Generalization of Strain Split Method for Locking Alleviation of Initially Curved Structures

This thesis discusses the generalization of the strain-split method (SSM) for the locking alleviation of curved structures. The generalization is achieved by using proper definitions of the stress and strain tensors along the curved-coordinate lines using the matrix of position vector gradients in the reference configuration. This matrix, which accurately captures the element geometry at the integration points, allows using consistent gradient transformation in the calculation of the stress and strain tensors. The generalized SSM implementation is used to develop benchmark problems for verifying the results and evaluating the performance of the absolute nodal coordinate formulation (ANCF) finite elements (FE). The focus of this study is on the Poisson locking that characterizes fully parameterized ANCF elements that employ different orders of interpolation in different directions. ANCF benchmark beam and plate problems are presented, and the obtained simulation results are compared with analytical solution as well as results obtained using commercial FE computer programs. These results are also compared with the results obtained using straight and curved ANCF beam and plate elements with no locking alleviation method in order to demonstrate the SSM effectiveness in alleviating the Poisson locking. It is shown that a much smaller number of ANCF elements is required to achieve approximately 0.9% difference from the results obtained using commercial FE computer programs.