T-splines-based panel method for aerodynamic topology optimization of engineering shell structures using isogeometric analysis

Engineering shell structures have been extensively used in aerospace, automotive and other fields, whose aerodynamic performance is significant in structural design. In the current work, the primary intention is to propose an aerodynamic topology optimization design framework for arbitrary engineering shell structures using the T-splines-based panel method and isogeometric analysis. Firstly, the T-splines-based isogeometric analysis formulation is developed for arbitrary shell structures using Bézier extraction, which can maintain the consistency of geometric model in an accurate representation and numerical model of shells. Secondly, a higher-order panel method is developed for calculating aerodynamic solutions with unidirectional effects using T-splines, where Neumann boundary conditions are imposed using the collocation method. Moreover, the source density distributions of engineering shells are solved numerically with T-spline blending function, and Bézier basis functions are applied to describe the velocity potential distributions, achieving an efficient solution of 3D potential flow problem and ensuring the stability and efficiency of aerodynamic computation. Thirdly, the mathematical formulation is developed for implementing aerodynamic topology optimization designs of engineering shells, in which an efficient T-splines-based topology description model using Bézier elements is developed and the sensitivity analysis is derived in detail. Finally, several engineering thin shells are studied to demonstrate the effectiveness of the proposed aerodynamic topology design framework, and the related numerical results also reveal the optimized shell topologies that perfectly cater for aerodynamic pressure distributions.