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.

缆索穹顶是缆索支撑结构系统，因其轻巧的外形和美观的效果而广泛用作竞技场，体育场和开放空间的大跨度屋顶。我们首先回顾矩阵理论，对销钉连接的索杆结构组件进行静态和运动学分析。该理论用于确定给定结构的自平衡预应力的潜在状态，并评估其对结构内部机制的加劲作用。然后，提出了同时优化非线性索杆结构系统的预应力和尺寸的问题。在最小化结构重量的同时施加了对内力和位移的约束。由此产生的优化问题通过基于顺序线性规划的基于梯度的方法得以解决。聚合约束函数的梯度是通过伴随灵敏度分析一致地计算的。优化方法适用于简单的说明性结构和实际的电缆穹顶的设计。结果表明，所提出的方法可以用适度的计算工作来确定优化的设计，并且与初始设计的猜测相比，在结构重量方面节省大量成本。