On Donati’s Theorem in Shell Theory
The Donati theorem has been formulated in connection with three-dimensional problems of the linear theory of elasticity. In this paper a simular theorem is considered for two-dimensional problems encountered in the linear theory of shells. As closely related topics the stress functions and compatibility equations in the shell theory are also studied. A shell is assumed to be deformed in accordance with the hypothesis of linear distribution of the displacement vector across the shell thickness. Thus, six local degrees of freedom of the shell are taken into account. The results obtained in the paper include, as a special case, the well-known stress functions and compatibility equations of the Kirchhoff-Love and Reissner theories.
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