Vol. 5, No. 6, 2010

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Stress smoothing holes in planar elastic domains

Shmuel Vigdergauz

Vol. 5 (2010), No. 6, 987–1006

The actual elastostatic problem of optimizing the stress state in a two-dimensional perforated domain by proper shaping of holes is considered with respect to minimization of the global variations of the boundary hoop stresses. This new criterion radically extends the rather restrictive equistress principle introduced by Cherepanov and results in a favorable response of the structure to an external load, with neither local stress concentrations nor underloading of other parts of the boundary. Mathematically, the variations provide an integral-type assessment of the local stresses which requires less computational effort than direct minimization of the stress concentration factor. The proposed criterion can thus be easily incorporated in the numerical optimization scheme previously developed by the author in the closely related context of energy optimization. It includes an efficient complex-valued direct solver and a standard evolutionary optimization algorithm enhanced with an economical shape parametrization tool. The effectiveness of the proposed scheme is illustrated through numerical simulations.

plane elasticity problem, Kolosov–Muskhelishvili potentials, shape optimization, hoop stresses, extremal elastic structures, genetic algorithm
Received: 30 May 2010
Revised: 11 October 2010
Accepted: 13 October 2010
Published: 1 January 2011
Shmuel Vigdergauz
Research and Development Division
The Israel Electric Corp. Ltd.
P.O.Box 10
31000 Haifa