Numerical simulation of structural dynamics using a high-order compact finite-difference scheme

A high-order compact finite-difference scheme is applied and assessed for the numerical simulation of structural dynamics. The two-dimensional elastic stress-strain equations are considered in the generalized curvilinear coordinates and the spatial derivatives in the resulting equations are discretized by a fourth-order compact finite-difference scheme. For the time integration, an implicit second-order dual time-stepping method is utilized in which a fourth-order Runge-Kutta scheme is used to integrate in the pseudo-time level. The accuracy and robustness of the solution procedure proposed are investigated through simulating different two-dimensional benchmark test cases in structural dynamics. A sensitivity study is also performed to examine the effect of the grid size on the accuracy and performance of the solution. The numerical results obtained by implementing the high-order compact finite-difference scheme are compared with the analytical solutions as well as the available numerical results which exhibit good agreement. The present work represents the first known implementation of the high-order compact finite-difference scheme in computational structural dynamics and that the solution methodology proposed is robust, accurate and efficient for such simulations. Note that the numerical solution procedure proposed to achieve high accurate results is simpler than the high-order finite-volume and finite-element formulations. The results obtained by applying the high-order compact finite-difference scheme can be considered as benchmark solutions for the assessment of the accuracy of other numerical methods applied for the simulation of structural dynamics problems.