Elimination of slip-locking in composite beam-column analysis by using the element-free Galerkin method

Abstract

In the numerical analysis of composite beam-columns inconsistencies in the shape functions of the transverse and longitudinal displacement fields may cause oscillations in the slip field and reduction in the accuracy of the results known as slip-locking which is typical of multi-field problems of this type. In order to eliminate slip-locking, matching field strategy is adopted herein by using the element free Galerkin method in which shape functions of the longitudinal displacement fields are obtained from the derivatives of shape functions of the transverse displacement fields. Continuous blending method is modified in order to couple element-free Galerkin and finite element methods when the matching field approach is used in the meshfree region. This modification allows for direct assembly of the stiffness matrices that are built for separate finite element and meshfree regions, the boundary conditions can be directly applied and the reaction forces can also be calculated directly from the structural stiffness matrix.