Optimum shell design of solar updraft towers

Solar towers are designed as extremely thin concrete shells, stiffened at the top and along the height by circular ring beams in order to provide a beam-like behaviour. The paper analyses the optimization of one kilometer-tower under wind and dead loads. A nonlinear constrained optimization problem is set with the aim of both minimizing the total amount of concrete and steel reinforcement and improving the structural performance. A key role in designing solar-updraft towers is played by the stiffening rings which increase the buckling stiffness of the tower and reduce wind induced tensile stresses by preventing ovalling deformations of the cross-section. Moreover, the quality of the structural response is also strictly related to the shape of the tower and the thickness distribution. In the light of this, the design variables of the optimization problem are carefully selected in order to control the stiffness level and the placement of the stiffening rings, the geometry of the tower which is given by the shape of the meridian treated as a free-form curve, the distribution of the wall thickness. The structural behaviour - with particular care to the areas with tensile stresses and buckling phenomena - as well as the thermodynamic efficiency of the tower, are considered in the nonlinear constraints of the problem. However, beside structural needs, economical aspects and formidable construction efforts dominate the design feasibility of such high-rise structures. Therefore, the objective function to be minimized is made up of a total actual cost obtained by introducing some suitably weighted and tuned coefficients.