A recently developed method of parameterizing complex shapes that one seeks to optimize differs from prior such methods in two major respects: (1) instead of entirely parameterizing the shapes, one parameterizes only shape perturbations (deformations of initial or baseline shapes) and (2) the deformations are computed by soft-objects animation (SOA) algorithms commonly used in computer graphics. This method is suitable for multidisciplinary design-optimization processes, in which shapes of structures are optimized along with other aspects of design (e.g., aerodynamics). This method can be applied, for example, to the shapes of both exterior aerodynamic surfaces and internal structural components of aircraft.
For example, in the case of an airplane wing (see figure), one starts with a known wing design and seeks to improve the performance of the wing by applying numerical optimization techniques to perturbed wing shapes. Small changes in the shape of a wing can engender substantial changes in aerodynamic performance; as a result, the perturbations between a baseline and an optimized wing design are typically very small. Perturbations of a wing shape can readily be expressed as changes in thickness, camber, twist, dihedral angle, shear, and planform; this fact affords a computational advantage in that fewer parameters are needed to express such changes than are needed to describe the wing shape in its full complexity.
SOA algorithms have been chosen for this method because they are powerful computational tools for modifying shapes. In particular, SOA algorithms are suitable for deforming models represented by either sets of polygons or sets of parametric curves and surfaces. The SOA algorithms treat the models as though they were made of rubber that can be twisted, bent, tapered, compressed, or expanded, while retaining their initial topologies. In this respect, SOA algorithms are ideal for parameterizing airplane models that have external skins as well as internal components like spars and fuel tanks. The SOA algorithms relate vertices of the computational grid of an analysis model to a small number of design variables. Consequently, the SOA algorithms can serve as part of the basis of an efficient shape-optimization technique.
This work was done by Jamshid A. Samareh of Langley Research Center. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Information Sciences category.