Benchmarking Optimisation at Conceptual Design Stage with Morphological Indicators

Thomas Vandenbergh

Research output: ThesisPhD Thesis


Within the framework of sustainable development we strive for constructions with a minimum volume of material. At conceptual design stage and only considering criteria on resistance and buckling, a clear hierarchy among different structural morphologies (i.e. shapes and topologies) can be established with morphological indicators. Morphological indicators are dimensionless numbers that represent a property of a structure (its volume, its maximal static displacement...) and only depend on a reduced number of variables, providing user-friendly and efficient tools to guide the designer during its exploration and comparison of different structural types. Up till now the theory of morphological indicators was essentially based on the consideration of a fully stressed design, privileging strength as the prior design constraint. Though using the indicator of displacement, we prove that when the limit on the maximal static displacement is exceeded, sizing based on a fully stressed design does not always guarantee an optimal solution. Hence, it is essential to provide information about the most restrictive design criterion during the first design steps and hereby avoid important a posteriori structural modifications due to the use of an inappropriate optimisation methodology. In this perspective we develop additional indicators, allowing the inclusion of additional design criteria. A first extension concerns instabilities. Analyzing the global planar buckling loads of three-hinged parabolic truss arches, we derive a new indicator ?cr, called the indicator of global planar stability. This indicator enables one to predict, whether truss(-arch) structures are prone to planar instabilities and the impact of morphological modifications on their stability and volume. The second important contribution handles vibration problems. We establish indicators and graphics enabling to assess the vibration response of beams, trusses and arches in terms of their first vertical eigenfrequency or their peak acceleration under fully developed resonance by harmonic excitation. The possible vibration reductions achieved by tuned mass dampers are also treated. We focus more in detail on the vibrations induced by pedestrians and draw design graphics for the evaluation of the peak acceleration levels at resonance and the rms-velocities under impulse for beams, trusses and parabolic arches. These new indicators and graphics enable to decide, without need for detailed calculations, whether strength or stiffness is the design determining criterion. If the fully stressed design complies with all the imposed stiffness constraints, we have a design for strength and the minimisation of the indicator of volume leads to a light, resistant and stiff solution. But if one of the stiffness constraints (on the static displacement, the global planar stability or the vibration response) is violated, one has to deal with a design for stiffness problem. Other optimisation methods should then be used. Some possible optimisation methods, based on numerical optimisation algorithms, are discussed and applied on a practical example. The results confirm the high efficiency of morphological indicators in design for strength, but also emphasize the need for alternatives in design for stiffness.
Original languageEnglish
Awarding Institution
  • Vrije Universiteit Brussel
  • Latteur, Pierre, Co-Supervisor, External person
  • De Wilde, Willy, Supervisor
Place of PublicationBrussels
Publication statusPublished - 2010


  • conceptual design


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