This paper presents an improved version of the traction method that was proposed as a solution to shape optimization problems of domain boundaries in which boundary value problems of partial differential equations are defined. The principle of the traction method is presented based on the theory of the gradient method in Hilbert space. Based on this principle, a new method is proposed by selecting another bounded coercive bilinear form from the previous method. The proposed method obtains domain variation with a solution to a boundary value problem with the Robin condition by using the shape gradient.
We present a numerical analysis and results using the traction method for optimizing domains in terms of which linear elastic problems are defined. In this paper we consider the application of the traction method, which was proposed as a solution to domain optimization problems in elliptic boundary value problems. The minimization of the mean compliance is considered. Using the Lagrange multiplier method, we obtain the shape gradient functions for these domain optimization problems from the optimality criteria. In this process we consider variations in the surface force acting on the boundary and variations in the stiffness function and the body force distributed in the domain. We obtain solutions for an infinite plate with a hole and a rectangular plate clamped at both ends.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.