Multi‐Objective Shape Design of Crane‐Hook Taking Account of Practical Requirement Available to Purchase

The main topic of this study is a shape design of a crane‐hook. In order to improve the performance of the crane‐hook, we formulate a multi‐objective optimization problem based on a FEM analysis. The displacement at the usual force applied point, the ratio between the total displacement against various load conditions and an $H2$‐norm of the dynamic behavior are adopted as the objective functions to be minimized. The crane‐hook dealt with in this study has a typical cross‐section of so‐called T‐shape. The cross‐section and the contour shape are adopted as the design variables. Continuous change of these design variables is expressed in terms of orthogonal polynomials and the Fourier series. The Particle Swarm Optimization (PSO) is used as the optimization procedure. The obtained crane‐hook design has a typical tapered shape similar to those of existing designs. The result shows the basic applicability of the proposed objective functions as well as the optimal design approach.