Contact deformation of an elastic composition of a half-plane and a strip of variable width

✍ Scribed by I.A. Soldatenkov

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 549 KB
• Volume: 65
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(01)00016-8

✦ Synopsis

Asymptotic dependences of the deformation on the contact stresses are derived for a strip of variable width bound to an elastic half-plane. Similar relations were previously obtained in [l] for a strip of constant width. 0 2001 Elsevier Science Ltd. All rights reserved.

1. RELATIONS FOR AN ELASTIC STRIP OF VARIABLE WIDTH

In thexy coordinate plane, we consider an elastic strip II of variable width (Fig. l), the upper boundary r+ of which is described by the function y = h+(x) and the lower boundaT r_ is rectilinear: y = -6. Below, we will use a prime on the symbol of a function to denote a derivative with respect to the x coordinate. For brevity, the arguments of functions may be omitted.

Suppose u and v are the displacements along the x and y axes, respectively and that wk (k = 1, . . . , 4) are the displacements of the boundaries of the strip: