Isogeometric Refinement for Shape Optimization with a Tunable Number of Variables

The classical funicularity concept for shell structures has been extended defining the Relaxed Funicularity (R-Funicularity). A parameter called generalized eccentricity has been used for this purpose, following that a shell is R-Funicular when the generalized eccentricity doesn’t exceed an admissibility limit. A shells’ shape optimization process aiming at finding R-Funicular analytical shells is here modified at the geometry definition level by describing the shells’ shape with spline surfaces and using the position of the control polygon vertices as optimization variables. An isogeometric (IG) refinement is applied in order to improve the local control of the shape in the optimization process. An advantage of this approach is that, since it introduces new vertices in the control polygon, the number of optimization variables becomes tunable. Namely, starting with the lowest number used to generate the initial geometry, the additional vertices can possibly be entered as new variables whenever a more accurate local control of the surface is needed. We present significant numerical examples.