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The Thick Elastic Spherical Shell Under Concentrated Torques †
Author(s) -
Bramble James H.
Publication year - 1959
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-9.4.492
Subject(s) - axial symmetry , spherical shell , shell (structure) , mathematics , harmonic function , torque , space (punctuation) , function (biology) , mathematical analysis , spherical harmonics , harmonic , stress (linguistics) , classical mechanics , geometry , physics , composite material , materials science , quantum mechanics , computer science , linguistics , philosophy , evolutionary biology , operating system , biology
IN this paper we consider a thick elastic spherical shell subjected to concentrated torques at the end‐points of a diameter. We prove that the solution is uniquely determined and derive an explicit expression for it. Extensive use is made of the fact that the stress function is closely related to an axially symmetric harmonic function, defined in a seven‐dimensional space.