Isogeometric double-objective shape optimization of free-form surface structures with Kirchhoff–Love shell theory

Abstract

Free-form surface structures are extensively utilized in practical engineering due to their rich architectural expression and strong visual impact. However, ensuring good mechanical behavior during the generation process of free-form surface structures has become a critical problem in the scientific community. Isogeometric analysis (IGA) is a widely adopted approach in various fields owing to its numerous advantages, such as geometric accuracy, high-order continuity, high precision, without traditional meshing, and ease of integration with CAD. The presented work adopts the NURBS surfaces to create geometric models, and developes an isogeometric discretization for free-form surfaces by formulating a shell analysis method based on Kirchhoff–Love hypothesis. The structural strain energy and the first natural frequency of the free-form surfaces are selected as the static and dynamic performance evaluation indices. The optimization objectives are to minimize the structural strain energy and maximize the first natural frequency, with the control point coordinates considered as the optimization variable. The double-objective shape optimization of the free-form surface structure is carried out using the particle swarm optimization technique. The effectiveness and performance of the proposed method are verified through five numerical examples, and the mechanical properties of the optimized structure are substantially improved.