Deformations Without Bending: Explicit Examples

@article{Pulov2019DeformationsWB,
  title={Deformations Without Bending: Explicit Examples},
  author={Vladimir Pulov and Mariana Ts. Hadzhilazova and Iva{\"i}lo M. Mladenov},
  journal={Geometry, Integrability and Quantization},
  year={2019}
}
Here we consider an interesting class of free of bending deformations of thin axial symmetric shells subjected to uniform normal pressure. The meridional kμ and the parallel kπ principal curvatures of the middle surfaces of such shells obey the non-linear relationship kμ = 2ak π + 3kπ , a = const. These non-bending shells depend on two arbitrary parameters, which are the principal radii rμ and rπ of some fixed parallel of the shell. Besides, these surfaces have no closed form description in… 
1 Citations
A New Approach to Rotational Weingarten Surfaces
Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the

References

SHOWING 1-6 OF 6 REFERENCES
On a Class of Linear Weingarten Surfaces
We consider a class of linear Weingarten surfaces of revolution whose principal curvatures, meridional kμ and parallel kπ , satisfy the relation kμ = (n + 1)kπ , n = 0, 1, 2, . . . . The first two
ONCE MORE THE MYLAR BALLOON
An alternative formulation of the original variational problem for the mylar balloon leads to the so-called Whewell parameterization of its prole curve. This allows a derivation of various formulas
Handbook of elliptic integrals for engineers and scientists
TLDR
The Handbook of Elliptic Integrals for Engineers and Scientists introduces an integral operator on the set of means and investigates its properties.
Stresses in Shells, Berlin, Springer
  • 1960
Thin Shell Theory, Leningrad, Sudpromgiz (in Russian)
  • 1962
Forms of Shells of Revolution Deforming Without Bending Under Uniform Pressure, DAN
  • AN SSSR
  • 1981