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A rational approach to mass matrix diagonalization in two‐dimensional elastodynamics
Author(s) -
Paraskevopoulos E. A.,
Talaslidis D. G.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1176
Subject(s) - piecewise , mathematics , constant (computer programming) , mass matrix , diagonal , quadrilateral , rank (graph theory) , mathematical analysis , matrix (chemical analysis) , stability (learning theory) , finite element method , geometry , physics , computer science , materials science , combinatorics , machine learning , nuclear physics , neutrino , composite material , thermodynamics , programming language
A variationally consistent methodology is presented, which yields diagonal mass matrices in two‐dimensional 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. Copyright © 2004 John Wiley & Sons, Ltd.