文档介绍：MATHEMATICAL
MODELING IN
CONTINUUM MECHANICS
SECOND EDITION
ROGER TEMAM
Universite´ Paris-Sud, Orsay and Indiana University
ALAIN MIRANVILLE
Universite´ de Poitiers
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge , UK
Published in the United States of America by Cambridge University Press, New York
Information on this title: 0521617239
© Cambridge University Press 2000, 2005
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First published in print format 2005
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Contents
Preface page ix
A few words about notations xi
PART I FUNDAMENTAL CONCEPTS IN CONTINUUM
MECHANICS
1 Describing the motion ofa system: geometry and kinematics 3
Deformations 3
Motion and its observation (kinematics) 6
Description of the motion of a system: Eulerian and
Lagrangian derivatives 10
Velocity field of a rigid body: helicoidal vector fields 13
Differentiation of a volume integral depending on a parameter 18
2 The fundamental law of dynamics 24
The concept of mass 24
Forces 30
The fundamental law of dynamics and its first consequences 32
Application to systems of material points and to rigid bodies 34
Galilean frames: the fundamental law of dynamics expressed
in a non-Galilean frame 38
3 The Cauchy stress