Comparative Analysis and Optimization of Different Cross- sections of Crane Hook Subject to Stresses According to Winkler-Bach Theory

Abstract

The paper presents comparative analysis and optimization of the geometric parameters of different cross-sections of crane hook at the critical places. The reduction of the cross-sectional area of crane hook is primary goal of this research. The selected sections are trapezoidal, elliptic, parabolic and their special cases. Criterion of maximum permissible stress in the characteristic points of cross-section is set as constraint function. Some geometric limits are taken, too. Stresses are observed according to Winkler-Bach theory. Optimization procedure is performed by using the method of Lagrange multiplier and GRG2 algorithm. The obtained results of optimization for different types of cross-sections are compared with each other and with the geometric values of standard hook solution.