Computationally efficient reduction of modal data from finite element models by nested sets of B-splines

This paper introduces a novel methodology for the reduction of modal data from complex finite element (FE) models, resulting in a highly accurate and computationally efficient model termed B-SAFE (B-spline-based Semi-Analytical Finite Element model). It is conceptually similar to a method based on nested sets of polynomials proposed earlier by the authors (Poly-SAFE) but provides greater accuracy in the case of complex structures and greater ease of use, limiting the need for user interventions and facilitating automated processing. B-SAFE is constructed via the reduction of a standard displacement-based FE model down to a semi-analytical function built from nested B-splines recursively fitted to modal data, which eliminates the need of high-order polynomials and heavy user-intervention required by Poly-SAFE for the case of complex modal patterns. The present work describes the non-trivial modifications to the original methodology, and shows how fewer and more efficient semi-analytical functions representing field variables such as displacement, strain and stress can be obtained. The new method is exemplified through a numerical case study of a 9.2. m composite wind turbine blade, showing that improved numerical stability and robustness as well as a systematic handling of general geometries can be obtained without user intervention.