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Taylor & Francis
Continuum Mechanics for Engineers, Third Edition / Edition 3

Continuum Mechanics for Engineers, Third Edition / Edition 3


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Continuum Mechanics for Engineers, Third Edition / Edition 3

Continuum Mechanics for Engineers, Third Edition provides engineering students with a complete, concise, and accessible introduction to advanced engineering mechanics. The impetus for this latest edition was the need to suitably combine the introduction of continuum mechanics, linear and nonlinear elasticity, and viscoelasticity for a graduate-level course sequence. An outgrowth of course notes and problems used to teach these subjects, the third edition of this bestselling text explores the basic concepts behind these topics and demonstrates their application in engineering practice.

Presents Material Consistent with Modern Literature

A new rearranged and expanded chapter on elasticity more completely covers Saint-Venant’s solutions. Subsections on extension, torsion, pure bending and flexure present an excellent foundation for posing and solving basic elasticity problems. The authors’ presentation enables continuum mechanics to be applied to biological materials, in light of their current importance. They have also altered the book’s notation—a common struggle for many students—to better align it with modern continuum mechanics literature. This book addresses students’ need to understand the sophisticated simulation programs that use nonlinear kinematics and various constitutive relationships. It includes an introduction to problem solution using MATLAB®, emphasizing this language’s value in enabling users to stay focused on fundamentals.

This book provides information that is useful in emerging engineering areas, such as micro-mechanics and biomechanics. With an abundance of worked examples and chapter problems, it carefully explains necessary mathematics as required and presents numerous illustrations, giving students and practicing professionals an excellent self-study guide to enhance their skills. Through a mastery of this volume’s contents and additional rigorous finite element training, they will develop the mechanics foundation necessary to skillfully use modern, advanced design tools.

Product Details

ISBN-13: 9781420085389
Publisher: Taylor & Francis
Publication date: 08/04/2009
Series: Computational Mechanics and Applied Analysis Series
Edition description: New Edition
Pages: 398
Sales rank: 692,954
Product dimensions: 7.20(w) x 10.10(h) x 1.10(d)

About the Author

G. Thomas Mase, Ph.D., is Associate Professor of Mechanical Engineering at California Polytechnic State University, San Luis Obispo, California. Dr. Mase received his B.S. degree from Michigan State University in 1980 from the Department of Metallurgy, Mechanics and Materials Science. He obtained his M.S. and Ph.D. degrees in 1982 and 1985, respectively, from the Department of Mechanical Engineering at the University of California, Berkeley. After graduate school, he has worked at several positions in industry and academia. Industrial companies Dr. Mase has worked full time for include General Motors Research Laboratories, Callaway Golf and Acushnet Golf Company. He has taught or held research positions at the University of Wyoming, Kettering University, Michigan State University and California Polytechnic State University. Dr. Mase is a member of numerous professional societies including the American Society of Mechanical Engineers, American Society for Engineering Education, International Sports Engineering Association, Society of Experimental Mechanics, Pi Tau Sigma and Sigma Xi. He received an ASEE/NASA Summer Faculty Fellowship in 1990 and 1991 to work at NASA Lewis Research Center (currently NASA Glenn Research Center). While at the University of California, he twice received a distinguished teaching assistant award in the Department of Mechanical Engineering. His research interests include mechanics, design and applications of explicit finite element simulation. Specific areas include golf equipment design and performance and vehicle crashworthiness.

Ronald E. Smelser, Ph.D., P.E., is Professor and Associate Dean for Academic Affairs in the William States Lee College of Engineering at the University of North Carolina at Charlotte. Dr. Smelser received his B.S.M.E. from the University of Cincinnati in 1971. He was awarded the S.M.M.E. in 1972 from M.I.T. and completed his Ph.D. (1978) in mechanical engineering at Carnegie Mellon University. He gained industrial experience working for the United States Steel Research Laboratory, the Alcoa Technical Center, and Concurrent Technologies Corporation. Dr. Smelser served as a fulltime or adjunct faculty member at the University of Pittsburgh, Carnegie Mellon University, and the University of Idaho and was a visiting research scientist at Colorado State University. Dr. Smelser is a member of the American Academy of Mechanics, the American Society for Engineering Education, Pi Tau Sigma, Sigma Xi, and Tau Beta Pi. He is also a member and Fellow of the American Society of Mechanical Engineers. Dr. Smelser’s research interests are in the areas of process modeling including rolling, casting, drawing and extrusion of single and multi-phase materials, the micromechanics of material behavior and the inclusion of material structure into process models, and the failure of materials.

George E. Mase Ph.D. (1920-2007) was Emeritus Professor, Department of Metallurgy, Mechanics and Materials Science (MMM), College of Engineering, at Michigan State University. Dr. Mase received a B.M.E in Mechanical Engineering (1948) from the Ohio State University, Columbus. He completed his Ph.D. in Mechanics at Virginia Polytechnic Institute and State University (VPI), Blacksburg, Virginia (1958). Previous to his initial appointment as Assistant Professor in the Department of Applied Mechanics at Michigan State University in 1955, Dr. Mase taught at Pennsylvania State University (instructor), 1950-1951, and at Washington University, St. Louis, Missouri (assistant professor), 1951- 1954. He was appointed associate professor in 1959 and professor in 1965, and served as acting chairperson of the MMM Department 1965-1966 and again in 1978 to 1979. He taught as visiting assistant professor at VPI during the summer terms, 1953 through 1956. Dr. Mase held membership in Tau Beta Pi and Sigma Xi. His research interests and publications were in the areas of continuum mechanics, viscoelasticity and biomechanics.

Table of Contents

Continuum Theory

Continuum Mechanics

Starting Over


Essential Mathematics

Scalars, Vectors and Cartesian Tensors

Tensor Algebra in Symbolic Notation - Summation Convention

Indicial Notation

Matrices and Determinants

Transformations of Cartesian Tensors

Principal Values and Principal Directions

Tensor Fields, Tensor Calculus

Integral Theorems of Gauss and Stokes

Stress Principles

Body and Surface Forces, Mass Density

Cauchy Stress Principle

The Stress Tensor

Force and Moment Equilibrium; Stress Tensor Symmetry

Stress Transformation Laws

Principal Stresses; Principal Stress Directions

Maximum and Minimum Stress Values

Mohr’s Circles For Stress

Plane Stress

Deviator and Spherical Stress States

Octahedral Shear Stress

Kinematics of Deformation and Motion

Particles, Configurations, Deformations and Motion

Material and Spatial Coordinates

Langrangian and Eulerian Descriptions

The Displacement Field

The Material Derivative

Deformation Gradients, Finite Strain Tensors

Infinitesimal Deformation Theory

Compatibility Equations

Stretch Ratios

Rotation Tensor, Stretch Tensors

Velocity Gradient, Rate of Deformation, Vorticity

Material Derivative of Line Elements, Areas, Volumes

Fundamental Laws and Equations

Material Derivatives of Line, Surface, and Volume Integrals

Conservation of Mass, Continuity Equation

Linear Momentum Principle, Equations of Motion

Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion

Moment of Momentum (Angular Momentum) Principle

Law of Conservation of Energy, The Energy Equation

Entropy and the Clausius-Duhem Equation

The General Balance Law

Restrictions on Elastic Materials by the Second Law of Thermodynamics


Restrictions on Constitutive Equations from Invariance

Constitutive Equations

Linear Elasticity

Elasticity, Hooke’s Law, Strain Energy

Hooke’s Law for Isotropic Media, Elastic Constants

Elastic Symmetry; Hooke’s Law for Anisotropic Media

Isotropic Elastostatics and Elastodynamics, Superposition Principle

Saint-Venant Problem

Plane Elasticity

Airy Stress Function

Linear Thermoelasticity

Three-Dimensional Elasticity

Classical Fluids

Viscous Stress Tensor, Stokesian, and Newtonian Fluids

Basic Equations of Viscous Flow, Navier-Stokes Equations

Specialized Fluids

Steady Flow, Irrotational Flow, Potential Flow

The Bernoulli Equation, Kelvin’s Theorem

Nonlinear Elasticity

Molecular Approach to Rubber Elasticity

A Strain Energy Theory for Nonlinear Elasticity

Specific Forms of the Strain Energy

Exact Solution for an Incompressible, Neo-Hookean Material

Linear Viscoelasticity

Viscoelastic Constitutive Equations in Linear Differential Operator Form

One-Dimensional Theory, Mechanical Models

Creep and Relaxation

Superposition Principle, Hereditary Integrals

Harmonic Loadings, Complex Modulus, and Complex Compliance

Three-Dimensional Problems, The Correspondence Principle



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