Unstructured grid method for stress wave propagation in elastic media Original Research Article

A new numerical method, named unstructured grid method, is presented to calculate two-dimensional stress wave propagation problems in elastic media. This method is based on the dynamic equilibrium equations of the investigated lumps that are formed among the auxiliary unstructured grids. The approach to the solution is obtained by calculating the node displacements and the central point stresses of the spatial grids alternately. The stability criterion of the method is given and tested numerically. Analysis of dispersion for numerical phase velocity is studied. The rule is provided to determine the spatial step size of discretization mesh so as to ensure the numerical accuracy of the unstructured grid method. Numerical results are compared with the available exact solutions and with the solutions of central difference method for demonstrating the good accuracy of the new method. The unstructured grid method possesses higher calculating speed than the central difference method. Finally, the dynamic behavior of a square plate with a hole under an impact loading is researched.