Optimization of the Stress-Strain State of Functional Gradient Structures with Stress Raisers

The problem of forming an optimal structurally inhomogeneous state in structures operating under power contact loads is considered from theoretical research and practical application standpoints. Based on the modern principles of mechanics of deformable solids in nonlocal (gradient) media, approaches to assessing the strength of structures, and methods of mathematical modeling, a variational formulation of the problem of establishing the optimal spatial distribution of properties that ensures the maximum increase in the performance of such products is proposed. As an optimality criterion, we have chosen a functional that allows us to assess the influence of physical and geometric parameters of stress raisers on both the local stress-strain state and the strength of the entire structure under frictional contact interaction. The Python version of the free finite element analysis package Fenics was used to realize the task on the computer. The problem of determining the strength properties of locomotive wheel bands containing both elliptical and circular stress raisers in a twodimensional formulation was studied. Based on a set of numerical studies, a “jump-like” character of the change in the value of contact weakening depending on the distance between the stress raisers was established. This should be considered in the predictive analysis of the behavior of bodies in contact interaction. Limiting parameters for the value of the depth of strengthening of structures with a plurality of stress raisers have been established, the excess of which is inappropriate during technological modification since, with its increase, the parameters of contact strength increase insignificantly.