Locking and shear scaling factors in C° bending elements

Two types of locking are identified in linear field C° elements: locking caused by shear resistance in constant curvature deformation and in linear curvature deformation, respectively. Locking of the first type can be ameliorated by decoupling constant curvature bending from shear, which in some elements can be achieved by selective reduced integration. Once the modes are decoupled, a scaling factor on the shear stiffness can be used to alleviate the second type of locking. These findings are explained in terms of a linear displacement, linear rotation beam element and applied to the improvement of a triangular plate element. It is shown that the resulting triangular plate element is free from locking and performs excellently in a wide variety of problems.