Application of an automatic refinement technique for B2-spline finite element modeling of thin-walled mechanical components

This paper presents a technique for the automatic refinement of a B-spline degenerate shell finite element model for the vibration analysis of curved thin and moderately thick walled structures. A B2-spline finite element shell is defined as a generalization of the B-spline shell element. The proposed element makes it possible the finite element solution on a subdomain inside a selected element to be locally refined without affecting the discretization of the connected elements. A degrees of freedom constraint condition is imposed so that the C0 continuity of the displacement field is restored on the boundaries of the refined subdomains. The choice of the elements to be refined, the position and the extension of the refining subdomains are carried out automatically by means of an iterative procedure. The adaptive technique adopts a pointwise error functional based on the system total potential energy density and a two-step process. The subdomains to be refined are identified by means of the functional value. The number of shape functions on a subdomain is iteratively increased until the difference of the total potential energy, calculated between two consecutive iterations, is below a user defined tolerance. A numerical example is presented in order to test the proposed approach. Strengths and limits of the approach are critically discussed