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Consistent diagonal mass matrices and finite element equations for one‐dimensional problems
Author(s) -
Schreyer Howard L.
Publication year - 1978
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.1620120708
Subject(s) - diagonal , finite element method , discretization , bernoulli's principle , mass matrix , mathematics , mathematical analysis , euler's formula , backward euler method , extended finite element method , base (topology) , mixed finite element method , geometry , physics , nuclear physics , neutrino , thermodynamics
The conventional dynamic variational approach and finite element base functions lead to non‐diagonal consistent mass matrics which are inappropriate for use with an explicit time integration scheme. In this work, it is shown that if orthogonal base function are used with a mixed variational formulation, then consistant diagonal mass matrices and corresponding sets of spatially discretized field equations are obtained. Although the approach is quite general, the theory is purposely illustrated by a detailed development for one set of base functions. Central difference time integration is incorporated for applications to one‐dimensional wave propagation and to Euler‐Bernoulli beams. Numerical examples are provided for elastic and elastic‐plastic materials.