Numerical Study of Optimal Material Distribution in Elastic Bodies by Topological Optimization Method

Abstract

The study is aimed at developing a universal topological optimization algorithm based on fundamental principles of elasticity theory and continuum mechanics. The objective of the study is to minimize the mass of a structure subjected to dynamic loads while maintaining its strength characteristics, which can be achieved by optimal distribution of material in the volume of the workpiece. An element of a tillage tool—a plate weighing 1.925 kg with maximum stresses of 176.8 MPa operating under variable mechanical stresses—was taken as a basic model Application of parametric modeling and systems approach implemented in the SysML language made it possible not only to select the best element for optimization, but also to develop a new geometry of the structural element (plate). The theory of elasticity, finite element method (FEM), and von Mises stress analysis were used as the physical foundations of the study. This algorithm was found to reduce the mass of the structural element to 1.585 kg, which corresponds to mass reduction by 17.67% while meeting the established requirements for the factor of safety (1.5 to 2.0). The presented method can be used both in aerospace engineering, materials science, machine tool engineering and automotive industry, where similar optimization principles can help to increase the efficiency of design solutions while reducing material consumption.