Object-oriented finite elements I. Principles of symbolic derivations and automatic programming Original Research Article

The development of a numerical finite element model for a given initial-boundary-value problem goes essentially through the derivation of a weak form, its discretization and finally the derivation of the matrix forms. These steps can, to a large extent, be automated, except for the ones which require intelligence or some form of decision making from the developer. The article outlines the essential steps of an interactive quasi-automatic approach and illustrates it in the example of a linear uniaxial bar formulation for dynamics. The implementation is done in SmalltalkV. A detailed description of the proposed environment is described in a companion article.