Anil W. Date
  • Published online:
    05 June 2012
    Print publication:
    08 August 2005
  • Introduction to Computational Fluid Dynamics is a textbook for advanced undergraduate and first year graduate students in mechanical, aerospace and chemical engineering. The book emphasizes understanding CFD through physical principles and examples. The author follows a consistent philosophy of control volume formulation of the fundamental laws of fluid motion and energy transfer, and introduces a novel notion of 'smoothing pressure correction' for solution of flow equations on collocated grids within the framework of the well-known SIMPLE algorithm. The subject matter is developed by considering pure conduction/diffusion, convective transport in 2-dimensional boundary layers and in fully elliptic flow situations and phase-change problems in succession. The book includes chapters on discretization of equations for transport of mass, momentum and energy on Cartesian, structured curvilinear and unstructured meshes, solution of discretised equations, numerical grid generation and convergence enhancement. Practising engineers will find this particularly useful for reference and for continuing education.

Fluid Dynamics for Physicists
  • T. E. Faber
  • Published online:
    05 June 2012
    Print publication:
    17 August 1995
  • It is over three hundred and fifty years since Torricelli discovered the law obeyed by fountains, yet fluid dynamics remains an active and important branch of physics. This book provides an accessible and comprehensive account of the subject, emphasising throughout the fundamental physical principles, and stressing the connections with other branches of physics. Beginning with a gentle introduction, the book goes on to cover Bernouilli's theorem, compressible flow, potential flow, surface waves, viscosity, vorticity dynamics, thermal convection and instabilities, turbulence, non-Newtonian fluids and the propagation and attenuation of sound in gases. Undergraduate or graduate students in physics or engineering who are taking courses in fluid dynamics will find this book invaluable, but it will also be of great interest to anyone who wants to find out more about this fascinating subject.

Non-equilibrium Statistical Mechanics and Turbulence
  • John Cardy, Gregory Falkovich, Krzysztof Gawedzki
  • Edited by Sergey Nazarenko, Oleg V. Zaboronski
  • Published online:
    05 June 2012
    Print publication:
    11 December 2008
  • Methods of non-equilibrium statistical mechanics play an increasingly important role in modern turbulence research, yet the range of relevant tools and methods is so wide and developing so fast that until now there has not been a single book covering the subject. As an introduction to modern methods of statistical mechanics in turbulence, this volume rectifies that situation. The book comprises three harmonised lecture courses by world class experts in statistical physics and turbulence: John Cardy introduces Field Theory and Non-Equilibrium Statistical Mechanics; Gregory Falkovich discusses Turbulence Theory as part of Statistical Physics; and Krzysztof Gawedzki examines Soluble Models of Turbulent Transport. To encourage readers to deepen their understanding of the theoretical material, each chapter contains exercises with solutions. Essential reading for students and researchers in the field of theoretical turbulence, this volume will also interest any scientist or engineer who applies knowledge of turbulence and non-equilibrium physics to their work.

The Mechanics and Thermodynamics of Continua
  • Morton E. Gurtin, Eliot Fried, Lallit Anand
  • Published online:
    05 June 2012
    Print publication:
    19 April 2010
  • The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Dynamics of the Atmosphere
  • A Course in Theoretical Meteorology
  • Wilford Zdunkowski, Andreas Bott
  • Published online:
    05 June 2012
    Print publication:
    10 April 2003
  • Dynamics of the Atmosphere consists of two parts: the first presenting the mathematical tools needed for a thorough understanding of the topics covered in the second part of the book. The second part begins with the derivation of the equation describing the atmospheric motion on the rotating earth. Subjects tackled in subsequent chapters include kinematics of the atmosphere (including vorticity and circulation theorems), wave motion in the atmosphere, inertial and dynamic stability, and turbulent systems in the atmosphere. Finally, newer methods of weather prediction, such as the spectral technique and the stochastic dynamic method, are introduced in order to demonstrate their potential for extending the forecasting range. Complete with numerous exercise sets and solutions, this textbook has been written for advanced undergraduate and graduate students of meteorology and other related sciences. It may also be used as a reference source by professional meteorologists and researchers in atmospheric science.

Turbulent Flows
  • Stephen B. Pope
  • Published online:
    05 June 2012
    Print publication:
    10 August 2000
  • This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up-to-date, comprehensive, designed for teaching, and is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. Part II is concerned with different approaches for modelling or simulating turbulent flows. The necessary mathematical techniques are presented in the appendices. This book is primarily intended as a graduate level text in turbulent flows for engineering students, but it may also be valuable to students in applied mathematics, physics, oceanography and atmospheric sciences, as well as researchers and practising engineers.

An Introduction to Ocean Turbulence
  • S. A. Thorpe
  • Published online:
    05 June 2012
    Print publication:
    11 October 2007
  • This textbook provides an introduction to turbulent motion occurring naturally in the ocean on scales ranging from millimetres to hundreds of kilometres. It describes turbulence in the mixed boundary layers at the sea surface and seabed, turbulent motion in the density-stratified water between, and the energy sources that support and sustain ocean mixing. Little prior knowledge of physical oceanography is assumed. The text is supported by numerous figures, extensive further reading lists, and more than 50 exercises that are graded in difficulty. Detailed solutions to the exercises are available to instructors online at www.cambridge.org/9780521859486. This textbook is intended for undergraduate courses in physical oceanography, and all students interested in multidisciplinary aspects of how the ocean works, from the shoreline to the deep abyssal plains. It also forms a useful lead-in to the author's more advanced graduate textbook, The Turbulent Ocean (Cambridge University Press, 2005).

A Physical Introduction to Suspension Dynamics
  • Élisabeth Guazzelli, Jeffrey F. Morris
  • Illustrated by Sylvie Pic
  • Published online:
    05 June 2012
    Print publication:
    24 November 2011
  • Understanding the behaviour of particles suspended in a fluid has many important applications across a range of fields, including engineering and geophysics. Comprising two main parts, this book begins with the well-developed theory of particles in viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.

Essentials of Heat Transfer
  • Principles, Materials, and Applications
  • Massoud Kaviany
  • Published online:
    05 June 2012
    Print publication:
    01 August 2011
  • This textbook teaches students the principles, materials and applications they need to understand and analyze heat transfer problems they will encounter in practice. The emphasis on modern practical problems (including thermoelectric cooling) in numerous examples, sets this apart from other titles. This book discusses heat transfer problems (in search of innovative and optimal solutions) and the engineering analysis, to motivate fundamental principles and analytical problem solving methods. By introducing heat flux tracking, students develop intuition about the central role of heat transfer in engineered systems. The energy conversion mechanisms (to and from thermal energy) are integrated into the treatment, thus allowing for realistic design of thermal systems. Microscale heat carriers are also covered. MATLAB® software is included, along with other rich materials available on the website, www.cambridge.org/kaviany. A complete solutions manual for the numerous exercises is available to qualified instructors.

Turbulence, Coherent Structures, Dynamical Systems and Symmetry
  • 2nd edition
  • Philip Holmes, John L. Lumley, Gahl Berkooz, Clarence W. Rowley
  • Published online:
    05 June 2012
    Print publication:
    23 February 2012
  • Turbulence pervades our world, from weather patterns to the air entering our lungs. This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures – recurrent patterns – in turbulent flows, it describes mathematical methods that reduce the governing (Navier–Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995. The book is ideal for engineering, physical science and mathematics researchers working in fluid dynamics and other areas in which coherent patterns emerge.

Fluid Mechanics
  • David Pnueli, Chaim Gutfinger
  • Published online:
    05 June 2012
    Print publication:
    27 November 1992
  • This text is intended for the study of fluid mechanics at an intermediate level. However, the presentation starts with basic ideas in order to form a sound conceptual structure that can support engineering applications and encourage further learning. Subjects treated include hydrostatics, viscous flow, similitude and order of magnitude, creeping flow, potential flow, boundary layer flow, turbulent flow, compressible flow, and non-Newtonian fluids.

Fundamentals of Atmospheric Modeling
  • 2nd edition
  • Mark Z. Jacobson
  • Published online:
    05 June 2012
    Print publication:
    05 May 2005
  • This well-received and comprehensive textbook on atmospheric processes and numerical methods has been thoroughly revised. This edition includes a wide range of new numerical techniques for solving problems in areas such as cloud microphysics, ocean-atmosphere exchange processes and atmospheric radiative properties. It also contains improved descriptions of atmospheric physics, dynamics, radiation, and aerosol and cloud processes. It is essential reading for researchers, scientists and advanced students to successfully study air pollution and meteorology.

Page 170 of 407