The wedge subjected to tractions: a paradox re-examined

✍ Scribed by T. C. T. Ting

• Publisher: Springer Netherlands
• Year: 1984
• Tongue: English
• Weight: 539 KB
• Volume: 14
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00041136

✦ Synopsis

The classical two-dimensional sohit~on for the stress distribution in an elastic wedge loaded by a uniform pressure on one side of the wedge becomes infinite when the wedge angle 2a satisfies the equation tan 2a. = 2a.. This paradox was resolved recently by Dempsey who obtained a solution which is bounded at a = a.. However, for a not equal but very close to a., the classical solution can still be very large as a approaches a.. In this paper we re-examine the paradox. We obtain a solution which remains bounded as a approaches a. and reproduces Dempsey's solution in the limit a= a.. At a = a. the stress distribution contains a (In r) term for general loadings. The (In r) term disappears under a special loading and the stresses are bounded for all r. Moreover, the solution is not unique. In other words, for the wedge angle 2a. under a special loading, infinitely many solutions exist for which the stresses are bounded for all r. We also obtain solutions which are bounded and approach Dempsey's solutions when 2a = *r and 2¢r. Again, under a special loading infinitely many solutions exist for which the stresses are bounded for all r. Care has been exercised in this paper to present the solutions in a form in which the terms r -x and In r are replaced by R -x and In R where R = r/r o is the dimensionless radial distance and r 0 is an arbitrary constant having the dimension of length.