The Fundamental Solution for a Consistent Complex Model of the Shallow Shell Equations




Coleman, Matthew P.

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Southwest Texas State University, Department of Mathematics


The calculation of the Fourier transforms of the fundamental solution in shallow shell theory ostensibly was accomplished by J. L. Sanders [J. Appl. Mech. 37 (1970), 361-366]. However, as is shown in detail in this paper, the complex model used by Sanders is, in fact, inconsistent. This paper provides a consistent version of Sanders's complex model, along with the Fourier transforms of the fundamental solution for this corrected model. The inverse Fourier transforms are then calculated for the particular cases of the shallow spherical and circular cylindrical shells, and the results of the latter are seen to be in agreement with results appearing elsewhere in the literature.



Shallow shell theory, Fundamental solution, Spherical shell, Cylindrical shell


Coleman, M. P. (1999). The fundamental solution for a consistent complex model of the shallow shell equations. <i>Electronic Journal of Differential Equations, 1999</i>(32), pp. 1-22.


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