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A contribution of the optimisation of structures using Morphological Indicators : (in)stability and dynamics

Friday, 24 March, 2006 - 17:00
Campus: Brussels Humanities, Sciences & Engineering campus
Jan Van Steirteghem
phd defence

Samyn and Latteur introduced Morphological Indicators (MI) to design structures at
the stage of conceptual design. The point of departure of the theory is to minimise the
volume of material. MI allow incorporating principles of optimisation in early design
stages. Their main advantage is that we only need to consider a very small number of
parameters. Moreover, the theory of MI uses dimensionless numbers which gives the
theory a universal character. The theory, established by Samyn and Latteur, allow
considering resistance, static stiffness and instability.

Latteur showed that buckling can influence the volume of material
significantly. We show that for structures, global or local, with a small structural
index, F/L², the influence of buckling on the volume of material is important.
Therefore, we propose stayed members that allow a given compression member to
work at a higher stress level, and by doing so decreasing the volume of material
significantly. Moreover, we develop a design procedure that allows designing stayed
members. Our design procedure accounts for imperfections and calculates the
necessary pretension. We provide some examples, which use this design procedure,
and show that the volume of material of compression members can decrease
significantly if we use stayed members. We show that this decrease is most
pronounced for compression members with a low structural index.

In this study we add dynamics to the theory of MI. By optimising structures
with respect to volume of material we obtain structures that are usually very sensitive
to dynamic loads. We establish an indicator of first natural frequency that allows
determining the first natural frequency of structures (beams and trusses) at the stage of
conceptual design. We show that this approach yields very accurate results. Moreover
we show that for important spans dynamics can become the dimensioning criterion
since we need to reduce the stress in the structure significantly to obtain acceptable
natural frequencies. Additionally, we show that we can use tuned mass dampers
(TMD) to reduce the dynamic accelerations (and displacements), in structures
subjected to dynamic loads, without a very large decrease of the stress level.

The results indicate that we have to consider a ‘design for stiffness’ approach
as well as a ‘design for strength’ approach. However, we emphasize that the goal
remains a minimal volume of material.