Optimal design of wind mill towers

In this paper the optimal shape for a minimum weight design of wind mill towers of linearly varying cross section, made of steel, is presented. The design variables are the top and bottom diameters, and the height and thickness of a given number of segments that comprise the tower of given height. The optimization is based on an analysis that considers the tower as a thin walled cantilever beam of variable cross section. The stress constraints are considered at all critical sections of the segments, whereas a displacement constraint is considered at the top of the tower. The optimal shape is deduced for the extreme storm conditions which remain critical for a wide range of parameters. The optimization problem is formulated as a non-linear mathematical programming problem. This is solved using different algorithms such as, the sequential linear programming method, the sequential quadratic programming, and the sequential convex programming method. To improve the convergence of the algorithms used, analytical expressions for the derivatives of the objective function and the constraints are developed using symbolic manipulation. The method was applied to the design of 50 towers of PPC installed at various Greek islands under the Hors Quota Program of EC. A series of parametric studies is performed to investigate the influence of several structural parameters on the design.