A Local Refinement Technique for B-Spline Finite Element Shell Modeling

This paper presents a refinement technique for a B2-spline degenerate isoparametric shell finite element model for the analysis of the vibrational behavior of thin and moderately thick-walled structures. Complex structures to be refined are modeled by means of FE B-spline patches assembled with C0 continuity as usual in FE technique. The model refinement was performed by adding, on the domain of the selected patch, a tensorial set of polynomial B-spline functions, defined on local clamped knot vectors, and normalizing all the functions so that the resulting displacement field remain polynomial and continuous overall the domain except on the boundaries of the refined subdomain. A degrees of freedom trasformation, based on the knot-insertion algorthim, is adopted in order to guarantee the C0 continuity of the displacement field on the boundaries of the refined subdomain. Two numerical examples are presented in order to test the proposed approach. The natural frequencies of two structures, computed by means of the proposed modelling technique, are compared with reference results available in the literature or computed by means of reference standard FE models. Strengths and limits of the approach are finally discussed.