Pure strain deformations of thin shells
Abstract
Pure strain deformations of a thin shell are deformations deprived of rotations in the sense of the polar decomposition theorem. It is shown that all pure strain deformations of a given shell midsurface are governed by a single second-order quasi-linear PDE. It is also shown that the problem of finding all such deformations can be reduced to the problem of finding all surfaces with a given third fundamental form (the inverse of the Gauss map) under the equivalence relation established by the condition of preservation of the lines of principal curvature.
Fields of Study & Subjects
Advanced Differential Geometry Research
Elasticity and Wave Propagation
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- CRC Press eBooks
- Pages
- 175–178
- Publication date
- 4 February 2026
- Language
- EN
- Document type
- Book chapter