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where the product V0A31 is negative.

This configuration is shown in Fig. 3.12-Left.

Fig. 3.12 Mirrors providing Coma3 mode z31 = A3jr3cos0. (Left) Solution in CTD class. (Right) Solution in VTD class y y x

Fig. 3.12 Mirrors providing Coma3 mode z31 = A3jr3cos0. (Left) Solution in CTD class. (Right) Solution in VTD class

3.4.2 Configuration in the VTD Class

A solution in the VTD class is obtained for the case of a null rigidity at the edge, D{a} = 0. This is provided in (3.42) if C2 = —Ci. Setting the Ci coefficient to 2/(3 + v), we obtain and from (3.22), Ai = 2Doa2/(3 + v) and A2 = -2Do/(3 + v). After substitution in Eq. (3.43), the bending moment is

Considering Mr and Vr at the edge r = a, and near the center for r = b small, we have

Vr {a, 0} = 8A3iDocos 0, Vr {b, 6} ~ A31D0 a2 cos 0 /b2, which corresponds to a prismatic external ring-force Vr = V0 cos 0 applied per unit length to a simply supported edge. This configuration is summarized as follows (Lemaitre [14]):

^ A tulip-shaped mirror provides a Coma 3 deformation mode z = A31 r3 cos 0, if a prismatic ring-force Vr = V0 cos 0 applied along its simply supported edge is in reaction to a moment applied near the center. Its thickness t = T3110 and characterizing features are and the net shearing force is

0 0

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