University of Illinois Urbana-Champaign

Elastic stability of conical shells loaded by uniform external pressure

Taylor, C.E.

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https://hdl.handle.net/2142/111822

Description

Title
Elastic stability of conical shells loaded by uniform external pressure
Author(s)
Taylor, C.E.
Issue Date
1957-04
Keyword(s)
  • Conical Shells
  • Elastic Stability
  • External Pressure
Abstract
Trefftz’s theory of elastic stability is applied to thin conical shells loaded by external hydrostatic pressure. By differential geometry, a strain energy expression is obtained based upon the assumptions that: (1) normals to the undeformed middle surface remain straight and normal to the deformed middle surface, (2) changes in the shell thickness have negligible effects on the strains in surfaces parallel to the middle surface, and (3) stresses perpendicular to the middle surfaces are negligible compared to the other stresses. The divergence theorem is used to express the volume enclosed by the deformed middle surface in terms of a surface integral. The change in volume during buckling multiplied by the hydrostatic pressure is set equal to the potential energy of the external forces. An approximate solution for the buckling pressure for complete conical shells is obtained by the Rayleigh-Ritz method. The inclusion of the additional quadratic terms in the energy expressions does not greatly affect the buckling pressures as obtained by the infinitesimal theory. However, the accurate strain energy expressions will be necessary if large deflection theory is to be applied to conical shells.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 117
  • 1967-0413
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/111822
Copyright and License Information
Copyright 1957 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.