A dynamic finite element preanalyser

In a mixed‐mode dynamic crack propagation problem using remeshing, certain elements in the neighbour‐hood of the propagating crack‐tips may have dimensions that do not comform to the allowable limit. Hence, they need to be refined by recursively bisecting the exclusive sides until a global conformity is achieved. ADFEP (a dynamic finite element preanalyser) has been written for this purpose. Apart from this objective, ADFEP has a wide spectrum of salient applications to various discretization related problems, such as automatic irregular generation, adaptive refinement and others. A simple energy criterion to determine the cut‐off frequency of a transient loading, and the concept of preprocessing the input loading using digital filters introduced by Valliappan and Murti 1 are employed. They constitute the first module of ADFEP. The second (main) module consists of element splitting procedures where algorithms based on graph theory and element splitting templates have been extensively used. The notion of a ‘cross digraph’ introduced to carry a multiple ‘weights’ and to avoid duplication in node‐generation, is especially useful in three‐dimensional element splitting techniques. Finally, numerical inverse isoparametric mapping techniques presented by Murti and Valliappan 2 are also used to interpolate the nodal quantity vectors at the newly generated nodes. These vectors are needed as initial values in subsequent iterations for a dynamic restart. This aspect, together with the node renumbering scheme, is included in the third module of ADFEP. Some illustrative examples are included to elucidate the effectiveness of ADFEP.