Explanation and elimination of shear locking and membrane locking with field consistence approach Original Research Article

In this paper, in the context of beam elements, shear locking and membrane locking are explained and cured in a unified way with a field consistence approach. In the view of field consistence approach, when transverse displacements are coupled with section rotations in Euler-Lagrangian equations and low order interpolations are adopted,shear locking will occur. Similarly, when in-plane displacements are coupled with section rotations in Euler-Lagrangian equations and low order interpolations are used, membrane locking will happen. The beam elements derived by field consistence approach are not only free of shear locking and membrane locking but also highly efficient, compared with their isoparametric counterparts. Although theoretically the internal forces/generalized strains in mixed variational principles can vary independently, they are neither independent to each other nor independent of displacement fields from the point of view of the field consistence approach.