Treatment of slip locking for displacement-based finite element analysis of composite beam-columns

摘要

In the conventional displacement-based finite element analysis of composite beam-columns that consist of two Euler-Bernoulli beams juxtaposed with a deformable shear connection, the coupling of the transverse and longitudinal displacement fields may cause oscillations in slip field and reduction in optimal convergence rate, known as slip locking. This locking phenomenon is typical of multi-field problems of this type, and is known to produce erroneous results for the displacement-based finite element analysis of composite beam-columns based on cubic transverse and linear longitudinal interpolation fields. This paper introduces strategies including the assumed strain method, discrete strain gap method, and kinematic interpolatory technique to alleviate the oscillations in slip and curvature, and improve the convergence performance of the displacement-based finite element analysis of composite beam-columns. A systematic solution of the differential equations of equilibrium is also provided, and a superconvergent element is developed in this paper. Numerical results presented illustrate the accuracy of the proposed modifications. The solutions based on the superconvergent element provide benchmark results for the performance of these proposed formulations.