Shell structures are material efficient structures capable of covering large spans with minimum weight. If concrete is used as the building material for the shell, it must be initially supported by a formwork. These generally rigid formworks, and their supporting falsework structure, are time and material consuming to construct. Recently, researchers have recommended the use of elastic gridshells as falsework system. Unfortunately, the design of such a system is complicated by large deformations of the bending elements. Moreover, since gridshells are inherently flexible, significant displacements generally occur when applying the wet concrete.

To overcome these difficulties, this paper presents a design tool to effectively design a gridshell serving as the falsework for a concrete shell. The gridshell is assumed to be constructed from an initially flat grid of straight slender rods, using cables with adjustable lengths to brace the erected gridshell. An optimization algorithm is proposed that fits the shape of the gridshell under the wet concrete loading to a given target shape by manipulating the lengths of the bracing cables. Meanwhile, the optimization algorithm reduces the construction effort by minimizing the number of cables, and the diameter of the grid rods. Moreover, feasibility of the design is ensured by constraining the axial force in the cables and limiting the displacements under increased loading. A gradient-based optimization scheme is adopted, and an implicit dynamic relaxation approach previously developed specifically for the simulation of bending-active structures is used to solve the nonlinear equilibrium equations. Nonlinear effects such as buckling of the grid rods are taken into account by using co-rotational beam elements. The resulting design tool is applied for the design of a scale model, demonstrating the feasibility of the suggested falsework system. The optimized design fits the target better, uses less cables, and is more resistant to additional loading compared to designs from existing design approaches. Comparisons between the numerical and physical models show deviations of up to around 2% of the larger span for the design load and smaller deviations for smaller loads, with differences attributed to small model scaling effects.

壳结构是材料有效的结构，能够以最小的重量覆盖大跨度。如果将混凝土用作壳体的建筑材料，则必须首先使用模板将其支撑。这些通常是刚性的模板及其支撑的模板结构，建造起来很费时间和材料。最近，研究人员建议使用弹性栅栏作为工作系统。不幸的是，这种系统的设计由于弯曲元件的大变形而变得复杂。此外，由于格栅壳体本身是柔性的，因此在施加湿混凝土时通常会发生明显的位移。

为了克服这些困难，本文提出了一种设计工具，可以有效地设计用作混凝土壳体框架的网格壳体。假定栅格壳由最初细长的直杆扁平栅格构成，并使用长度可调的电缆支撑竖立的栅格壳。提出了一种优化算法，通过控制支撑电缆的长度，使湿混凝土荷载下的格栅壳形状适合给定的目标形状。同时，优化算法通过最小化电缆的数量和栅杆的直径来减少施工工作量。此外，通过限制电缆中的轴向力并在增加的载荷下限制位移来确保设计的可行性。采用基于梯度的优化方案，先前专门为弯曲主动结构的仿真而开发的隐式动态松弛方法用于求解非线性平衡方程。通过使用同向旋转的梁单元，可以考虑非线性效应，例如栅栏杆的屈曲。最终的设计工具被用于比例模型的设计，证明了所建议的脚手架系统的可行性。与现有设计方法相比，优化设计可以更好地适应目标，使用更少的电缆，并且能够抵抗额外的负载。数值模型与物理模型之间的比较表明，对于设计载荷，偏差高达最大跨度的2％左右；对于较小载荷，偏差较小，且差异归因于较小的模型缩放效果。