Hierarchical shape optimization for complex shell structures considering global and local shape perturbations
Published in Struct. Multidiscip. Optim., 2025
Shell structures effectively resist external loads due to their characteristic geometric shapes. Shape optimization can further enhance the mechanical performance of shell structures while preserving structural topology. This paper proposes a novel shape design concept based on the hierarchical shape representation. We use a NURBS network to control the global surface geometry and explicit spline components to capture local geometric features. The hierarchical representation enables coordinated control of both global shape and local details using a small number of design variables, thereby reducing the computational burden of the optimization problem. During the optimization process, the hierarchical shape variations are implemented by applying global and local perturbations to the discrete triangular mesh of the shell surface. By employing the computational conformal mapping technique, we obtain the parametric domain of the initial model, in which the hierarchical perturbations are constructed. The surface cutting operation and the multi-patch stitching scheme are employed to preprocess the geometry for extension to complex shell structures. Numerical examples are provided to validate the effectiveness, efficiency, and generality of the proposed hierarchical shape design method for complex shell structures.