The Fundamental Solution for a Shallow Shell With an Arbitrary Quadratic Midsurface

[+] Author and Article Information
J. G. Simmonds, M. R. Bradley

Department of Applied Mathematics and Computer Science, University of Virginia, Charlottesville, Va.

J. Appl. Mech 43(2), 286-290 (Jun 01, 1976) (5 pages) doi:10.1115/1.3423825 History: Received September 01, 1975; Online July 12, 2010


The complex-valued differential operator associated with the linear Marguerre equations for a constant thickness, elastically isotropic shallow shell with an arbitrary quadratic midsurface consists of the biharmonic operator minus the imaginary unit i times a constant coefficient second-order differential operator. The fundamental solution of this differential operator is denoted by g(r, θ; κ), where r and θ are polar coordinates and κ is the (dimensionless) Gaussian curvature of the midsurface at the origin. Via a double Fourier transform, a plane wave or Whittaker representation is obtained for g(r, θ; κ). From this is extracted a series representation for g(r, θ; κ) in powers of r2 , with coefficients depending on ln r, θ, and κ. The results are shown to agree with the known special cases for κ = 1, 0, and −1.

Copyright © 1976 by ASME
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In