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Fig. 8.18 Quasi-conical thickness distribution T(p) providing a parabolic flexure from Table 8.4. The infinite branch in (-lnp)1/3 at the central region is very narrow. The branch can be given a finite length with a small section area for the substitution of a central load to the central force, thus avoiding infinite local stresses

Fig. 8.18 Quasi-conical thickness distribution T(p) providing a parabolic flexure from Table 8.4. The infinite branch in (-lnp)1/3 at the central region is very narrow. The branch can be given a finite length with a small section area for the substitution of a central load to the central force, thus avoiding infinite local stresses

A flexure sag ratio can be derived for comparing the sag of the quasi-conical plate to that of the constant thickness plate. Since the normalized thickness t is the same in (8.68) and (8.75) - same mass normalization -, for identical materials we obtain

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