In 1970, F. Y. M. Wan derived a single, complex-valued ordinary differential equation for an elastically isotropic right circular conical shell (“On the Equations of the Linear Theory of Elastic Conical Shells,” Studies Appl. Math., 49, pp. 69–83). The unknown was the Fourier component of a complex combination of the midsurface normal displacement and its static-geometric dual, a stress function. However, an attempt to formally replace the Fourier index by a partial derivative in the circumferential angle results in a partial differential equation, which is eighth order in . The present paper takes as unknowns the traces of the bending strain and stress resultant tensors, respectively, and derives static-geometric dual partial differential equations of fourth order in both the axial and circumferential variables. Because of the explicit appearance of Poisson ratios of bending and stretching, these two equations cannot be combined into a single complex-valued equation. Reduced equations for beamlike (axisymmetric and lateral) deformations are also derived.
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July 2008
Research Papers
An Alternative to F. Y. M. Wan’s Single Equation for an Elastic Right Circular Conical Shell
J. G. Simmonds
J. G. Simmonds
Fellow ASME
Department of Civil Engineering,
e-mail: jgs@virginia.edu
University of Virginia
, Charlottesville, VA 22904-4742
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J. G. Simmonds
Fellow ASME
Department of Civil Engineering,
University of Virginia
, Charlottesville, VA 22904-4742e-mail: jgs@virginia.edu
J. Appl. Mech. Jul 2008, 75(4): 041022 (6 pages)
Published Online: May 19, 2008
Article history
Received:
June 10, 2007
Revised:
September 15, 2007
Published:
May 19, 2008
Citation
Simmonds, J. G. (May 19, 2008). "An Alternative to F. Y. M. Wan’s Single Equation for an Elastic Right Circular Conical Shell." ASME. J. Appl. Mech. July 2008; 75(4): 041022. https://doi.org/10.1115/1.2875798
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