A Survey of Shape Parameterization Techniques

This paper provides a survey of shape parameterization techniques for multidisciplinary optimization and highlights some emerging ideas. The survey focuses on the suitability of available techniques for complex conngurations, with suitability criteria based on the ee-ciency, eeectiveness, ease of implementation, and availability of analytical sensitivities for geometry and grids. The paper also contains a section on eld grid regeneration, grid deformation , and sensitivity analysis techniques. Nomenclature B Bernstein polynomial c polynomial coeecients f response J cell Jacobian k spring stiiness N B-spline basis function P coordinates of NURBS control point R coordinates of deformed model r coordinates of baseline model U deformation vector u independent parameter coordinate V baseline cell volume v design variable vector W NURBS weights Subscripts f eld (volume) grid g geometry i control point index j grid point index k grid point index m element index p degree of Bernstein polynomial and B-spline basis function s surface grid small positive number Superscripts i polynomial power n number of design variables