Industrial Application of Object-Oriented Mathematical Modeling and Computer Algebra in Mechanical Analysis

In this paper, we present the first programming environment and modeling language which integrates inheritance within a computer algebra language. This environment and language, called ObjectMath (Object oriented Mathematical language for scientific computing), is currently being used for industrial applications in advanced mechanical analysis, but is generally applicable to other areas. Using ObjectMath, it is possible to model classes of equation objects, to support inheritance of equations, and to solve systems of equations. The ObjectMath environment is designed to handle realistic problems. This is achieved by allowing the user to specify transformations and simplifications of formulae in the model, in order to arrive at a representation which is efficiently solvable. Such algebraic transformations can conveniently be supported since ObjectMath models are translated into the Mathematica computer algebra language. When necessary, equations can be transformed to C++ code for efficient numerical solution. The motivation for this work is the current low-level state of the art in programming for scientific computing. Much numerical software is still being developed the traditional way in FORTRAN. This is especially true in application areas such as machine elements analysis, where complex non-linear problems are standard. We also report some experience from successful use of a prototype version of ObjectMath in representing and solving a 3-dimensional example model of 200 equations describing a rolling bearing. The re-use of equations through inheritance reduced the model by a factor of two, compared to a direct representation of the model in the Mathematica computer algebra language.