Mechanics of Solids

Volume III: Theory of Viscoelasticity, Plasticity, Elastic Waves, and Elastic Stability

Buch | Softcover

XV, 647 Seiten

1984 | 1. Softcover reprint of the original 1st ed. 1973
Springer Berlin (Verlag)
978-3-540-13162-5 (ISBN)

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Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par ticular kinds of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti vated wherever there were mathematicians. The magisterial treatise of LOVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary l of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words "either do not have any adequate successor[ s] . . . or, at least, refuse to be super seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.

The Linear Theory of Viscoelasticity.- A. Introduction.- B. Foundations of the linear theory.- C. Quasi-static linear viscoelasticity.- D. Dynamic linear viscoelasticity.- References.- Theory of Elastic Stability.- A. Introduction.- B. Abstract dynamical systems.- C. Definitions of stability.- D. Stability theorems for abstract dynamical systems.- E. Eigenfunction analyses.- F. Stability of elastic bodies.- G. Liapounov functions for finite thermoelasticity.- H. Liapounov stability in the class of non-linear perturbations.- I. The energy criterion for stability.- J. Stability for a fixed surface and under dead loads in the class of small incremental displacements.- K. Stability under dead surface loads in the class of small incremental displacements.- L. Instability under dead surface loads from the equations of linear incremental displacement.- M. Logarithmic convexity.- N. Extension of stability analysis for traction boundary conditions.- O. Stability in special traction boundary value problems.- P. Stability in the class of linear thermoelastic displacements under dead loads.- Q. Classification of stability problems with non-dead loading.- R. Stability under weakly conservative loads.- S. Stability with time-dependent and position-dependent data.- T. Stability under follower forces.- U. Dissipative forces.- References.- Growth and Decay of Waves in Solids.- I. Introduction.- II. Preliminaries.- III. Acceleration waves in elastic bodies.- IV. One dimensional waves in bodies of material with memory.- V. One dimensional waves in elastic bodies.- VI. One dimensional waves in elastic non-conductors of heat.- VII. One dimensional waves in inhomogeneous elastic bodies.- References.- Ideal Plasticity.- A. The basic equations.- B. Plane problems.- C. The general plane problem.- D. Boundary-value problems.- Some reference books.- Topics in the Mathematical Theory of Plasticity.- A. Introduction.- B. Foundation of the theory.- C. General theorems.- D. Torsion problems.- References.- Namenverzeichnis - Author Index.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).

Erscheint lt. Verlag	1.6.1984
Co-Autor	P. J. Chen, G. M. C. Fisher, H. Geiringer, Knops Robin J., M. J. Leitman, T. W. Ting, E. W. Wilkes
Zusatzinfo	XV, 647 p.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 244 mm
Gewicht	1080 g
Themenwelt	Naturwissenschaften ► Geowissenschaften ► Geophysik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Mechanik
Schlagworte	Chen • Elasticity • Elastische Welle • Plastizität • Stabilität • stability • Viskoelastizität • Waves
ISBN-10	3-540-13162-0 / 3540131620
ISBN-13	978-3-540-13162-5 / 9783540131625
Zustand	Neuware