Topology optimization under uncertainty

Topology optimization is a systematic and general computational tool for designing high performance
structures. The technique is diff erent from shape optimization methods in
that it seeks the best layout of material within the design domain by allowing for
variations in both its boundary and its connectivity. While the power of topology
optimization has been demonstrated in literature, deterministic conditions are often assumed,
meaning various sources of uncertainty that exist either in the design variables
or in the other parameters that de fine the system are disregarded. These uncertainties,
whether attributed to inherent variability in the system parameters or incomplete knowledge
of their exact values, if not included in a systematic way, may lead to designs that
are less efficient under real-world engineering conditions.

Imperfection-sensitivity and nonlinear behavior of thin-walled structures

The discrepancy between the experimentally measured and theoretically/computationally determined failure
loads, when the failure is due to loss of stability, is more tangible for thin-walled structures. W.T. Koiter
was the first to explain this phenomenon. He showed that for structures with unstable critical
state, it is the size and shape of geometric imperfections that will determine the extent by which
the failure load may differ from what is obtained from analyzing a perfect model. However, it
is quite obvious that any attempt towards investigating this matter would not be a realistic one
if it doesn’t take into account the uncertain nature of these imperfections.

Dynamics of structure-equipment interactions

The composite equipment-structure systems possess three dynamic characteristics. These
characteristics are 1) tuning-which occurs when the natural frequency of the oscillator is equal to
one or more natural frequencies of the structure 2) interaction-which has to do with the feedback
eff ect between the motions of the oscillator and the structure and 3) non-classical damping-which
occurs when the damping characteristics of the oscillator is di fferent from that of the modes of
the structure