Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces
For engineers designing thin shell structures, this method provides a regularised shape optimisation framework that avoids sub-optimal oscillatory geometries, though it is an incremental improvement over existing isogeometric optimisation techniques.
This paper introduces a multiresolution isogeometric shape optimisation method for thin shell structures using subdivision surfaces, achieving compliance minimisation (stiffness maximisation) while preventing jagged geometries. The approach is demonstrated on three examples, showing effective regularisation and control over feature size.
We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based shape optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently refined control mesh. During iterative shape optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. This multiresolution approach provides a means for regularising the optimisation problem and prevents the appearance of sub-optimal jagged geometries with fine-scale oscillations. The finest control mesh for optimisation is chosen in accordance with the desired smallest feature size in the optimised geometry. The proposed approach is applied to three optimisation examples, namely a catenary, a roof over a rectangular domain and a freeform architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries is investigated in detail.