1. Manuals cited in the Referencesection). Once the basis vectors are generated automatically, engineering team must decide on the optimization problem formulation. Currently, the process for static, durability, and noise, vibration, and harshness (NVH) constraints has been validated. Other more complicated responses may also be included in the optimization problem, assuming efficient procedures exist to support gradient analysis of the specific responses. The FE and shape optimization models constitute the input to the structural optimizer (Bremicker et al., 1992). The optimizer generates a final design that represents alocal optimum amongalllinear combinations of the shape variables defined in the shape design model.
2. The following steps must be followed to generate the basis vectors when defining polynomial shape variables: 1) generate a domain model that consists of a number of domain elements each ofwhich encompasses FE grids and elements, 2) generate the node sets associated with the domain model, and 3) generate perturbation vectors of the domain nodes. A secondary domain model may be required for special cases involving onedimensional elements; the reader is encouraged to consult the reference by Altair (1994) for these cases.
3. Once these steps are completed, the actual basis vector generation can resume. This process links the perturbation vectors of the FE grids to those of theshapevariables (polynomial or harmonic). In both cases of the polynomial and harmonic variables, this linking follows directly as a result of the displacement-enforced static (Choi and Chang, 1991) and eigenmode FE analysis, respectively. This mapping then allows the perturbation vectors of the FE grids to be determined asa function of the changes in the design variables. 4 EXAMPLES