Shear Locking in B-Spline Based Finite Element Formulations
B-spline based finite element formulations (i.e. ) are similar to conventional finite element formulations in that they both are based on the Rayleigh-Ritz procedure and both employ polynomial basis functions that have compact support. The principal difference between the two formulations is that finite elements based on splines have basis functions with the required continuity built in, while the conventional finite element method uses basis functions which must be “assembled” together in a certain way to achieve the required continuity. In this paper we concentrate on the problem of shear locking (see for example, –) and will explain it by considering the size of the effective approximation space in the thin beam limit. We demonstrate the use of this new explanation by formulating a general Timoshenko model where displacement and rotation are discretized using independent B-spline based discretizations. Unlike , we allow discretizations of varying continuity for a given degree, and we allow the displacement and rotation to be interpolated on different domain discretizations. It will be shown that level of continuity as well as the domain discretization can also precipitate shear locking. We will explain this behavior and demonstrate with examples.
KeywordsFinite Element Formulation Spline Space Require Continuity TIMOSHENKO Beam Model Polynomial Basis Function
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