# Winkler Support Model and Nonlinear Boundary Conditions Applied to 3D Elastic Contact Problem Using the Boundary Element Method

• J. Vallepuga-Espinosa
• Lidia Sánchez-González
• Iván Ubero-Martínez
Article

## Abstract

This work presents a numerical methodology for modeling the Winkler supports and nonlinear conditions by proposing new boundary conditions. For the boundary conditions of Winkler support model, the surface tractions and the displacements normal to the surface of the solid are unknown, but their relationship is known by means of the ballast coefficient, whereas for nonlinear boundary conditions, the displacements normal to the boundary of the solid are zero in the positive direction but are allowed in the negative direction. In those zones, detachments of nodes might appear, leading to a nonlinearity, because the number of nodes that remain fixed or of the detached ones (under tensile tractions) is unknown. The proposed methodology is applied to the 3D elastic receding contact problem using the boundary element method. The surface tractions and the displacements of the common interface between the two solids in contact under the influence of different supports are calculated as well as the boundary zone of the solid where the new boundary conditions are applied. The problem is solved by a double-iterative method, so in the final solution, there are no tractions or penetrations between the two solids or at the boundary of the solid where the nonlinear boundary conditions are simulated. The effectiveness of the proposed method is verified by examples.

## Keywords

Boundary element method Elastic contact problem Winkler support model Nonlinear boundary conditions

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© The Chinese Society of Theoretical and Applied Mechanics 2019

## Authors and Affiliations

• J. Vallepuga-Espinosa
• 1
• Lidia Sánchez-González
• 2
• Iván Ubero-Martínez
• 1
1. 1.Departamento de Tecnología Minera, Topografía y de EstructurasUniversidad de LeónLeónSpain
2. 2.Departamento de Ingenierías Mecánica, Informática y AeroespacialUniversidad de LeónLeónSpain