抄録
In this paper, we present a numerical method to optimize the cross section shape of solid structures, which is often needed at the preliminary stage in the structural designs of automotives and airplanes and so on. The cross section area is minimized subject to sectional properties such as moments of inertia of area, center of gravity, boundary length. The problem is formulated as a distributed optimization problem, or a non-parametric optimization problem. The shape gradient function is derived using the Lagrange multipliers and the material derivative method. The traction method, or a gradient method in Hilbert space is employed to determine the smooth optimal shape using the derived shape gradient function. The validity of this method is verified to obtain the optimal shape of cross section under the constraints of sectional properties through an example.
