“…This method has been applied to many shape optimization problems, such as elastic problems (Azegami et al, 1995;Shimoda et al, 1996), heat conduction problems (Katamine et al, 2001(Katamine et al, , 2003, and viscous flow problems (Katamine and Azegami, 1994;Katamine et al, 2005Katamine et al, , 2007Katamine et al, , 2009) in mechanical engineering. The traction method applies the gradient method of a distributed system and uses the shape gradient function of the domain variation that is theoretically derived from the optimization problem.…”