A Solution to Shape Optimization Problem of Thin Walled Cross Section in Structural Design

Abstract

In this paper, we present a numerical solution to optimize thin walled cross section shape of a solid structure, which is often demanded at the early stage in structural designs. The thin walled cross section is minimized subject to the constraints of sectional properties including the torsional constant, the moment of inertia of area, the center of figure and the share center of figure. The problem is formulated as a distributed shape optimization problem, and the shape gradient function is derived using the Lagrange multipliers and the material derivative method. The traction method, which was proposed as a gradient method in the Hilbert space, is applied to determine the smooth optimal shape. The constraint conditions are efficiently satisfied using the modified feasible direction method. The validity of this method is verified through several design examples for obtaining the optimal shape of the thin walled cross section under the constraints of sectional properties.