MEMBRANE AND BENDING STRESSES IN SHALLOW, SPHERICAL SHELLS
Abstract
The present work is concerned with the nature of the interior solution and the influence coefficients of shallow, spherical, thin, elastic shells (or equivalently a shallow, thin, elastic, paraboloidal shell of revolution) which are homogeneous, isotropic, closed at the apex, and of uniform thickness. The investigation is carried out within the framework of the usual shallow shell theory for small displacements and negligible transverse-shear deforma tions. Exact interior solutions are obtained for shells acted upon by edge loads and edge moments. The constants of integration associated with these interior solutions are expanded asymptotically in inverse powers of a large parameter. Retaining only the leading term of these expansions leads (in most cases) to known approximate results. Explicit expressions for the second-order terms are obtained. It is shown that these second-order terms play a significant role in a certain class of problems. The relative importance of the membrane and inextensional bending stresses in the interior of the shell is discussed. The exact and asymptotic influence coefficients are obtained. The interior stress state of shells subjected to polar harmonic axial surface loads is also investigated by the same procedure. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 11, 1964
- Accession Number
- AD0607457
Entities
People
- F.y. Wan
Organizations
- Massachusetts Institute of Technology