In-plane nonlinear postbuckling and buckling analysis of Lee's frame using absolute nodal coordinate formulation

In this study, four absolute nodal coordinate formulation (ANCF)-based approaches are utilized in order to predict the buckling load of Lee's frame under concentrated load. The first approach employs the standard two-dimensional shear deformable ANCF beam element based on the general continuum mechanics (GCM). The second approach adopts the standard ANCF beam element modified by the locking alleviation technique known as the strain-split method. The third approach has the standard ANCF beam element with strain energy modified by the enhanced continuum mechanics formulation. The fourth approach utilizes the higher-order ANCF beam element based on the GCM. Two buckling load estimation methods are used, i.e., by tracing the nonlinear equilibrium path of the load-displacement space using the arc-length method and applying the energy criterion, which requires tracking eigenvalues through the dichotomy scheme. Lee's frame with different boundary conditions including pinned-pinned, fixed-pinned, pinned-fixed, and fixed-fixed are studied. The complex nonlinear responses in the form of snap-through, snap-back, and looping phenomena during nonlinear postbuckling analysis are simulated. The critical buckling loads and buckling mode shapes obtained through the energy criterion-based buckling method are obtained. After the comparison, higher-order beam element is found to be more accurate, stable, and consistent among the studied approaches.