Journal of Theoretical
and Applied Mechanics

14, 2, pp. 261-271, Warsaw 1976

Optymalne kształtowanie wirującego pręta z uwzględnieniem nieliniowości fizycznej materiału

Antoni Gajewski
The subject of the paper is minimal weight design of a rod of length l that carries a concentrated mass Q at x=l and rotates at constant velocity omega about an axis through x=0 that is perpendicular to the rod. It has been assumed that material of the rod is characterized by nonlinear dependance between stress and strain. Physical law can describe nonlinearly-elastic, elastic-plastic as well as rheological behaviour of materials. On the basis of the general formulation of the problem, optimal design of the rod for minimum axial displacement at x=l has been done under the constraint that the volume is equal to the given value (in dual formulation). The optimal shapes of the rod obtained for different values of exponent n in the case of power physical law, presented graphically, essentially depend on the form of the physical law.