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Asymptotic Approach to Optimal Structural Design with Brittle-Fracture Constraints

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Mechanics of Composite Materials and Structures

Part of the book series: NATO Science Series ((NSSE,volume 361))

Abstract

Questions raised in this paper are related to an important class of problems concerning shape optimization of brittle or quasi-brittle structures with cracks. Considered optimization problems consist in finding the boundary of the body or some geometrical parameters such that the cost functional (the weight or material volume) attains a minimum, while satisfying prescribed bounds on stress intensity factors.

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References

  1. Haug, E. J., Arora, J. S. (1979) Applied Optimal Design, Wiley, New-York.

    Google Scholar 

  2. Banichuk, N. V. (1983) Problems and Methods of Optimal Structural Design, Plenum Press, N.-Y.

    Book  Google Scholar 

  3. Haftka, R. T., Gurdal, Z. (1993) Element of Structural Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands

    Google Scholar 

  4. Banichuk, N. V. (1990) Introduction to Optimization of Structures, Springer-Verlag New-York.

    Book  MATH  Google Scholar 

  5. Augusti, G., Baratta, A., Casciati, F. (1984) Probabilistic Methods in Structural Engineering, Chapman and Hall.

    Google Scholar 

  6. Augusti, G., Casciati, F. (1979) Further Studies on Structural Design for Maximum Expected Utility, Proc. 3rd Int. Conf. On Applications of Statistics and Probability in Soil and Strural Engineering (ICASP3), Sydney, Vol. 2, pp. 676–700.

    Google Scholar 

  7. Wang, J., Karihaloo B. L. (1995) Optimum in the Situ Strength Design of Composite Laminates, Proc. of the First World Congress of Structural and Multidisciplinary Optimization, Pergamon, N-Y., pp. 259–266.

    Google Scholar 

  8. Yu, X., Choi, K. K., Chang, K.-H. (1997) A Mixed Design Approach for Probabilistic Structural Durability, Structural Optimization, Vol. 14, pp. 81–90.

    Article  Google Scholar 

  9. Banichuk, N. V. (1998) Problems of Optimum Design Based on the Mechanics of Quasi-brittle Fracture, Physics-Doklady, Vol. 43 No. 1 Translated from Doklady Akademii Nauk a Journal of the Russian Academy of Sciences, Vol. 358, No 1 (1998).

    Google Scholar 

  10. Banichuck, N. V. (1996) Free Boundaries Optimization Under Fracture Mechanics Constraints, Analele Stiintifice, Universitatii, “OVIDIUS”, Constanta, Vol. 5, N 1, pp. 13–20.

    Google Scholar 

  11. Banichuk, N. V., Ragneda, F. K., Serra, M. (accepted for publication) Probabilistic Approaches for Optimal Beam Design Based on Fracture Mechanics, Meccanica, International Journal of the Italian Association of Theoretical and Applied Mechanics.

    Google Scholar 

  12. Banichuck, N. V. (1998) Optimal Design of Quasi-Brittle Elastic Bodies with Cracks, Int. J. Mechanics of Structures and Machines, Vol. 26, N 4, pp. 365–376.

    Article  Google Scholar 

  13. Sih, G. S., Liebowitz H., Fracture, Liebowitz, H., Ed. (1971) Mathematical Fundamentals, New York, Academic, Vol. 2

    Google Scholar 

  14. Hutchinson, J. W. (1979) A Course on Nonlinear Fracture Mechanics. Technical University of Denmark, Lyngby.

    Google Scholar 

  15. Hellan, K. (1984) Introduction to Fracture Mechanics, New York, Mc Graw-Hill.

    Google Scholar 

  16. Timoshenko, S. P., Gere, J. M. (1972) Mechanics, Van Nostrand Reinhold Company, New-York.

    Google Scholar 

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© 1999 Springer Science+Business Media Dordrecht

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Banichuk, N.V. (1999). Asymptotic Approach to Optimal Structural Design with Brittle-Fracture Constraints. In: Soares, C.A.M., Soares, C.M.M., Freitas, M.J.M. (eds) Mechanics of Composite Materials and Structures. NATO Science Series, vol 361. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4489-6_31

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  • DOI: https://doi.org/10.1007/978-94-011-4489-6_31

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5871-8

  • Online ISBN: 978-94-011-4489-6

  • eBook Packages: Springer Book Archive

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