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Implementation of a crack propagation constraint within a structural optimization software

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Abstract

A crack propagation constraint related to the stress intensity factor is examined for the minimum-weight design optimization of a composite blade-stiffened panel. A low-fidelity approach uses a closed-form solution for the stress intensity factor, while a high-fidelity approach uses the stress distribution around the crack. Structural optimizations are performed by low- and high-fidelity approaches for a number of panels configured with different values of the load, crack length, and blade height. Response surface (RS) approximations are then constructed for the optimal weight as a function of the three configuration variables. The computational cost, numerical noise, and accuracy for the two approaches are compared. An additional constraint in the low-fidelity solutions is found to be active for some of the configurations, increasing the difference between the low-fidelity and high-fidelity optima. It is shown that outlier analysis helps to identify the configurations with the largest difference.

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References

  1. Anderson, T.L. 1995: Fracture Mechanics: Fundamentals and Applications, 2nd edn. Boca Raton: CRC Press

  2. Gürdal, Z.; Haftka, R.T. 1985: Design of stiffened composite panels with a fracture constraint. Comput. Struct. 20, 457–465

    Google Scholar 

  3. Gürdal, Z.; Haftka, R.T. 1988: Automated design of composite plates for improved damage tolerance. In: Whitcomb, J.D. (ed.) Composite Materials: Testing and Design. ASTM-STP 972, pp. 5–22

  4. Harris, C.E.; Morris, D.H. 1985: A damage tolerant design parameter for graphite/epoxy laminated composites. J. Compos. Techn. Res. 7, 77–81

    Google Scholar 

  5. Holland, P.W.; Welsch, R.E. 1977: Robust regression using iteratively reweighted least-squares. Commun. Stat. Theory Methods 6, 813–827

    Google Scholar 

  6. Khuri, A.I.; Cornell, J.A. 1996: Response Surfaces: Designs and Analyses. New York: Marcel Dekker

  7. Kim, H.; Papila, M.; Mason, W.H.; Haftka, R.T.; Watson, L.T.; Grossman, B. 2001: Detection and repair of poorly converged optimization runs. AIAA J. 39, 2242–2249

    Google Scholar 

  8. Liu, B.; Haftka, R.T.; Akgun, M.A. 2000: Two-level composite wing structural optimization using response surfaces. Struct. Multidisc. Optim. 20, 87–96

    Google Scholar 

  9. Myers, R.H.; Montgomery, D.C. 1995: Response Surface Methodology: Process and Product Optimization Using Designed Experiments. New York: John Wiley & Sons

  10. Nees, C.D.; Canfield, R.A. 1998: Methodology for implementing fracture mechanics in global structural design of aircraft. J. Aircraft 35, 131–138

    Google Scholar 

  11. Papila, M.; Haftka, R.T. 1999: Uncertainty and wing structural weight approximations. 40th AIAA/ASME/ASCE/AHS/ASC Proc. Struct., Struct. Dyn. Mater. Conf. (held in St Louis), Vol. 2, pp. 988–1002

  12. Papila, M.; Haftka, R.T. 2000a: Response surfaces for optimal weight of cracked composite panels: noise and accuracy. 8th AIAA/USAF/NASA/ISSMO Symp. Multidisc. Anal. Optim. (held in Long Beach), AIAA-00-4755

  13. Papila, M.; Haftka, R.T. 2000b: Response surface approximations: noise, error repair and modeling errors. AIAA J. 38, 2336–2343

  14. Papila, M.; Vitali, R.; Haftka, R.T.; Sankar, B.V. 2001: Optimal weight of cracked composite panels by an equivalent strain constraint. 42nd AIAA/ASME/ASCE/AHS/ASC Proc. Struct., Struct. Dyn. Mater. Conf. (held in Seattle), AIAA-01-1207

  15. Poe, C.C. Jr.; Sova, J.A. 1980: Fracture toughness of boron/aluminum laminates with various proportions of 0 and ±45 plies. NASA TP-1707

  16. Poe, C.C. Jr. 1983: A unifying strain criterion for fracture of fibrous composite laminates. Eng. Fract. Mech. 17, 153–171

    Google Scholar 

  17. Ragon, S.A.; Gürdal, Z.; Haftka, R.T.; Tzong, T.J. 1997: Global/local structural wing design using response surface techniques. Proc. AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn. Mater. Conf. (held in Kissimmee), AIAA-97-1051

  18. Rankin, C.C.; Brogan, F.A.; Loden, W.A.; Cabiness, H.D. 1998: STAGS User Manual ver. 3.0. Palo Alto: Lockheed Martin Missiles & Space Co. Inc. Advanced Technology Center

  19. SAS Institute Inc. 1998: JMP Statistics and Graphics, and User’s Guides, Version 3. SAS Campus Drive Cary, NC 27513

  20. Stark, P.B. 2001: SticiGui: Statistics Tools for Internet and Classroom Instruction with a Graphical User Interface. http://oz.berkeley.edu/users/stark/SticiGui (last accessed 10/27/2001)

  21. Thomsen, N.B.; Wang, J.; Karihaloo, B.L. 1994: Optimization – a tool in advanced materials technology. Struct. Optim. 8, 9–15

    Google Scholar 

  22. Vaidya R.S.; Sun C.T. 1996: Fracture criterion for notched thin composite laminates. Proc. AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn. Mater. Conf. (held in Salt Lake City), pp. 331–338, AIAA-96-1354

  23. Vaidya R.S.; Klung J.C.; Sun C.T. 1997: Effect of ply thickness and crack tip damage on failure of notched composite laminates. Proc. AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn. Mater. Conf. (held in Kissimmee), AIAA-97-1184

  24. Vitali, R.; Haftka, R.T.; Sankar, B.V. 1998: Correction response surface approximations for stress intensity factors for composite stiffened plates. Proc. AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn. Mater. Conf. (held in Long Beach), pp. 2917–2922 AIAA-98-2047

  25. Vitali, R; Sankar B.V. 1999: Correction response surface design of stiffened composite panel with a crack. 40th Proc. AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn. Mater. Conf. (held in St. Louis)

  26. Vitali, R.; Haftka, R.T.; Sankar, B.V. 2002: Multi-fidelity design of stiffened composite panel with a crack. Struct. Multidisc. Optim. Congr. 23(5), 347–356

    Google Scholar 

  27. VMA Engineering: GENESIS User Manual, Version 4.0, 1767 S. 8th Street, Suite M-200, Colorado Springs, CO 80906

  28. Whitney, J.M.; Nuismer, R.J. 1974: Stress fracture criteria for laminated composites containing stress concentrations. J. Compos. Mater. 8, 253–265

    Google Scholar 

  29. Wiggenraad, J.F.M.; Vercammen, R.W.A.; Arendsen, P.; Ubels, L.C. 2000: Design optimization of stiffened composite panels for damage resistance, 41st Proc. AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn. Mater. Conf. (held in Atlanta), AIAA-00-1374

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Papila, M., Haftka, R. Implementation of a crack propagation constraint within a structural optimization software. Struct Multidisc Optim 25, 327–338 (2003). https://doi.org/10.1007/s00158-003-0329-0

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  • DOI: https://doi.org/10.1007/s00158-003-0329-0

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