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.

Abstract

This work is devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into quadrilateral elements. This automatically generates meshes composed entirely by quadrilaterals over complex geometries (there is no need for a previous step where triangles are generated). A background mesh with the desired element sizes allows to obtain the preferred sizes anywhere in the domain. The final mesh can be viewed as the optimal one given the objective function is defined. The recursive algorithm induces an efficient data structure which optimizes the computer cost. Several examples are presented to show the efficiency of this algorithm.

Abstract

This work devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into quadrilateral over complex geometries (there is not need for a previous step where triangles are generated). A background mesh with the desired element sizes allows to obtain the preferred sizes anywhere in the domain. The final mesh can be viewed as the optimal one given the objective function defined. The recursive algorithm induces an efficient data structure which optimizes the computer cost. Several examples are presents to show the efficiency of this algorithm