E-Book, Englisch, Band 107, 752 Seiten, eBook
Antman Nonlinear Problems of Elasticity
Erscheinungsjahr 2013
ISBN: 978-1-4757-4147-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 107, 752 Seiten, eBook
Reihe: Applied Mathematical Sciences
ISBN: 978-1-4757-4147-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.
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Weitere Infos & Material
I. Background.- II. The Equations of Motion for Extensible Strings.- III. Elementary Problems for Elastic Strings.- IV. Planar Equilibrium Problems for Elastic Rods.- V. Introduction to Bifurcation Theory and its Applications to Elasticity.- VI. Global Bifurcation Problems for Strings and Rods.- VII. Variational Methods.- VIII. The Special Cosserat Theory of Rods.- IX. Spatial Problems for Cosserat Rods.- X. Axisymmetric Equilibria of Cosserat Shells.- XI. Tensors.- XII. Three-Dimensional Continuum Mechanics.- XIII. Elasticity.- XIV. General Theories of Rods and Shells.- XV. Nonlinear Plasticity.- XVI. Dynamical Problems.- XVII. Appendix. Topics in Linear Analysis.- XVIII. Appendix. Local Nonlinear Analysis.- XIX. Appendix. Degree Theory.- References.