文档介绍：Aerodynamic Shape Optimization Based on Free-form
Deformation
Jamshid A. Samareh∗
Multidisciplinary Optimization Branch
NASA Langley Research Center
Hampton, VA 23681
This paper presents a free-form deformation technique suitable for aerodynamic shape
optimization. Because the proposed technique is independent of grid topology, we can treat
structured and putational fluid dynamics grids in the same manner. The
proposed technique is an alternative shape parameterization technique to a trivariate
volume technique. It retains the flexibility and freedom of trivariate volumes for CFD shape
optimization, but it uses a bivariate surface representation. This reduces the number of
design variables by an order of magnitude, and it provides much better control for surface
shape changes. The proposed technique is simple, compact, and efficient. The analytical
sensitivity derivatives are independent of the design variables and are puted for
use in a gradient-based optimization. The paper includes plete formulation and
aerodynamics shape optimization results.
Nomenclature
B = B-spline basis functions
C = product of B-spline basis functions
I = maximum number of points in u-direction
J = maximum number of points in v-direction
M = number of surface points
V = control points
W = weights
b = baseline grid
m,n = grid point number
r = coordinates (x, y, z)
v = design variable vector
ξ,η= surface bivariate coordinates
I. Introduction
Over the past several decades, aerodynamic shape optimization (ASO) has been essfully applied for two-
dimensional and simple three-dimensional configurations. Four distinct steps are involved in ASO: 1) geometry
parameterization; 2) surface grid generation; 3) volume grid generation, regeneration, or deformation; and 4)
computational fluid dynamics (CFD) function and sensitivity analyses. Automatic grid generation and grid
sensitivity analysis are