ON A THEORY OF SHELLS.
LEHIGH UNIV BETHLEHEM PA CENTER FOR THE APPLICATION OF MATHEMATICS
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A technique is given for reducing the three-dimensional continuum theory to a two-dimensional shell theory, which allows a great deal of freedom in choosing the most appropriate form of shell theory for a particular problem. The two-dimensional equations obtained can be identified with director theories of shells by suitably interpreting the directors. An example is given using a particular form of the technique which shows that the shell equations reduce to the classical membrane equations as the thickness of the shell tends to zero, assuming only that the transverse normal stress across the thin shell is small compared to the other normal stresses. Author