The CAD FEM Gap
Finite Element Analysis uses a shape representation of structures of Finite Elements. In 3D space, each element is a trivariate (volumetric) parametric polynomial. The polynomials most often are of degree two or lower, but higher order elements are also used. The shape is normally represented with few details. Exact continuity between elements is required.
CAD uses boundary structures to representation a solid., i.e. the inner of a volume does not have an explicit representation. The boundaries are represented as surface sets where each surface is a NURBS surface, an elementary surface like plane, cylinder or torii, or a trimmed version thereof. The shape is designed for production, therefore all details are included in the representation. On the other hand, the concept of trimming leads to gaps and overlaps in the model. Trimming was introduced into the representation to achieve a shape flexibility not covered by tensor product NURBS surfaces as these surfaces are inheritely four sided.
Volumetric CAD became industrial in the 1990s while Finite element analysis was well established in 1970. This implies that the shape representation in FEA was already set when CAD solid models were introduced while the FEA shape representation is not sufficient for design for production.
A CAD model is not designed with numeric analysis in mind, but analysis is still a part of the production process. To facilitate numerical analysis, the CAD model is remodelled, or meshed, to be represented in the format of FEA. This is done by approximating the outer boundary of the CAD solid by triangular or quadrilateral lower order polynomials. This process often leads to a crude approximation of the initial shape. Moreover, a shape simplification is normally applied to remove the details irrelevant to the analysis. Based on this surface mesh, the volume is filled with tetrahedral or hexahedral elements.
The process described above is cumbersome and a real bottleneck in the numerical analysis process. Furthermore, the shape approximation may be critical. It can falsify the analysis result, it makes shape optimization very complicated, and leads to inconsistencies in fluid structure interaction.