Decaying/conserving implicit scheme and non-linear instability analysis of 2D frame structures

In this work we deal with the geometric instability problem of the two-dimensional elastic frame structures undergoing large overall motion. The geometrically exact beam model with total Lagrangian formulation is used to obtain the solution to non-linear instability problems with large pre-buckling displacements. We have proposed, in particular, the use of the conserving and decaying scheme for dynamic analysis that can deal with instability problems of this kind with no need for structural damping, whereas it is necessary when a classical time integration scheme like Newmark is used. This scheme is an extension of time-integration energy conserving scheme presented in Ibrahimbegovic and Mamouri [1], redesigned to introduce desirable properties of controllable energy decay in higher modes, which improve its stability and accuracy. The efficiency of the proposed scheme in non-linear instability is illustrated by a number of numerical simulations.