Modern Approaches to Solving the Contact Problem of Pressing a Doublestamp Stamp Into an Elastic Half-Space

Abstract

The work is devoted to solving indentation problems into an elastic half-space of a cylindrical punch with a flat base by the vertical force. The force is aimed through the center of the base. The cross-section of the stamp is a doubly connected area bounded by two concentric lines. A concise review of methods for solving problems of analyzing the contact interaction of cylindrical dies with an elastic half-space is given. The solution of the problem in the form of decomposition by a small parameter is used when the equation of the edge curves depends on the same small parameter. To achieve it, in each approximation, the problem of indentation of a stamp with a doubly connected contact area in the form of a non-circular ring is reduced to a similar problem of indentation of a stamp with a contact area in the form of a circular ring. The software in the Java language has been developed for processing the analytical solution according to the obtained calculation formulas. With the help of the ANSYS software package, a finite element model of the contact interaction of an absolutely rigid stamp with an elastic half-space has been created. Numerical modeling was carried out using a licensed version of the program, free of charge. Several problems have been solved for square rings of different widths. The distribution of pressure under the stamp over different sections and the deepening of the stamp have been obtained. The pressure distribution graphs are plotted. When considering several test problems to assess the adequacy of the finite element model, the numerical results are compared with the results obtained analytically. The resulting model can analyze and predict loads, wear, and fracture of the contact area. The research prospects can include the solution of several problems of analysis of the stress-strain state of the interaction of dies of a complex shape with an elastic half-space, as well as groups of stamps of a complex shape, and the analysis of behavior models depending on the properties and characteristics of an elastic half-space.
 Keywords: contact problem, stamp, stress-strain state, modeling, JAVA language, finite element analysis, ANSYS software package.