Shape control optimization of complex inflatable membrane structures based on position-based dynamics with application to ice shells

The large-span ice shell is a novel structural form that utilizes inflatable membrane formwork and water-spraying construction methods, making its shape and functionality more practical and innovative. The design of the inflatable formwork is crucial for the construction of ice shell, and it is a reverse design aiming to achieve “shape matching” with the design scheme firstly, and the mechanical performance only needs to satisfy the construction loads. The most form-finding methods were difficult to meet the rapid analysis of complex shapes, and primarily focused on the reasonable stress distribution, resulting in significant shape deviations. Therefore, a shape control method for complex modeling inflatable formwork that focused on “construction forming accuracy” and combined “mechanical feasibility” was proposed in this study. Firstly, an optimization model for controlling the shape of the inflatable formwork was established. The objective function was defined as the shape deviation between the ice shell design scheme and the inflatable membrane formwork, and optimized by dynamic weighting factors. The elastic modulus was set as the optimization variable, and a smooth kernel function was employed to reduce the number of optimization variables to achieve smooth continuous control of the membrane surface. Meanwhile, the form-finding method based on Position-based dynamics was established to achieve real-time inflatable simulation, greatly improving computational accuracy and convergence efficiency. Finally, through typical cases, it was demonstrated that the method can reduce shape deviations to 1/10 of those achieved by traditional methods, while improving computational efficiency by about ten times. This validated the effectiveness and superiority of the proposed method. This study can improve the efficiency of shape control of inflatable membrane, and greatly promote the engineering application of ice shells and membrane structures.