Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces

TL;DR

This paper presents a multiresolution isogeometric shape optimisation method for thin shell structures using subdivision surfaces, enabling regularised, smooth, and optimally stiff geometries through a progressive refinement process.

Contribution

It introduces a multiresolution subdivision surface approach for shape optimisation of shells, combining geometry modelling, analysis, and optimisation in a unified framework.

Findings

Multiresolution approach prevents jagged geometries.

Optimisation results depend on subdivision scheme and control mesh.

Method successfully applied to architectural shell examples.

Abstract

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.