Optimal design for plates and relaxation

摘要

The optimal design problem for a plate of variable thickness assuming the Kirchhoff model for pure bending of symmetric plates is studied. It is well known that this problem has no solution. The relaxation procedure is thus necessary, leading naturally to homogenisation.Following the ideas of Tartar, a new procedure is proposed, giving the known result of Munoz and Pedregal. Some applications of the proposed method for more general materials are presented.