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Object-Oriented Mathematical Modelling--Applied to Machine Elements

D. Fritzson
Peter Fritzson
Organization: MathCore Engineering AB
L. Viklund
J. Herber
Journal / Anthology

Computers & Structures
Year: 1994
Volume: 51
Issue: 3
Page range: 241-253

Machine element analysis has a goal of describing function and other aspects of machine elements in a theoretical form. This paper shows how ideas from object-oriented modeling can be applied to machine element analysis. The models thus obtained are both easier to understand, better structured, and allow a higher degree of re-use than conventional models. An object-oriented model description is natural and suitable for machine element analysis. As a realistic example an equational model of rolling bearings is presented. The structure of the model is general, and applies to many types of rolling bearings. The model and one solution require approximately 200+200 equations. The model is extensible, e.g. simple submodels of detailed properties can be made more complex without altering the overall structure. The example model has been implemented in a language of our own design, ObjectMath (Object-oriented Mahematical language for scientific computing). Using ObjectMath, it is possible to model classes of equation objects, to support multiple and single inheritance of equations, to support composition of equations, and to solve systems of equations. Algebraic transformations can conveniently be done 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 re-use of equations through inheritance reduced the size of the model by a factor of two, compared to a direct representation of the model in the Mathematica computer algebra language.

*Engineering > Mechanical and Structural Engineering