Citation:
Sherar PA, Thompson CP, Xu B, Zhong B. (2011) A novel shape optimization method using knot insertion algorithm in B-spline and
its application to transonic airfoil design. Scientific Research and Essays, Volume 6, Issue 27, pp. 5696-5707
Abstract:
A new method using the cubic B-spline curves with nominal uniform knot set to
parameterize the geometry is proposed to deal with shape optimization problems.
In the method, the control points of the B-spline curves are set to be the
design variables in the optimization scheme. A knot insertion algorithm has been
introduced in order to keep the geometry unchanged whilst increasing the number
of control points at the final optimization stage. The super-reduced idea and
the mesh refinement are also employed to deal with the equality constraint and
speed up the optimization process. The method is applied to two problems. The
first is a 2-dimensional Poisson problem, and the second is an airfoil design
problem. In both applications, the results show that the new method is much more
efficient when compared with the traditional methods. In the airfoil design
problem, the drag of the airfoil has been reduced significantly with much less
function calls.
