Development of a high-order compact finite-difference total Lagrangian method for nonlinear structural dynamic analysis

A high-order compact finite-difference total Lagrangian method (CFDTLM) is developed and applied to nonlinear structural dynamic analysis. The two-dimensional simulation of thermo-elastodynamics is numerically performed in generalized curvilinear coordinates by taking into account the geometric and material nonlinearities. The spatial discretization is carried out by a fourth-order compact finite-difference scheme and an implicit second-order accurate dual time-stepping method is applied for the time integration. The accuracy and capability of the proposed solution methodology for the nonlinear structural analysis is investigated through simulating different static and dynamic benchmark problems including large deformations, large displacements and Hookean/neo-Hookean materials. The solution method is demonstrated to be free of shear-locking behavior. The results obtained by the present solution algorithm are compared with the analytical solution and the numerical results of the finite element and finite volume methods to examine the accuracy and robustness of the solution method proposed. A grid study is also performed to investigate the grid size effect on the accuracy and performance of the solution. Indications are that the solution methodology proposed is accurate for simulating nonlinear structural dynamics problems.