Simulation of two-dimensional elastodynamic problems using a new adaptive physics-based method

In this paper, an adaptive physics-based method is developed for solving wave motion problems in two dimensions (i.e., lamb waves). The solution of the problem has two main parts. In the first part, after discretization of the domain, a physics-based method is developed considering the conservation of mass and the balance of momentum. In the second part, adaptive points are determined using wavelet theory. This part is well done using Deslauries–Dubuc (D–D) like wavelets. After solving the problem in the first step, the domain of the problem is discretized by the same cells attending loading and characteristics of the structure. After the first trial solution, the D–D interpolation shows the lack and redundancy of points in the domain. These points will be added or eliminated for the next solution. This process may be repeated for achieving adaptive mesh for each step. Finally, the results of the proposed method are compared with the results available in the literature. This comparison shows excellent agreement between the obtained results and those already reported.