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

Winkler Support Model and Nonlinear Boundary Conditions Applied to 3D Elastic Contact Problem... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Solida Sinica" Springer Journals

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

, Volume 32 (2): 19 – Apr 1, 2019
19 pages

/lp/springer-journals/winkler-support-model-and-nonlinear-boundary-conditions-applied-to-3d-sWJTmhLmuu
Publisher
Springer Journals
2019 The Chinese Society of Theoretical and Applied Mechanics
ISSN
0894-9166
eISSN
1860-2134
DOI
10.1007/s10338-018-00073-4
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

"Acta Mechanica Solida Sinica"Springer Journals

Published: Apr 1, 2019

Keywords: Theoretical and Applied Mechanics; Surfaces and Interfaces, Thin Films; Classical Mechanics

### References

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