Weak shape formulation of free boundary problems
Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.
Würfel und reguläres Tetraeder als Maximum und Minimum.