An improved formulation of the parabolic isoparametric element for explicit transient analysis

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.