A triangular grid method is presented to calculate propagation problems of elastic stress waves in 2-D orthotropic materials. This method is based on the dynamic equilibrium equations of the computational cells formed among the auxiliary triangular grids. The solution is obtained by calculating alternately the nodal displacements and the central point stresses of the spatial grids. The numerical results are compared with the corresponding solutions of the finite element method. Comparisons show that the triangular grid method yields a higher calculational speed than the finite element method. The stress concentrations are investigated from wave-field analyses when the stress wave propagates within an orthotropic plate with a hole. Finally, the presented numerical method is used to study the features of wave propagation and diffraction in a square orthotropic plate with a hole when an impact load is applied to the top of the plate. IntroductionIt is well known that the methods for numerically simulating propagation problems of elastic stress waves are generally classified into finite element [1, 2], finite difference [3, 4] and boundary element methods [5]. The grid method [6, 7] provides a new approach for stress-wave propagation in elastic material with simple programming. This method incorporates the advantages of the finite element and finite difference methods and is similar to the finite element method in the discretization of a numerical mesh, and to the staggered grid difference scheme [8] in computation. Thus, there are no requirements for calculating and storing the stiffness matrix, so computational cost and memory requirements are small. The numerical results indicate that the grid method is an accurate and efficient numerical method for analyzing wave propagation problems.In this paper, we aim to develop an accurate, efficient and versatile numerical scheme for analyzing stress-wave propagation in orthotropic materials due to an impact load. We extend the grid method for modeling elastic stress-wave propagation in 2-D orthotropic materials. The angle , defined between the x axis of the global coordinates and the principal direction of an orthotropic material, can have any value. The algorithm formulation based on the triangular grids is discussed in detail. Numerical simulations are performed for the stress-wave