Comparative study of finite element method, isogeometric analysis, and finite volume method in elastic wave propagation of stress discontinuities

摘要

We present a comparison of Finite Element Method, Isogeometric Analysis, and Finite Volume Method in numerical simulation of one-dimensional elastic wave propagation problems with stress discontinuities. The special attention is paid to accuracy of tested numerical methods and the appearance of spurious oscillations and dissipation effects occurring close to theoretical sharp wavefronts. FEM and FVM are widely accepted as numerical methods used for numerical solution of hyperbolic (wave-like) problems. IGA, the spline variant of FEM, is a modern strategy for numerical solution of partial differential equations. This method is based on splines as shape functions in FEM content. In IGA and FEM, the Newmark method, the central difference method, the generalized-α method and the Park method are employed as time integrators. All the tested numerical strategies are applied for elastic wave propagation in a bar. At the end, main advantages and disadvantages of the numerical methods in wave propagation are summed up.