Modeling of solids for three-dimensional finite element analysis

The geometric modeling of solid objects is a major problem within the design analysis loop of the engineering design process. Models are analyzed by various computer programs to predict their performance. The format of each model is usually different for each analysis routine. The existence of several versions of model, each of which may be independently modified, results in severe inconsistencies. The solution to this problem is to model the object at a higher level of abstraction. All other models are derived from the one high level model and all modifications are made to this model. The proposed form of the high level model is an extension of the parametric representation used for work with curves and surfaces. Representations of bivariate forms are extended to schemes for trivariate forms. The analysis of interest to this work has been the finite element method. The formulation of the finite element method was investigated to provide a geometric criterion for evaluation of the model for analysis. A new technique has been developed for deriving improved analysis models from the trivariate representation. Computer programs have been implemented to demonstrate these ideas and four examples are included.