ANALYSIS OF NONLINEAR MODEL PROBLEMS BY THE FINITE ELEMENT METHOD OF LINES--II. SHAPE OPTIMIZATION OF ELASTIC BARS IN TORSION
As the second paper in this series of nonlinear applications of the finite element method of lines (FEMOL), the present paper applies this method to shape optimization problems by presenting a FEMOL analysis 
of the optimization of elastic bars in torsion. Firstly,with the domain boundaries fixed, a set of ordinary differential equations (ODEs) for pure torsion is derived by means of the variational method. Next the changes of nodal lines at end-points on the free boundaries are taken as shape variables 
which arc incorporated into the ODE system by using the trivial ODE technique with the supplementary BCs provided by the optimality conditions. As a result, the free boundary problem in ODEs is transformed in to a standard nonlinear ODE problem and solved by standard ODE solvers. Numerical examples are given to show the great convenience, efficiency and accuracy of the present approach.