APPLICATION OF SPECTRAL FINITE ELEMENT METHOD IN ANALYSIS OF TRANSIENT ELASTODYNAMIC PROBLEMS

Dealing with wave propagation phenomena using classical finite element method (FEM) results in some inefficiencies and inaccuracies in the solution. Spectral finite element method (SFEM) as a method based on FEM, presents some new features that makes it much more suitable and useful for solving wave propagation problems. The excellent characteristic of SFEM is that the mass matrix is diagonal because of the choice of the Lagrange interpolation function supported on Legendre-Gauss-Lobatto (LGL) points in conjunction with LGL integration rule. Therefore numerical calculations can be significantly efficient in comparison with the classical FEM. On the other hand choice of high order elements using specific shape functions gives us the possibility to increase the accuracy of the solution while decreasing the total number of elements used for the domain of the problem thus decreasing the analysis time. In this paper, a SFEM-based code is represented and verified, and then some wave propagation problems in elastic solid domains are solved using this code showing the capabilities of SFEM in solving elastodynamic problems. Some problems are solved using different spectral elements, and analysis time, accuracy of the solution and costs of analysis in different solutions is compared to analytical and/or numerical solutions available in the literature.

Keywords:

Spectral finite element method , finite element method , elastodynamics , dynamic analysis