Continuum Mechanics using Mathematica®

1. Front Matter

   Pages i-xii

   PDF

2. Elements of Linear Algebra

   Pages 1-43

3. Vector Analysis

   Pages 45-76

4. Finite and Infinitesimal Deformations

   Pages 77-107

5. Kinematics

   Pages 109-129

6. Balance Equations

   Pages 131-153

7. Constitutive Equations

   Pages 155-169

8. Symmetry Groups: Solids and Fluids

   Pages 171-187

9. Wave Propagation

   Pages 189-243

10. Fluid Mechanics

    Pages 245-316

11. Linear Elasticity

    Pages 317-366

12. Other Approaches to Thermodynamcis

    Pages 367-378

13. Back Matter

    Pages 379-388

    PDF

The motion of any body depends both on its characteristics and the forces acting on it. Although taking into account all possible properties makes the equations too complex to solve, sometimes it is possible to consider only the properties that have the greatest in?uence on the motion. Models of ideals bodies, which contain only the most relevant properties, can be studied using the tools of mathematical physics. Adding more properties into a model makes it more realistic, but it also makes the motion problem harder to solve. In order to highlight the above statements, let us ?rst suppose that a systemS ofN unconstrainedbodiesC ,i=1,. . . ,N,issu?cientlydescribed i by the model of N material points whenever the bodies have negligible dimensions with respect to the dimensions of the region containing the trajectories. ThismeansthatallthephysicalpropertiesofC thatin?uence i the motion are expressed by a positive number, themass m , whereas the i position of C with respect to a frame I is given by the position vector i r (t) versus time. To determine the functionsr (t), one has to integrate the i i following system of Newtonian equations: m¨ r =F ?f (r ,. . . ,r ,r ? ,. . . ,r ? ,t), i i i i 1 N 1 N i=1,. . .

• calculus
• electricity
• fluid mechanics
• linear algebra
• mathematical physics
• mechanics
• plasticity
• thermodynamics

"[The authors] bring a fresh quality to this subject. Their book of 11 chapters rigorously and clearly introduces various attributes often lacking in other books. Starting with basic linear algebra, the book migrates smoothly to curvilinear coordinates. There, the authors analyze different coordinates and introduce singular surfaces important in porous media analysis. From that point onward the authors present balance and constitutive equations common to other classical books. However, this book resourcefully goes a step further by applying Mathematica in order to clarify key concepts; this attractive feature is one of the book's strengths. In each Mathematica case, the authors define the aim of the program, description of the problem, and relative algorithm. All chapters are well written, particularly the last four on wave propagation, linear elasticity, and other topics including shock waves, Rayleigh waves, and SH waves. Given this book's elucidative and concise approach, the scientific community should look forward to reading the second volume, to treat mixtures, phase change, magnetoelastic bodies, and other important topics. Summing Up: Highly recommended. Graduate students through professionals."                                         —Choice

"The book will be an invaluable reference for all those with active interest in the areas of continuum mechanics and its fundamental applications: balance laws, constitutive axioms, linear elasticity, fluid dynamics, waves, etc. It may serve as a supplement to any of the standard textbooks for undergraduate students, graduate students, and researchers in applied mathematics, mathematical physics, and engineering."                                 —Zentralblatt MATH

• Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Napoli, Italy

  Antonio Romano, Addolorata Marasco

• Dipartimento di Ingegneria Strutturale e Geotecnica, Politecnico di Torino, Torino, Italy

  Renato Lancellotta

Policies and ethics