and after substitution in (2.14), we obtain the rigidity qR , 2,

The interest of VTDs is to avoid the application of moments at the boundaries. We can select a null bending moment at the edge, Mr(a) = 0. From (2.11), this is satisfied by taking the rigidity D(a) = 0. Therefore, the rigidity is

Fig. 2.2 Variable Curvature Mirrors derived from the VTD class. Dimensionless thicknesses t20 with p = r/a and p E [ 0,1 ] (after Lemaitre [35]). Up-left: Uniform loading and reaction at the edge, t20 = (1 —p2)1/3. Up-right: Axial force at center and edge reaction, t20 = (—lnp2)1/3. Down: Uniform loading and central reaction, t20 = (p2 — lnp2 — 1)1/3

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