Optimization of cross-section of hollow prismatic bars in torsion

The problem of optimal shape design of a doubly connected prismatic bar in torsion is formulated and solved numerically by the finite element method. The cost function is torsional rigidity of the domain, constraint is the constant area of the cross-section while shape parameters are co-ordinates of the finite element nodes along the variable boundary. The variable boundary is either the inner or outer boundary of the domain. A dual problem of minimizing the area at the constant torsional rigidity is also considered. The problem is solved directly by optimizing the cost function with respect to the shape parameters. Numerical examples are given for two benchmark problems.