Both the shape of the shell and the layout of the lattice determine the structural efficiency of a gridshell. The shape of the shell determines to what extent the structure acts as a membrane rather than a plate. Membrane action is preferred as it leads to a much higher material efficiency. The layout of the lattice should be designed in such a way that the material distribution logically follows the distribution of stresses. To design a gridshell, two types of numerical tools are available: formfinding methods and numerical optimization techniques.

Usually in practice, only formfinding techniques are used to define the shape of a gridshell. In order to use these tools, there are some parameters the designer must choose (i.e. the design variables). Also the layout of the lattice must be chosen a priori. The formfinding method then finds an equilibrium position for all the nodes in the initial grid within the given boundary conditions. However, sometimes the physical meaning or impact of certain variables is unclear, making it difficult for the designer to find the most structurally efficient design. Numerical optimization techniques are able to solve this problem. These methods find the best choice of design variables regarding a specific objective (e.g. minimal material use).

Numerical optimization methods are relatively well-known in the literature, but only a few papers discuss numerical optimization for the design of gridshells. The optimization methods that do also apply for gridshells have the following shortcomings: (1) they do not account for buckling, (2) they use metaheuristic solving strategies such as genetic algoritms, which are computationally very costly, or (3) they do not optimize the layout of the lattice and the shape of the shell simultaneously. The flaws in these methods can lead to sub-optimal or even unrealistic or unfeasible designs.

The objective of this project is to develop an efficient method for the optimal design of gridshells, considering the shape of the shell as well as the layout of the lattice. The aim is to combine the advantages of formfinding (to find a relatively efficient design taking into account designer preferences) and numerical optimization (to find the most efficient design within these constraints) by the simultaneous application of both methods. This will imply an important step forward compared to current practice, where the shape of the gridshell is usually chosen a priori by means of formfinding, and the layout of the lattice is determined a posteriori by means of numerical optimization. To ensure that the method converges within a reasonable time, only gradient-based approaches will be used. Moreover, buckling, geometric imperfections, and buildability constraints will be taken into account.

Thrust Network Analysis, developed by Philippe Block at the Massachusetts Institute of Technology in 2009, is a method to find the shape of a shell structure in which only compression forces occur. This thesis investigates how Thrust Network Analysis can be used to design a new liturgical space in the city of Scherpenheuvel. The thesis thus provides designers who want to use the method with sufficient theoretical background as well as an elaborate example, which can serve as a strong basis to explore the method for themselves.

First a literature study is conducted, focussing primarily on the PhD dissertation of Philippe Block. Based on this literature study, the theory behind the method is discussed. Secondly, a small-scale example is implemented in MATLAB to explore the basic functionality of the method. Finally, the method is tested in a present-day design problem. More specifically, Thrust Network Analysis is used to design a new liturgical space in Scherpenheuvel. The method is evaluated by performing a finite element calculation on the obtained shell structure and comparing it to the expected results.

The literature study shows that the method is easy to understand and that it can be used in a very intuitive way. The implementation in MATLAB reveals much of its functionality. After making the design, one can conclude that the method is exceptionally well-suited for the design of a church. However, the question arises if the typical shapes that the Thrust Network Analysis method produces are equally applicable for other designs. Moreover, the reliability of the method does not seem optimal, as tension forces do seem to appear in the obtained shell. Like other formfinding methods, Thrust Network Analysis only takes one load case into account. In reality however, loading is not limited to a single load case, which can lead to unwanted bending moments in the structure. To solve this problem, Numerical optimization methods can be added to take multiple loading conditions into account.