Continuum Mechanics using Mathematica®: Fundamentals, Methods, and Applications

✍ Scribed by Antonio Romano, Addolorata Marasco (auth.)

• Publisher: Birkhäuser Basel
• Year: 2014
• Tongue: English
• Leaves: 489
• Series: Modeling and Simulation in Science, Engineering and Technology
• Edition: 2
• Category: Library

✦ Synopsis

This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica® provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics and state changes (see A. Romano, A. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhäuser), 2010, ISBN 978-0-8176-4869-5). Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and one appendix * Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity. This second edition expands the key topics and features to include: * Two new applications of fluid dynamics: meteorology and navigation * New exercises at the end of the existing chapters * The packages are rewritten for Mathematica 9 Continuum Mechanics using Mathematica®: Fundamentals, Applications and Scientific Computing is aimed at advanced undergraduates, graduate students and researchers in applied mathematics, mathematical physics and engineering. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics.

✦ Table of Contents

Front Matter....Pages i-xv
Elements of Linear Algebra....Pages 1-45
Vector Analysis....Pages 47-82
Finite and Infinitesimal Deformations....Pages 83-113
Kinematics....Pages 115-135
Balance Equations....Pages 137-161
Constitutive Equations....Pages 163-177
Symmetry Groups: Solids and Fluids....Pages 179-196
Wave Propagation....Pages 197-250
Fluid Mechanics....Pages 251-322
Linear Elasticity....Pages 323-372
Other Approaches to Thermodynamics....Pages 373-384
Fluid Dynamics and Meteorology....Pages 385-428
Fluid Dynamics and Ship Motion....Pages 429-461
Back Matter....Pages 463-480

✦ Subjects

Mechanics; Continuum Mechanics and Mechanics of Materials; Theoretical and Applied Mechanics; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics