A linear thick curved beam element

Abstract

Early attempts to derive curved beam and shell elements in a curvilinear system were dramatically unsuccessful. This was wrongly attributed to the failure of these elements to recover strain-free rigid body displacement modes in a curvilinear co-ordinate description. Recent evidence points to a 'membrane locking' phenomenon that arises when constrained strain fields corresponding to inextensional bending are not 'consistently' recovered. This accounts for, more completely and precisely, the failure of such elements. In this paper, a simple linear two-noded C⁰ continuous thick curved beam element based on a curvilinear deep shell theory is derived free from shear and membrane locking. Lack of consistency in the shear and membrane strain-field interpolations in their constrained physical limits (Kirchhoff and inextensional bending limits, respectively) causes very poor convergence due to locking and severe spurious oscillations in stress predictions. Error estimates for these are made and verified. Field-consistent strain interpolations remove these errors and produce the most efficient linear element possible.