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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 bemagnanimity 发表于 2025-3-22 10:19:22
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 detaillymphedema 发表于 2025-3-22 16:03:17
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 smabadinage 发表于 2025-3-22 21:03:51
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珠宝 发表于 2025-3-22 21:27:16
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希望 发表于 2025-3-23 04:04:23
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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.