A new hybrid computational framework and validations for handling steady-state problems with contact boundaries

A hybrid computational framework consisting of Eulerian boundary zone concept augmented to Lagrangian finite element formulations with moving meshes is proposed for effectively handling the steady-state problems. This is in conjunction with a novel L-stable time discretized framework that is necessary in conjunction with the hybrid formulations to enable computationally attractive features for practical problems. The L-stable algorithm is developed and implemented and is of second order accuracy and modified for nonlinear dynamic systems with frictional contact boundaries. No nonlinear iterations are necessary for the non-linear dynamic system of equations, and one only needs to update the artificial damping matrix once at every time step for non-linear dynamic problems. The proposed method is suitable for steady state problems with complex contact boundary conditions.