The 2008 Olympics, being hosted by Beijing, China, will reportedly have the largest and most unusual swimming centre ever built. The design of the structure for the swimming centre was inspired by the shape of an array of soap bubbles and is highly repetitive and constructible, whilst appearing to the casual observer to be very random and organic. The centre has been named the Water Cube and houses all of the pools for the Olympic swimming and diving competitions, together with seating and facilities for 17,000 spectators.
Arup Australia is the company responsible for the design of the Water Cube, and the company has been supported throughout the design process by Strand7 Pty, Sydney, Australia, and the use of its finite element analysis (FEA) software. A comprehensive 3D structural model of the Water Cube was created and imported directly into Strand7 software. The FEA model comprised 24,000 beam elements with 12,000 nodes. There were 750,000 beam loads in 55 basic load cases, which were considered in 200 load combinations. The beam loads are derived from wind and snow pressure loads, which were applied to the external translucent cladding and in turn transmitted to the structural members. Using the Strand7 patch element it was a simple procedure to automatically convert these pressure loads to the relatively complex distributed beam load definitions. The Strand7 software suite offers a tool that automatically defines the load patches over a gridwork of beam elements, similar to a mesh generator. Once the patches were defined, pressure and other loads assigned to the patches were then automatically transferred to the underlying beams according to their associated tributary areas.
The most significant aspect of the analysis for this project was the seismic design. Strand7 has for many years been capable of transient dynamic and spectral seismic analyses. The latest Strand7 Release — Version 2.3 — has added the capability to take site specific seismic time histories and simply create equivalent spectral curves. There is also the option to include the equivalent quasi-static seismic analysis as used in Eurocode EC8, AS1170.4 and other codes. In the case of the Water Cube, a Spectral Response analysis was performed. This used the results from a natural frequency analysis that calculated 4424 modes to achieve the 90% mass participation required for an accurate spectral response solution.
Optimisation of the structural design was required to ensure that the weight of the building could be kept to a minimum without sacrificing strength. Through the use of the Strand7 Application Programming Interface (API) the optimisation process was taken to levels never before possible, according to the company. Each of the 24,000 beam elements, subject to 200 load combinations, was checked at five points against 13 different equations in the Chinese structural code. Every member and node had the potential to be different and hence considerable optimisation processing was required. All this optimisation was automated with a VBA script within Excel, so it did not require particularly sophisticated computer programming or languages.
The Strand7 API allows users to interact with Strand7 via an external computer program. This provides the user with the capability to bypass the Strand7 Interactive Environment and to perform specialised functions. The API provides a totally transparent way of interacting with the Strand7 data and repetitive tasks can be easily automated. The API allows new Strand7 model files (binary ST7 files) to be created from scratch, existing Strand7 model files to be modified, the Strand7 solvers to be executed and results to be extracted and processed. These powerful features were all utilised in the Water Cube analysis.
Using the Strand7 API, a single iteration of the entire Water Cube design optimisation process took only one hour. Arup took advantage of the Strand7 Sparse Solver to facilitate this. This enhanced solver allows very large models to be solved in a much reduced time compared with other solvers commonly found in structural analysis software. The complete optimisation process took about 25 iterations and led to a phenomenal weight saving, which brought the weight of the Water Cube down to a very light 100 kg/m2.
Apart from the global analyses, Strand7 was also used to perform elasto-plastic analysis of the beam connection details within the Water Cube. The accuracy of the results of these non-linear analyses was confirmed by full scale testing. It is envisaged that the Water Cube will be one of the major draws at the 2008 Olympics.
Strand7 is developed in Sydney by Ltd. In addition to the FEA software, Strand7 also offers training, ongoing software support and engineering consultancy services. Full product details and a fully functional demonstration version are available from the website.
