On the optimal shape of a rigid body supported by an elastic membrane
The authors prove the existence of a solution to the problem of minimizing the Dirichlet potential (energy of deformation of a linear elastic membrane) that supports a rigid body, under any of the following assumptions: (i) the height of the body is constrained, or (ii) the volume of the body is prescribed. The result is obtained by applying a direct method after having stated a simpler equivalent problem.
scientific article; zbMATH DE number 1383358
scientific article