Vol. 1, No. 2, 2006

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 3, 249–351
Issue 2, 147–247
Issue 1, 1–146

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
Cover
Editorial Board
Research Statement
Scientific Advantage
Submission Guidelines
Submission Form
Subscriptions
Author Index
To Appear
 
ISSN: 1559-3959
The stress-minimizing hole in an elastic plate under remote shear

Shmuel Vigdergauz

Vol. 1 (2006), No. 2, 387–406
Abstract

Conformal mappings provide an elegant formulation for planar elastostatic problems. Here, the mapping function coefficients are used in a new manner as design variables in the genetic-algorithm (GA) approach to find a piecewise smooth optimal shape of a single traction-free hole in an elastic plate that minimizes the local stresses under remote shear. This scheme is sufficiently fast and accurate to numerically show that the sought-for shape generates tangential stress of constant absolute value, equal to 30% less than the stress concentration factor (SCF) for the commonly used circular hole. The shape has four symmetrically located corners, and the stress changes sign while remaining finite as it rounds each corner. This is the same shape as the energy-minimizing contour identified in 1986 by the author and Cherkaev for the same load. Other nontrivial examples are given to demonstrate the potential of the approach. Methodologically, this article continues the optimization study first conducted by the author and Cherkaev (J. Appl. Math. Mech. 50:3 (1986), 401–404) and subsequently by Cherkaev et al. (Internat. J. Solids Structures (35):33, 4391–4410).

Keywords
plane elasticity problem, Kolosov–Muskhelishvili potentials, shape optimization, effective energy, extremal elastic structures, genetic algorithm
Milestones
Received: 29 September 2005
Revised: 16 December 2005
Accepted: 23 January 2006
Published: 1 June 2006
Authors
Shmuel Vigdergauz
R&D Division
The Israel Electric Corporation, Ltd.
P.O.Box 10
Haifa 31000
Israel