Displacement-based methods for calculating the buckling load and tracing the post-buckling regions with Dynamic Relaxation method

This paper prepares new features for applying the Dynamic Relaxation (DR) method in buckling and post-buckling structural analyses. Here, controlling the displacement’s increment is the main concept so that the minimum residual displacement and the minimum kinetic energy criteria are designed for updating the load factor in DR iterations. These new formulations do not affect the DR’s stability and they are successfully applied to both viscous and kinetic DR algorithms. Numerical analyses of structures with snap-through and snap-back behaviors show that the accuracy and the convergence rate of the suggested methods are higher than the well-known existing approaches such as the arc-length technique, especially, if they are combined with the kinetic DR algorithm. Calculating the buckling load is another interesting application of the proposed methods, performed here. In this manner, the suggested DR algorithms could numerically present the accurate buckling load of structures.

► Two new formulations derive for updating the load factor of DR method based on controlling displacement’s increment.
► These formulations combine with both kinetic and viscous algorithms.
► The proposed DR schemes are successfully used for tracing the statical path and calculating the buckling load of structures.