Gradient-based prestress and size optimization for the design of cable domes

Cable domes are cable-strut structural systems widely used as large span roofs of arenas, stadiums, and open spaces for their lightweight forms and aesthetic impact. We first recall the matrix theory for the static and kinematic analysis of pin-jointed cable-strut structural assemblies. This theory is used to identify potential states of self-equilibrated prestress for a given structure, and to evaluate their stiffening effect on the structure internal mechanisms. Then, a problem for simultaneous optimization of prestress and size of nonlinear cable-strut structural systems is formulated. Constraints on internal forces and displacements are imposed while the structural weight is minimized. The resulting optimization problem is solved with a gradient-based approach based on sequential linear programming. The gradients of the aggregated constraint functions are consistently calculated with adjoint sensitivity analyses. The optimization approach is applied to the design of a simple illustrative structure and of a realistic cable dome. The results show that the proposed approach can identify optimized designs with modest computational efforts, and with significant savings in terms of structural weight compared to initial design guesses.