Optimization of lumping schemes for plane square quadratic finite element in elastodynamics

Abstract

The effectiveness of explicit direct time-integration methods is conditioned by using diagonal mass matrix which entails significant computational savings and storage advantages. In recent years many procedures that produced diagonally lumped mass matrices were developed. For example, the row sum method and diagonal scaling method (HRZ procedure) can be mentioned. In this paper, the dispersive properties of different lumping matrices with variable mass distribution for the plane square 8-node serendipity elements are investigated. The dispersion diagrams for such lumping matrices are derived for various Courant numbers, wavelengths and the directions of wave propagation.

Keywords

• Wave propagation
• Dispersion analysis
• Serendipity finite elements
• Lumped mass matrix