A KIRCHHOFF THIN SHELL THEORY,
Abstract
A mathematical theory for the deformations of isotropic shells under the applications of edge forces is presented. The theory is obtained by imposing the principal of virtual work on the calss of deformations which satisfy the Kirchhoff hypotheses, i.e. those deformations which carry normals to the undeformed middle surface into normals to the deformed middle surface with no change in length along normals. It is not assumed that displacements, strains, or slopes are small. Although in the derivation of the model it is not assumed that the shell is thin, the theory is not expected to be physically realistic unless the shell is in fact thin. Imposing the principal of virtual work yields a system of differential equations for the three components of position of the deformed middle surface and six relations between the applied edge forces and the deformed middle surface. It is shown that the system of differential equations can be expressed as a tenth order system. The six relations between edge forces and deformed middle surface contain two arbitrary functions and hence represent four boundary constraints on the deformed middle surface when the edge forces are prescribed. To be physically realistic one of the arbitrary functions should be chosen to be zero. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1963
- Accession Number
- AD0426481
Entities
People
- Chester B. Sensenig
Organizations
- New York University