Optimal Shape Design of Axisymmetric Shells for Crack Initiation and Propagation Under Cyclic Loading

ABSTRACT

This paper describes a problem of axisymmetric shell optimization under fracture mechanics and geometric constraints. The problem is formulated as the weight (volume of a shell material) minimization and the meridional contour of the shell is taken as the design variable. The shell is made from quasi-brittle materials and through cracks arising are admitted. It is supposed that the shell is loaded by cyclic forces. A crack propagation process related to the stress intensity factor is described by the Paris fatigue law. The problem of finding the meridian shape (geometric design variable), of the shell having the smallest mass subject to constraint on the cyclic number for fatigue cracks, is investigated using a minimax (guaranteed) approach worked out in the theory of optimization under incomplete information. Optimal designs of the shells are found numerically with the application of genetic algorithms.

Key Words:

• Axisymmetric shells
• Fatigue crack propagation constraint
• Genetic algorithms
• Optimal shape

ACKNOWLEDGMENT

The support from the RAS Programme “Accumulation of damages, fracture and …”; RFFI “South” (N.94) “Methods of optimal structural design under cyclic loadings, ” FCP “Integration of Science and Education” of Russian Ministry of Education (grant NE 02-4.0-0181) and NWO N.047.014.007 for scientific research is greatly acknowledged.

Notes

Communicated by S. Velinsky.