B-spline finite element method in one-dimensional elastic wave propagation problems

Abstract eng:
In this paper, the spline variant of finite element method (FEM) is tested in one-dimensional elastic wave propagation problems. The special attention is paid to propagation of stress discontinuities as an outcome of the shock loading and also to spurious oscillations occurring near theoretical wavefronts. Spline variant of FEM is a modern strategy for numerical solution of partial differential equations. This method is based on spline basic functions as shape, testing functions in FEM content. For examples, B-splines, T-splines, NURBS and more others could be applied. For one-dimensional problems, B-spline representation is sufficient. B-spline basis functions are piecewise polynomial functions. It was shown, that B-spline shape functions produce outstanding convergence and dispersion properties and also appropriate frequency errors in elastodynamics problems. In this initial work, accuracy, convergence and stability of the B-spline based FEM are studied in numerical modelling of one-dimensional elastic wave propagation of stress discontinuities. For the time integration, the Newmark method, the central difference method and the generalized-α method are employed.

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