
Accession Number : AD0606237
Title : ON THE DETERMINATION OF STRESSES AND DISPLACEMENTS FOR UNSYMMETRICAL DEFORMATION OF SHALLOW SPHERICAL SHELLS,
Corporate Author : THOMPSON RAMO WOOLDRIDGE INC LOS ANGELES CALIF
Personal Author(s) : Reissner,Eric
Report Date : 16 SEP 1957
Pagination or Media Count : 36
Abstract : The report is concerned with problems of bending of thin, elastic, shallow spherical shells of uniform thickness. Explicit expressions are derived, in terms of stress function and axial displacement component, for radial and circumferential displacement components. It is shown that certain univalued portions of the solution for stress function and axial displacement components give rise to multivalued expressions for radial and circumferential displacement components. A new type of solution of the differential equations is derived which is multivalued insofar as the stress function is concerned but given univalued expressions for all quantities which should be univalued. It is shown that this type of solution is needed for the analysis of problems for which a resultant side force is acting along the edge of a symmetrical circular boundary of the shell. The nature and form of this sideforce solution differs in important respects from the corresponding known solution for the case of a flat plate. No direct transition is possible from the shell solution to the corresponding flatplate solution. As a specific application, a shell is considered which is supported at its outer edge and which has a small symmetrical rigid insert.
Descriptors : (*ELASTIC SHELLS, DEFORMATION), (*STRESSES, ELASTIC SHELLS), ELASTIC PROPERTIES, SHELLS(STRUCTURAL FORMS), SPHERES, DEFLECTION, MOMENTS, MATHEMATICAL ANALYSIS, BOUNDARY VALUE PROBLEMS, DIFFERENTIAL EQUATIONS, SIMULTANEOUS EQUATIONS, NUMERICAL INTEGRATION, DIFFERENTIAL GEOMETRY
Distribution Statement : APPROVED FOR PUBLIC RELEASE