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Titlebook: Nonlinear Problems of Elasticity; Stuart S. Antman Book 19951st edition Springer Science+Business Media New York 1995 Extension.angular mo

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书目名称Nonlinear Problems of Elasticity
编辑Stuart S. Antman
视频videohttp://file.papertrans.cn/668/667666/667666.mp4
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Nonlinear Problems of Elasticity;  Stuart S. Antman Book 19951st edition Springer Science+Business Media New York 1995 Extension.angular mo
描述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 th
出版日期Book 19951st edition
关键词Extension; angular momentum; bifurcation; elasticity; mechanics; momentum; tensor
版次1
doihttps://doi.org/10.1007/978-1-4757-4147-6
isbn_ebook978-1-4757-4147-6Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer Science+Business Media New York 1995
The information of publication is updating

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Introduction to Bifurcation Theory and its Applications to Elasticity,t. If the thrust is slowly increased beyond a certain critical value, called the ., the rod assumes a configuration, called a ., that is not straight. See Fig. 1.1. This process is called .. Depending on the precise mode of loading and the nature of the rod, the transition to a buckled state can be
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Global Bifurcation Problems for Strings and Rods, problems (like those described in Ex. V.5.6). We concentrate on effects caused by the nature of constitutive response. We develop techniques by which we can convert given boundary-value problems into mathematical forms suitable for global analysis, and techniques by which we can extract very detail
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Variational Methods,ose of showing how some very useful physical insights can be easily extracted from the basic theory. The reader should review Secs. II.10 and III.3. We require a mathematical setting somewhat different from that used in bifurcation theory; the technical aspects of this setting are given below in sma
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The Special Cosserat Theory of Rods,pace by suffering flexure, torsion, extension, and shear. We call the resulting geometrically exact theory the .. In Sec. 2 we outline an honest derivation of the governing equations for elastic and viscoelastic rods. Here we scarcely pause for motivation, interpretation, and justification of our re
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Axisymmetric Equilibria of Cosserat Shells,id-surface extension, and shear. These are the equations we shall analyze in the next few sections. We limit our attention here to statics, deferring to Chap. XIV the general formulation of dynamical equations for problems lacking symmetry. Our approach imitates that of Sec. IV.1. We define a . to b
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Elasticity,. The classical form of the balance of linear momentum is . where . is the first Piola-Kirchhoff stress tensor, . is the prescribed body force intensity per unit reference volume, and . is the mass density per unit reference volume.
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