Numerical Solution for Min-Max Shape Optimization Problems. (Minimum Design of Maximum Stress and Displacement).

DOI IR IR HANDLE Web Site View 2 Remaining Hide 5 Citations 12 References Open Access

Bibliographic Information

Other Title
  • Numerical Solution for Min-Max Shape Op

Search this article

Abstract

This paper presents a numerical shape optimization method for continua that minimizes some maximum local measure such as stress or displacement. A method of solving such min-max problems subject to a volume constraint is proposed. This method uses the Kreisselmeier-Steinhauser function to transpose local functionals to global integral functionals so as to avoid non-differentiability. With this function, a multiple loading problem is recast as a single loading problem. The shape gradient functions used in the proposed traction method are derived theoretically using Lagrange multipliers and the material derivative method. Using the traction method, the optimum domain variation that reduces the objective functional is numerically and iteratively determined while maintaining boundary smoothness. Calculated results for two- and three-dimensional problems are presented to show the effectiveness and practical utility of the proposed method for min-max shape design problems.

Journal

Citations (5)*help

See more

References(12)*help

See more

Details 詳細情報について

Report a problem

Back to top