A. Tafreshi et Rt. Fenner, DESIGN SENSITIVITY ANALYSIS USING THE BOUNDARY-ELEMENT METHOD, Journal of strain analysis for engineering design, 28(4), 1993, pp. 283-291
A directly differentiated form of boundary integral equation with resp
ect to geometric design variables is used to calculate shape design se
nsitivities. This allows the coupling of an optimizing technique and a
boundary element elastic stress analyser to form an optimum shape des
ign algorithm in two dimensions. Hermitian cubic spline functions used
to represent boundary shapes offer considerable advantages in fitting
a wide range of curves, and in the automatic remeshing process. They
also reduce the need for optimization constraints to avoid impractical
designs during the optimization procedure. The boundary element metho
d offers advantages over the finite element method, and is applicable
to a wide range of shape optimization problems.