Keywords: structural patterns, multi-criteria, optimisation, simulated annealing, vertical buildings, perimeter structure.

More than four decades of research in structural optimisation has provided a broad range of computational methods for optimising structural features such as shape, topology and member sizes. Most research, however, has focussed on the single criterion of efficiency, which is usually defined as minimum weight, and is the main concern in certain engineering applications. Nevertheless, considering that there are other criteria that can also be optimised for a building structure, such as expressiveness and environmental sustainability, a multi-criteria optimisation approach that can incorporate these different types of criteria is more appropriate in the design of building structures.

More recently, the demand for vertical structures has increased enormously especially for creating denser cities in a resource scarce era because of environmental considerations. Thus, the need to design an optimum vertical structure is very significant. Structural pattern, a high level feature that includes information on geometry, granularity and member sizes, is the feature that can be manipulated to optimise the vertical structure so that it contributes positively to the four criteria of efficiency, economy, expressiveness and environmental sustainability. Thus, in this paper, the integration of structural design within the overall building design process is posed as a multi-criteria optimisation problem.

This paper investigates the optimality of non-routine structural patterns employed on the perimeter of vertical buildings, compared with the traditional orthogonal arrangement, in terms of the four criteria. Two types of patterns are investigated; non-routine regular and irregular, and for each pattern type, two cases are considered; medium-rise case with vertical loads and high-rise case with horizontal wind loads. The non-routine regular patterns; triangular, hexagonal and diamond; are selected for investigation from those used in recent buildings and/or available in nature, and the non-routine irregular patterns are generated by the application of shape grammar rules to an initial design.

The feasibility of the non-routine regular patterns are achieved by manipulating the geometry and granularity of the patterns, and the member sizes are then optimised through an iterative process that maximises the efficiencies by selecting members from a discrete sections library. Performance measures are defined for each of the four criteria and the overall performance for each of the patterns is then determined by the simple additive weighting method. The results show that for both medium and high-rise cases the triangular pattern is the optimum, while the three non-routine patterns are more optimal than the benchmark rectangular pattern.

In investigating the optimality of non-routine irregular patterns, the eifForm software was used initially to generate and optimise irregular two-dimensional patterns, based on the built-in criteria of efficiency, economy and aesthetics, by modifying shape, topology and size in the simulated annealing process. The optimised two-dimensional patterns were then used to assemble three-dimensional perimeter structures and optimised using the process described above for the regular patterns. The results show that the irregular patterns are more optimal than the rectangular pattern especially for the high-rise case, where lateral loads dominate. The rectangular patterns are, however, more efficient for the medium-rise case.

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