A physics-based fast algorithm for structural responses of generalized rotationally axisymmetric structures: the generalized rotation-superposition method



Fast calculations are required not only in the traditional applications such as sensitivity analysis, optimization design, reliability assessment, and uncertainty quantification, but also imminently in the emerging digital twin technology. The three categories of structural analysis methods, analytical methods, numerical simulations, and surrogate models, are playing different roles in engineering and scientific applications due to their different features. A great number of researches illustrated that combinations of numerical simulations and surrogate models can make the best use of the advantages and bypass the disadvantages, significantly obtaining the balance between precision and efficiency. However, due to the inefficiency of complex structural computations, the conflict between the amount of data requirements and the feeding capacity of numerical simulations sometimes arises. At this point, there is a greater development potential in helping numerical simulations to improve data supplying efficiencies, and then improve the final precisions by supplying more sufficient data for regression or training. This study just aims at this growth point and focuses on a novel physics-based fast method as an enhancer for data supplying from numerical simulations to surrogate models. The fast algorithm, namely generalized rotation-superposition method, is proposed for fast calculating linear elastic responses of generalized rotationally axisymmetric structures under arbitrary mechanical loads. This method breaks through the limitations of the previous basic rotation-superposition method in rotational similarity of load and structural axisymmetry, and greatly expands its application scope. This paper firstly introduces the basic theory of the rotation-superposition algorithm, establishes the theoretical model of the generalized rotation-superposition method, and verifies the effectiveness and accuracy using finite element simulations. Then, through a complex case study, the applicability of the generalized rotation-superposition method for complex engineering problems and its advantages in efficiently obtaining massive amounts of data are further illustrated. This proposed method can build a bridge between numerical simulations and surrogate models, further improving the computational efficiencies and precisions for a specific class of structural response problems in both traditional applications and emerging digital twin applications.