Automating the CAD/CAE dimensional reduction process

Dimensional reduction is a simplification technique that eliminates one or more dimensions from a boundary value problem. It results in significant computational savings with minimal loss in accuracy. Existing dimensional reduction methods rely on a lower-dimensional geometric entity called the mid-element that is unfortunately ill defined for irregular thin solids.The main objective of this paper is to propose a new theory of 'skeletal dimensional reduction' that is superior to existing mid-element based methods in that it unambiguous and can be easily automated. The proposed method is based on a popular skeletal representation of geometry that is well defined for all thin solids. By exploiting the unique properties of a skeletal representation it is shown how boundary value problems, specifically 2-D Laplacian problems, over complex 'beam-like' solids can be systematically reduced to lower-dimensional problems over the skeleton. Further, in the special case of a regular thin solid, the skeletal reduction simplifies, as expected, into a mid-element based dimensional reduction.