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Consistent diagonal mass matrices and finite element equations for one-dimensional problems

✍ Scribed by Howard L. Schreyer

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
703 KB
Volume
12
Category
Article
ISSN
0029-5981

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✦ Synopsis

Abstract

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.

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