Optimal Design of Gridshells

Gridshells are shell structures built from discrete elements such as wood, composite, or steel bars. Due to the three-dimensional character of their shape, gridshells are potentially very efficient: when properly designed, light-weight gridshells can cover very large spans. They can be categorized in two groups: unstrained gridshells consist of prefabricated members, all straight or pre-bent, while strained gridshells are composed of continuous rods bent on site into the shape of the shell. The behavior of the latter is harder to model, because the large displacements associated with their erection process should be taken into account. The design of strained gridshells is usually based on form-finding techniques that simulate this erection process. Form-finding techniques can provide the designer with a large degree of control over the shape of the gridshell, but there is no guarantee that the design is feasible; an additional structural analysis has to be performed to verify this. Consequently, an iterative trial and error process is often needed to fine-tune the design to fulfill all requirements. This thesis investigates the numerical optimization of strained gridshells to automatically generate the most efficient design for a given objective, while accounting for practical and design related constraints. In order to obtain realistic designs in a time efficient way, the complex bending behavior is modeled using co-rotational beam elements in combination with a novel, fast-solving dynamic relaxation approach, which is shown to be equivalent to the Newton- Raphson method for certain conditions. Two typical design challenges are considered in particular: the design of a strained gridshell with the most material efficient shape, and the design of a strained gridshell with a predefined target shape. Multiple load cases and practical constraints are taken into account to make sure the optimized design is feasible. Furthermore, the optimization problem is solved efficiently using gradient-based optimization algorithms. The developed optimization framework is applied to two case studies. The first case study consists of the design and construction of a simply supported strained gridshell prototype, for which the overall stiffness is maximized by optimizing the erection forces. As a second case study, a small-scale strained gridshell model representing the falsework for a concrete shell is designed and built, where the undeformed length of the bracing cables is optimized to fit the gridshell to a predefined target shape under wet concrete loading. For both considered optimization problems, the numerical results show an important step forward compared to current design approaches: feasible designs that perform notably better than non-optimized designs are automatically generated. The considered case studies demonstrated that the developed optimization framework is especially useful for situations where existing design approaches are inadequate, for example when the supports are incapable of carrying thrust forces, or as falsework for concrete shells.

Jaar van publicatie:2019

Toegankelijkheid:Open