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Energy Inequalities and Error Estimates for Axisymmetric Torsion of Thin Elastic Shells of Revolution


Ho, Chee Leung (1968) Energy Inequalities and Error Estimates for Axisymmetric Torsion of Thin Elastic Shells of Revolution. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ARTK-6968.


The problem motivating this investigation is that of pure axisymmetric torsion of an elastic shell of revolution. The analysis is carried out within the framework of the three-dimensional linear theory of elastic equilibrium for homogeneous, isotropic solids. The objective is the rigorous estimation of errors involved in the use of approximations based on thin shell theory.

The underlying boundary value problem is one of Neumann type for a second order elliptic operator. A systematic procedure for constructing pointwise estimates for the solution and its first derivatives is given for a general class of second-order elliptic boundary-value problems which includes the torsion problem as a special case.

The method used here rests on the construction of “energy inequalities” and on the subsequent deduction of pointwise estimates from the energy inequalities. This method removes certain drawbacks characteristic of pointwise estimates derived in some investigations of related areas.

Special interest is directed towards thin shells of constant thickness. The method enables us to estimate the error involved in a stress analysis in which the exact solution is replaced by an approximate one, and thus provides us with a means of assessing the quality of approximate solutions for axisymmetric torsion of thin shells.

Finally, the results of the present study are applied to the stress analysis of a circular cylindrical shell, and the quality of stress estimates derived here and those from a previous related publication are discussed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mechanics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Knowles, James K.
Thesis Committee:
  • Unknown, Unknown
Defense Date:19 September 1967
Funding AgencyGrant Number
Ford FoundationUNSPECIFIED
Record Number:CaltechTHESIS:12072015-103241369
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9308
Deposited On:07 Dec 2015 19:12
Last Modified:02 Apr 2024 18:13

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