A rational approach to mass matrix diagonalization in two-dimensional elastodynamics

A variationally consistent methodology is presented, which yields diagonal mass matrices in twodimensional elastodynamic problems. The proposed approach avoids ad hoc procedures and applies to arbitrary quadrilateral and triangular finite elements. As a starting point, a modified variational principle in elastodynamics is used. The time derivatives of displacements, the velocities, and the momentum type variables are assumed as independent variables and are approximated using piecewise linear or constant functions and combinations of piecewise constant polynomials and Dirac distributions. It is proved that the proposed methodology ensures consistency and stability