Interactive Equilibrium Modeling
L. Lachauer
2010 - 2015

In this dissertation, new approaches to the design of non-standard building structures with efficient static behaviour are presented. Computer-aided modelling tools enable architects to design spectacular buildings with complex geometry; through strong numerical methods, civil engineers are able to statically analyse and design corresponding structures. The often strong separation between architectural and structural design processes largely results in inefficient structural behaviour and high consumption of resources. The aim is to develop a structural design methodology which combines principles of static equilibrium with computer-aided design concepts. For this purpose, an interactive modelling approach is described, enabling the designer to iteratively bring together design idea and efficient structural behaviour. On the one hand, the relevance of this dissertation lies in its contribution to reducing the gap between free architectural design and scientific structural design. On the other hand, the relevance lies in the systematisation and facilitation of the design process for geometrically complex building structures with efficient force flow. The presented modelling approaches are built upon the conceptual framework of truss models, combined with computational form-finding methods. In a first step, tailored equilibrium modelling methods for selected typologies of structures, e.g. curved bridges or branching columns, are developed. Each of these modelling methods is based on well-defined structural concepts. Through customised, case-specific adaptation of standard formfinding techniques, the boundary conditions of the underlying structural concepts are inscribed in these interactive modelling processes. In a second step, a general equilibrium modelling approach is developed, which allows generic boundary conditions to be defined to address different structural concepts. This general modelling approach is based on a new technique to solve formfinding problems with constraints both on the form and on the inner forces. For this purpose, the Force Density Method has been extended in a new way. Previously, several approaches were formulated in order to add boundary conditions to the Force Density Method, but these were largely driven by specific construction and fabrication properties. Here, general constraints are used to enable early-stage structural design explorations with a high degree of geometric control. The flexibility of the new method is demonstrated in nine prototypical case studies. The first group of cases demonstrates that the method enables the exploration of the inherent geometric freedom of renowned structural typologies. The second group of cases demonstrates that the method is also suited for creating new typologies, by combining and merging given structural models. The following contributions to the body of knowledge have been made: tailored modelling approaches for selected structural typologies were developed; a general equilibrium modelling approach based on a new extension of the Force Density Method was formulated; case studies illustrating the modelling process of selected structures were presented. Furthermore, the new solving technique for form-finding problems with boundary conditions establishes the conceptual basis for a new computer-aided structural design tool.

Keywords: structural design, computer-aided design, geometric modelling, architectural geometry, equilibrium solutions, strut-and-tie models, constrained form finding, Force Density Method

Parametric model of a roof with efficiently shaped trusses

last modified 26.1.2016