Nonlinear Theory of Thin Shells

Abstract

We shall base all our discussion of the deformation of thin shells upon the first Kirchhoff hypothesis. Let the middle surface S of the undeformed thin shell be associated with the orthogonal curvilinear coordinates α ₁, α ₂. The position vector $\overline{\rho}$ of an arbitrary point M _z on the equidistant surface S _z (S _z ∥S) is given by Eq. (1.39), where z ∈ [–h/2, +h/2] and h is the thickness of the shell. The coordinate vectors and the Lamé coefficients satisfy Eqs. (1.42, 1.49).

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

David Hilbert