On Representation and Discretization of Finite Element Analyses

The use of B-spline geometric representation and subdivision mechanism is explored for use in finite element analysis. On the representation issue, an attribute modelling technique is introduced to model the problem specification and the result interpretation. This modelling technique relies on the true representation of the domain geometry such that all the problem parameters are associated with the geometry as nongeometric attributes. It allows the user to specify a problem domain independent of the choices of mesh configuration. The analysis results are also treated as associated attributes and are blended into the original domain geometry, e.g., shape deformation and energy distribution are simulated by rendering color pictures. On the discretization issue, an adaptive algorithm is designed to generate near-optimum meshes. This algorithm synthesizes the result distribution from the previous analysis run with the domain geometry by using the former as heuristics to subdivide the latter into element geometry. The subdivided geometry reflects the grading of the result such that near-optimum results can be obtained from the synthesized mesh, i.e., smaller (and more) elements are populated in more critical areas. The algorithm is self-adaptive and requires minimum user input. An experimental implementation includes linkages between a geometric modeller and an analysis code such that a closed engineering cycle is formed. Example structural analyses are performed for planar domains, three dimensional shell domains and three-dimensional solid domains.