Predicting and avoiding shear locking in beam vibration problems using the B-spline field approximation method Original Research Article

The B-spline field approximation method is used to construct discrete models of straight Timoshenko beams. The traditional Timoshenko beam discretization treats deflection and rotation as the independent field variables and permits the use of C0 discretizations, but can sometimes exhibit unwanted shear locking behaviour. In this paper a new explanation of shear locking is presented and is used in selecting a variety of B-spline interpolation fields that can be predicted not to suffer from shear locking. It is also exploited in an adaptation of a Timoshenko model where deflection and shear strain are independently discretized field variables. This requires a C1 discretization of the deflection, but avoids shear locking in every case, and allows for a more economical solution than previous implementations of this formulation. As a means of illustrating the performance characteristics of the formulation presented in the paper the vibration characteristics of these models are compared with traditional finite element models; for this problem the B-spline method outperforms the finite element method and has the advantage of an easy predictability of the locking behaviour that can be expected.