Premium
An improved formulation of the parabolic isoparametric element for explicit transient analysis
Author(s) -
Donea J.,
Laval H.
Publication year - 1979
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290070103
Subject(s) - galerkin method , method of mean weighted residuals , weighting , mathematics , transient (computer programming) , finite element method , element (criminal law) , field (mathematics) , function (biology) , mathematical analysis , structural engineering , engineering , computer science , physics , pure mathematics , evolutionary biology , acoustics , law , political science , biology , operating system
Abstract The difficulties encountered in the use of standard, Galerkin‐type, parabolic isoparametric elements for explicit transient analysis are illustrated. These are associated with the mass lumping procedure as well as with incoherencies in the nodal loads induced by the element local field. To overcome these difficulties, it is suggested that the parabolic element equations be formulated by a weighted residual method in which the weighting functions are the usual serendipity functions modified by an appropriate bubble‐shape function. It is shown that such a formulation enables all the shortcomings of the Galerkin approach to be overcome. An example problem indicates the extent of improvement in results that can be obtained by the proposed method.