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Shell Theory — A First Approximation

In: Mechanics, Boundary Layers and Function Spaces

Author

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  • Diarmuid Ó Mathúna

    (Dublin Institute for Advanced Studies)

Abstract

The configuration of a plate, namely, a three-dimensional figure cut from a right cylinder by two mutually reflecting surfaces symmetrically placed with respect to a plane normal to the generators of the cylinder, is generalized in the shell by replacing the plane of symmetry by an arbitrary base surface, which, by analogy, is termed the midsurface. For a figure defined on the base surface by one or more simple closed curves, which we collectively call the edge-curve, the ruled surface, generated by the normals to the midsurface along the edge-curve, defines a region of space. Introducing the two faces, namely two surfaces mutually reflecting with respect to the midsurface, so that, on every normal to the latter, the intercept between the faces is bisected by the midsurface, then the portion of the ruled surface lying between the faces will be referred to as the edge-surface. The figure enclosed by the edge-surface and the two faces is a shell and for any point on the midsurface the normal intercept between the faces measures the shell-thickness at that point.

Suggested Citation

  • Diarmuid Ó Mathúna, 1989. "Shell Theory — A First Approximation," Springer Books, in: Mechanics, Boundary Layers and Function Spaces, chapter 0, pages 141-215, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4556-8_4
    DOI: 10.1007/978-1-4612-4556-8_4
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