Optimization Problems of Contact Mechanics with Uncertainties

Abstract

This article proposes a technique to optimize the shape of a rigid shell (stamp) interacted with elastic medium. As opposed to traditional optimization problems, where the loading configuration is specified, the loads are assumed uncertain in considered formulations and incorporated as unknown variables in the optimization problem statement. Guaranteed approach based on worst case scenario is applied as for formulation as for solution of the considered optimization problems with incomplete data on external forces. As a result, the optimal designs obtained are insensitive to load variations within a given admissible set.

Keywords:

• Contact problems
• Guaranteed approach
• Shape optimization
• Uncertainties

ACKNOWLEDGMENT

The article is performed under support of RFBR (grant No. 08-08-00025-a), RAS Program No. 13, Program of Support of Leading Scientific Schools (grant No. 169.2008.1).

Notes

^# Communicated by S. A. Velinsky.