# Form Finding and Optimization

### Form ﬁnding and size optimization

Implementation of beam elements and size optimization in real time

form ﬁnding using dynamic relaxation

###### JENS OLSSON

Master’s thesis in Architectural Engineering

Department of Applied Mechanics, Division of Dynamics

CHALMERS UNIVERSITY OF TECHNOLOGY

Gothenburg, Sweden 2012

In the pursuit of performance-based architecture there is an increased demand for integration between engineers and architects, between analysis and design. The key to make wise choices early in a design process, has previously been based on experience from prior work and experiments with physical models. With modern computational power those choices can be supplemented with real-time feedback from analysis tools.

But few programs are designed for the type of light weight, real-time analysis that can be useful in the exploration of an architectural concept. This has been the target for a research and development team, SMART Solutions, at Buro Happold. SMART Form is a tool for performance-based architecture as a plug-in for the 3D modeling software Rhinoceros.

It combines analysis and rationalization of complex geometries with form finding and sculpting of structures, driven by a dynamic relaxation solver. The plugin transforms the 3D modeling software to a virtual physical environment, influenced by various forces and a gravitational field. It enables sketching and sculpting of eﬃcient compression (shells and gridshells) and tension structures (cable nets and membranes).

The purpose for the thesis by Jens Olsson has been to advance SMART Form by implementing beam elements and explore how bending action can be used in the form finding process, allowing for a compromise between initial geometry and fully form found geometry. Automatic sizing of the beam elements is also implemented as a method to evaluate form.

The thesis leads to an investigation of how to conduct conceptual structural design, and how this process can potentially be approached diﬀerently with the means of real-time feedback from analysis, form finding and sizing. In order to allow for real-time analysis an iterative technique called dynamic relaxation is used as the computational solver.

As a result of the exploration of form finding with bending action a method called Limit control form finding was developed. This method enables form optimization of the most critical parts of a structure by specifying a limit for the bending capability of the elements. It was found to work in a good way for 2D structures but sometimes resulting in a less appealing, wrinkled looking grids for 3D structures.

Dynamic relaxation is found to be a suitable method for real time analysis, although with some important issues regarding speed. The number of iterations needed to reach convergence is concluded to depend on the relation between local and global stiﬀness for each node in the structure. Hence the method works eﬃciently for some types of structural configuration (for example gridshells with a locally weak direction), while a conventional matrix solver would perhaps be more suitable for other cases (for example space truss structures).

The implemented functionality, such as form finding using cables, limit control and automatic sizing is demonstrated with a couple of test cases. One of which is the Exeter gridshell roof where engineers at Buro Happold have been involved from the concept design to the realized structure. The real design process for the project is shown and new approach based on real time feedback is demonstrated.

With the new functionality implemented during the thesis, SMART Form has become a much more sophisticated tool, and a great improvement for the design process of the Exeter roof could be made. Due to the possibilities of a quick and eﬃcient collaborative design process, that comes with the new tool, it seems to oﬀer great potential in bridging between engineers and architects in structural concept design.

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