J q T20 2 t2

a2 2 qE2

showing that the radial and tangential stresses are identical V r - as for a CTD [see (2.10)] - and maximal at the center of the substrate.

• VTD Type 2 - Axial force at center and reaction at edge: The substrate is deflected by an axial force F applied to its center that gives rise to a reaction —F at the edge. If we consider an equivalent uniform load q applied to all its surface, we can define the central force by F = na2q, and the associated shearing force by na2q + 2nrQr = 0, thus

After substitution and integration of (2.14), the rigidity is represented by

0 0

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