shape of the meridian curve; class of Lipschitz functions; axisymmetric mixed boundary value problems; four different cost functionals; approximate piecewise linear solutions; finite element technique; convergence; existence; appropriate weighted Sobolev spaces; axisymmetric elliptic problems; body of revolution; elastic equilibrium
The shape of the meridian curve of an elastic body is optimized within a class of Lipschitz functions. Only axisymmetric mixed boundary value problems are considered. Four different cost functionals are used and approximate piecewise linear solutions defined on the basis of a finite element technique. Some convergence and existence results are derived by means of the theory of the appropriate weighted Sobolev spaces.