T22

aVo A22 E

where the product V0A22 is negative.

This CTD configuration is displayed in Fig. 3.20-Left.

_ x

Fig. 3.20 Mirrors providing Astm3 mode Z22 = A22r2cos20. (Left) Solution in CTD class. (Right) Solution in VTD class

3.5.2 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. From (3.53), this is provided whenever A2 = -A\/a2. Setting the coefficient A1 = D0, we obtain A2 = -D0/a2 and

D r2

D0 a2

After substitution in Eq. (3.55), the bending moment and and the net shearing force are respectively

At the edge, this provides Mr{a, O} = 0; the net shearing force distribution Vr is fully generated from applying to the edge

This simple configuration corresponds to an external ring-force in cos 2O applied per length unit to a simply supported edge summarized as follows (Lemaitre [14]):

^ A cycloid-like shaped mirror provides an Astm 3 deformation mode z = A22 r2 cos 2 O, if a ring-force Vr = V0cos2O is applied along its simply supported edge. This force distribution is self-reacting. The thickness t = T22 t0 and characterizing features are

0 0

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