For a typical design problem of a plate of variable thickness, we analyze the one-dimensional situation through a variational reformulation to discover that, in contrast with the higher dimensional case, there are optimal solutions. Another typical interpretation of this simplification is that of the optimal shape of a bending beam. The mechanism employed for the existence issue is the direct method for the new formulation. Optimality conditions are then pursued.
periodic plate; optimal design; direct method; optimality conditions
