Robust optimization towards reducing response variation by efficient NURBS finite element inverse analysis

Real structures are inevitably subject various uncertainties due to manufacturing tolerance, assemblage error, and in-service degradation, etc. As a result, structural vibratory responses may exhibit significant variation with respect to the nominal one under ideal situation. Excessive response variation is detrimental to the safe and reliable operation of structures. This research explores the possibility of mitigating structural vibratory response variation by modifying the mean surface geometry design. That is, we assume the uncertainties remain unchanged, and attempt to reduce response variation by perturbing the nominal geometry. Essentially, this is equivalent to identifying necessary change of parameters defining the structural surface geometry towards robust optimization. Mathematically, such a problem is intrinsically challenging, because 1) a very large number of elements are necessary to describe subtle change of surface geometry when conventional finite element method is employed; and 2) inverse identification under uncertainty is typically carried out using Monte Carlo simulation type analysis which is computationally prohibitive. In this paper, we present a novel, efficient way of robust geometry optimization towards reducing response variation. We adopt the NURBS finite element, i.e., the non-uniform rational B-spline finite element method, which can directly describe complex surface geometry as well as its modification smoothly. To improve the analysis efficiency, we develop a sensitivity-based approach to directly extract the response variation, and then use such prediction to identify optimal modification of the geometry that yield the minimized response variation. This new methodology is illustrated by case analyses on wind turbine structures.