Continuum Mechanics using Mathematica®: Fundamentals, Applications and Scientific Computing (Modeling and Simulation in Science, Engineering and Technology) - Hardcover

Romano, Antonio; Lancellotta, Renato; Marasco, Addolorata

Hardcover

ISBN 10: 0817632409 ISBN 13: 9780817632403

Verlag: Birkhäuser, 2005

Inhaltsangabe

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,. . .

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This book's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. The book covers essential principles and fundamental applications, and provides a solid basis for a deeper study of more challenging and specialized problems related to elasticity, fluid mechanics, plasticity, materials with memory, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes.
Key topics and features:
* Concise presentation strikes a balance between fundamentals and applications
* Requisite mathematical background carefully collected in two introductory chapters and two appendices
* Recent developments highlighted through coverage of more significant applications to areas such as porous media, electromagnetic fields, and phase transitions
Continuum Mechanics using Mathematica® 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 the field.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2005
• Sprache: Englisch
• ISBN 10: 0817632409
• ISBN 13: 9780817632403
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 400
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar