Some optimization problems for elastic bodies

Two optimization problems for finite deformations of an elastic body are formulated. In the first problem, the motion that gives minimum value (maximum value) to a certain functional is chosen from a single family of controllable motions. The necessary conditions for optimality are stated for one specific problem of this type. In the second problem, the minimizing (maximizing) motion is chosen from the class of all possible motions connecting two configurations of the body. The necessary conditions for the optimality of singular solutions are obtained for one specific example of this type.This work was supported by the Pokrajinska Zajednica za Naucni Rad, Novi Sad, Yugoslavia.