An object-oriented framework for finite element programming

Abstract

This work describes an ongoing effort, initiated in early 1990s, in the development of a finite element analysis system, called FEMOOP, based on the object-oriented programming (OOP) paradigm. The overall class organization of the program will be presented and the main features will be thoroughly discussed. One important feature is the capability of treating multi-dimension finite element models in the same object oriented, generic fashion. This is accomplished through the definition of two OOP classes: Analysis Model and Shape. The former is responsible for handling the specific aspects related to the differential equation that governs the element behavior, while the latter deals with the geometric and field interpolation aspects of the element. Another interesting feature of FEMOOP is the generic handling of natural boundary conditions. This is implemented through the automatic creation of fictitious elements responsible for translating these boundary conditions into nodal coefficients of the solution matrices and forcing vectors. These elements are instances (objects) of a class called Load Element. At the global level, another class (Control) is responsible for the implementation of the algorithm that controls the analysis of the problem, from which a derived class, called Equilibrium Path, handles the ifferent path-followingmethods implemented in the program.