Stability analysis of plane serendipity finite element for explicit linear elastodynamics

Abstract eng:
The central difference method is widely used for the numerical solution of the transient elastodynamics problems by the finite element method. The effectiveness of this explicit conditional stable direct time integration methods is limited by using diagonal mass matrix, which entails significant computational savings and storage advantages. However, for the serendipity type element the construction of such diagonalized matrices is not uniquely defined and various class of lumped mass matrices can be assembled. In this paper the stability analysis for the plane square serendipity finite element is performed for various class of lumped mass matrices. ´

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