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Torsion and Thermal Stress Systems in a Thick Plate Containing a Spherical Cavity
Author(s) -
Fox N.
Publication year - 1961
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/s3-11.1.276
Subject(s) - torsion (gastropod) , axial symmetry , thermal , mathematics , axis of symmetry , geometry , circular symmetry , cavity wall , rotational symmetry , plane symmetry , mechanics , classical mechanics , materials science , physics , composite material , thermodynamics , anatomy , medicine
This paper completes the analysis of axially symmetric stress systems in a thick plate containing a spherical cavity, the centre of which lies midway between the faces. The author's paper (1) dealt with the non‐thermal torsion‐free system, and the object of the present paper is to apply similar methods to the analysis of the torsion and steady thermal stress systems. Numerical work is carried out on the following problems. (i) The spherical cavity rotated as a rigid body through a small angle about the axis of symmetry, the plane faces being kept ( a ) stress‐free, ( b ) fixed. (ii) The surface of the cavity maintained at a constant temperature and stressfree, the faces maintained at a different temperature and stress‐free. Comparison is made with the elementary approximate solutions obtained by neglecting the effect of the faces.