Abstract
This chapter is devoted to a rigorous proof of the application procedure of the method of dimensionality reduction to contacts with elastomers. The proof is based on Radok’s principle of functional equations. It proceeds from a solution of a similar elastic problem which then is carried over to the original problem by replacing the material properties. We will show in detail how Radok’s method of functional equations is used for the replacement of the material properties.
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Notes
- 1.
The mathematically sound way consists of taking the incompressibility into account in Eq. (19.29) and only then, taking the Laplace transformation. It is, however, easy to see that this procedure leads to the same result.
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Kürschner, S., Popov, V.L., Heß, M. (2015). Appendix 3: Replacing the Material Properties with Radok’s Method of Functional Equations. In: Method of Dimensionality Reduction in Contact Mechanics and Friction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53876-6_19
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DOI: https://doi.org/10.1007/978-3-642-53876-6_19
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