A template tutorial: panels, families, clones, winners and losers

Abstract

The article has a dual historical and educational theme. It is a tutorial on finite elements templates for two-dimensional structural problems. The exposition focused on the four-node plane stress element of flat rectangular geometry, called here the “rectangular panel” for brevity. This is one of two oldest two-dimensional structural elements, soon to reach its gold anniversary. On the other hand, the concept of finite element templates is a recent development. Interweaving the old and the new throws historical perspective into the “golden age” of discovery of finite elements. Templates provide a framework in which diverse element development methods can be fitted, compared and traced back to the sources. On the technical side templates have the virtue of facilitating the unified implementation of back to the sources. On the technical side templates have the virtue of facilitating the unified implementation of element families as well as the construction of custom elements. As an illustration of customization power, the Appendix presents the construction of a four noded bending optimal trapezoid that has eluded FEM investigators for several decades.