Variable thickness membrane

This program in C determines the optimal distribution of thickness along the radius of an axisymmetric membrane such that when the membrane is prestressed by radial displacement imposed on its boundary and then subjected to a given hydrostatic pressure exerted by an optical liquid, it deforms into a prescribed shape. The adjustable input parameters are specified at the beginning of the program. Young's modulus and the applied pressure are assumed to have unit values (scaling of the results to the general case is easy, as described in the paper).