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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:25:58 +0000On the exponential decay of stresses in circular elastic cylinders subject to axisymmetric self-equilibrated end loads
https://resolver.caltech.edu/CaltechAUTHORS:20151207-102452675
Authors: {'items': [{'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'J. K.'}}, {'id': 'Horgan-C-O', 'name': {'family': 'Horgan', 'given': 'C. O.'}}]}
Year: 1969
DOI: 10.1016/0020-7683(69)90067-5
Methods involving energy-decay inequalities are applied to the axisymmetric end problem for a circular elastic cylinder. Explicit lower bounds in terms of Poisson's ratio are obtained for the rate of exponential decay of stresses, and these are compared with results of other authors.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/f9dbz-j4g42Eigenvalue problems associated with Korn's inequalities
https://resolver.caltech.edu/CaltechAUTHORS:20151124-103729126
Authors: {'items': [{'id': 'Horgan-C-O', 'name': {'family': 'Horgan', 'given': 'C. O.'}}, {'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'J. K.'}}]}
Year: 1971
DOI: 10.1007/BF00251798
We shall discuss a class of problems associated with certain inequalities which apparently originated in the work of A. KORN [1, 2] on the linear theory of elasticity. To describe these inequalities we consider a vector field u(x), continuously differentiable on the closure R + B of a bounded domain R with boundary B in two or three dimensions. Let x, be coordinates in a given rectangular Cartesian coordinate system, and denote by u_i the components of u in this system.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3sqpf-wav69The effect of nonlinearity on a principle of Saint-Venant type
https://resolver.caltech.edu/CaltechAUTHORS:20141104-103601635
Authors: {'items': [{'id': 'Horgan-C-O', 'name': {'family': 'Horgan', 'given': 'C. O.'}}, {'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'J. K.'}}]}
Year: 1981
DOI: 10.1007/BF00041940
This paper establishes a principle of Saint-Venant type associated with finite anti-plane shear of a cylinder whose cross-section is a semi-infinite strip. The long sides of the strip are traction-free, and the short side carries an arbitrarily distributed shear traction. At the infinity in the strip, the deformation is prescribed to be one of simple shear, and the associated shear stress is uniform. The analysis is based on the fully nonlinear theory of finite elastostatics and is carried out for a special class of homogenous, isotropic incompressible materials. It is shown that, along the parallel sides of the strip, the nonvanishing component of shear stress differs from its average value (taken across the strip) by an exponentially decaying function of the distance from the end. A lower bound is given for the rate of decay.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pan05-54491Recent Developments Concerning Saint-Venant's Principle
https://resolver.caltech.edu/CaltechAUTHORS:20141104-131016828
Authors: {'items': [{'id': 'Horgan-C-O', 'name': {'family': 'Horgan', 'given': 'Cornelius O.'}}, {'id': 'Knowles-J-K', 'name': {'family': 'Knowles', 'given': 'James K.'}}]}
Year: 1983
DOI: 10.1016/S0065-2156(08)70244-8
This chapter provides an overview of the recent developments concerning Saint-Venant's principle. The task of determining, within the framework of the linear theory of elasticity, the stresses and displacements in an elastic cylinder in equilibrium, under the action of loads that arise solely from tractions applied to its plane ends has come to be called Saint- Venant's problem. Saint-Venant's construction does not permit the arbitrary preassignment of the point-by-point variation of the end tractions giving rise to these forces and moments; indeed, this variation is essentially determined as a consequence of the special assumptions made in connection with his so-called semi-inverse procedure. The early work of Saint-Venant and Boussinesq furnished the seeds from which grew a large number of more general assertions, most referring to elastic solids of arbitrary shape and many being rather imprecise, concerning the effect on stresses within the body of replacing the tractions acting over a portion of its surface by statically equivalent ones. Such propositions usually went by the name of Saint-Venunt's principle, despite the fact that Saint-Venant's original conjecture was intended to apply only to cylinders. This chapter discusses in detail about flow in a cylinder, a representation for the exact solution, and energy decay for other linear elliptic second-order problem. Linear elastostatic problems are also stated in the chapter.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5xq1m-kgh38