A general solution procedure is described for the optimal design of flywheel forms. A continuously differentiable thickness function is developed with undetermined coefficients and closed form solutions for the volume and kinetic energy derived. The two-point boundary value problem which results from the solution of the differential equation for the radial and tangential stresses is solved by the shooting method. The stress components are then combined to form the total stress at each radial location through the application of distortion energy theory. The problem is then formulated as a nonlinear programming problem and solved for various design objectives including minimizing the flywheel volume, maximizing the kinetic energy, and minimizing the stress deviations from the limiting design stress.

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