document: We consider the shape optimisation of two- and three-dimensional solids by combining multiresolution subdivision surfaces with immersed finite elements. As widely discussed in isogeometric analysis literature, the geometry representations used in today’s computer aided design (CAD) and finite element analysis (FEA) software are inherently incompatible [1]. This is particularly limiting in shape optimisation during which a given CAD geometry model is to be iteratively updated based on the results of a finite element computation. The inherent shortcomings of present geometry and analysis representations have motivated the proliferation of various shape optimisation techniques. In the most prevalent approaches a surrogate geometry model [2–8] or the analysis mesh [9,10] instead of the true CAD model is optimised, see also [11] and references therein. Generally, it is tedious or impossible to map the optimised surrogate geometry model or analysis mesh back to the original CAD model, which is essential for continuing with the design process and later for manufacturing purposes. Moreover, geometric design features are usually defined with respect to the CAD model and cannot be easily enforced on the surrogate model. Recently, the shape optimisation of shells, solids and other applications using isogeometric analysis has been explored; that is, through directly optimising the CAD geometry model [12–15].
doc_bio_tags: O O O B I O O O O B O B I I I O B I I O O O O B I O O B I O O O B I I B O B I I B O O O O O O O O O O B I O O O O B O O O O O O O O O O O O O B I I O O O O O B I I I O O O O O O B I O O O O O O O B I I O O O B I O O O O O B O O O O O O O O O O O O O O O O O O B I I I O B I O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B I O O B I O B B O O O O B I O O O O O O B I O B O O O
extractive_keyphrases: analysis mesh cad combining multiresolution subdivision surfaces computer aided design directly optimising fea finite element analysis finite element computation geometry and analysis representations geometry representations immersed finite elements isogeometric analysis optimised surrogate geometry model shape optimisation shells solids surrogate geometry model surrogate model
abstractive_keyphrases: cad geometry model cad model isogeometric analysis literature shape optimisation techniques two- and three-dimensional solids