On the basis of the improved theory of plates, which makes it possible to determine all the components of the stress tensor, we study the thermally stressed state of a finite round plate with a concentric inclusion of a different material. We obtain the exact analytic solution of the corresponding boundary-value problem for the system of singularly perturbed equations, valid for any ratios between the diameters of the plate and the inclusion. In the contact zones the stresses differ significantly (both quantitatively and qualitatively) from those predicted by the classical plate theories. The results obtained make it possible to draw a number of conclusions that are useful for estimating the strength of electrovacuum devices. Four figures. Bibliography: 5 titles.
By applying the improved theory of plates, which makes it possible to determine all components of the stress tensor, we study the stressed state of glass disks under axisymmetric bending. We obtain a closedform solution of the corresponding boundary-value problem for systems of singularly perturbed equations. It is shown that the size of the zone of "pure" bending--the domain with uniformly stretched surface-differs from those known in the literature. The results obtained make it possible to determine the optimal geometric parameters of the punch-glass disk-support system in strength testing of the glass by the method of axisymmetric bending.
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