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Developing advanced numerical schemes that are able to directly handle the trimmed and multipatch parameterizations of CAD models is all the more relevant, as the ultimate goal in this book is to perform the shape optimization of realistic structures. Indeed, we want to avoid modifying the parameterization of the whole complex model at every iteration of an optimization process. Illustrations are provided in Figures 1.20 and 1.21 for the case of the movement of a hole within a plate and of a stiffener on a panel, respectively. We seek to leave the discretization of the plate (respectively, panel) unchanged if only the position and shape of the hole (respectively, stiffener) are to be optimized. Thanks to trimming objects and non-conforming interfaces, each geometric sub-part has an independent parameterization, which facilitates the definition of its movements and its relations with a “good” analysis model (note that in the case of a plate with a hole, severe mesh distortion can occur with the boundary fitted alternative). Otherwise, this would lead to a method that is too cumbersome to be able to perform shape optimization properly, and in a reasonable time. Since it is of crucial importance for the computation and optimal design of complex structures, the discussion regarding the analysis-suitable model issue is not restricted to this section: additional insights will be given in the remaining chapters of this book.

Figure 1.20. The discretization of the plate needs to be updated at each modification of the hole when a boundary fitted model is used and mesh distortion may happen. Envisaging the trimmed model coming from CAD (i.e. the plate without the hole and the boundary of the hole) enables us to keep the mesh of the plate untouched, regardless of the position and shape of the hole. For a color version of this figure, see www.iste.co.uk/bouclier/IGA.zip

Figure 1.21. The discretization of the panel needs to be updated at each shape modification of the stiffener when a matching multipatch model is used. Envisaging a model with non-conforming discretization enables us to keep the mesh of the panel untouched, regardless of the position and the shape of the stiffener. For a color version of this figure, see www.iste.co.uk/bouclier/IGA.zip