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Mathematics and Mechanics of Solids
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Two-Dimensional Approximation of Eigenvalue Problems in Shallow Shell Theory

S. Kesavan

N. Sabu

The Institute of Mathematical Sciences, C.L. T Campus, Taramani, Chennai 600 113, India

The authors consider a thin, linearly elastic shell clamped along its lateral surface and study the corresponding eigenvalue problem. Under specific assumptions of the geometry of the shell, it is shown that, as the thickness of the shell tends to zero, the eigenvalues converge to those of a two-dimensional problem involving only the vertical component of the eigenvector.

Mathematics and Mechanics of Solids, Vol. 4, No. 4, 441-460 (1999)
DOI: 10.1177/108128659900400403
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