Abstract
Optimum laminate configuration for minimum weight of filament-wound laminated conical shells is investigated subject to a buckling load constraint. In the case of a composite laminated conical shell, due to the manufacturing process, the thickness and the ply orientation are functions of the shell coordinates, which ultimately results in coordinate dependence of the stiffness matrices (A,B,D). These effects influence both the buckling load and the weight of the structure and complicate the optimization problem considerably. High computational cost is involved in calculating the buckling load by means of a high-fidelity analysis, e.g. using the computer code STAGS-A. In order to simplify the optimization procedure, a low-fidelity model based on the assumption of constant material properties throughout the shell is adopted, and buckling loads are calculated by means of a low-fidelity analysis, e.g. using the computer code BOCS. This work proposes combining the high-fidelity analysis model (based on exact material properties) with the low-fidelity model (based on nominal material properties) by using correction response surfaces, which approximate the discrepancy between buckling loads determined from different fidelity analyses. The results indicate that the proposed multi-fidelity approaches using correction response surfaces can be used to improve the computational efficiency of structural optimization problems.
Similar content being viewed by others
References
Almroth BO, Brogan FA, Meller E, Zele F, Petersen HT (1973) Collapse analysis for shells of general shape. User’s manual for STAGS-A computer code, Technical report AFFDL TR-71-8
Bakr MH, Bendler JW, Madsen K, Sondergaard J (2000) Review of space mapping approach to engineering optimization and modeling. Optim Eng 1:241–276
Baruch M, Arbocz J, Zhang GQ (1994) Laminated conical shells- considerations for the variations of the stiffness coefficients. AIAA-1994-1634, AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference, 35th, Hilton Head, SC, Apr. 18–20, 1994, Technical Papers. Pt. 5 (A94-23876 06-39), Washington, DC, American Institute of Aeronautics and Astronautics, 1994, p. 2505–2516
Draper NR, Smith H (1998) Applied regression analysis, 3rd edn. Wiley, New York
Goldfeld Y, Sheinman I, Baruch M (2003) Imperfection sensitivity of conical shells. AIAA J 41(3):517–524
Goldfeld Y, Arbocz J (2004) Buckling of laminated conical shells taking into account the variations of the stiffness coefficients. AIAA J 42(3):642–649
Goldfeld Y, Arbocz J, Rothwell A (2005) Design and optimization of laminated conical shells for buckling. Thin walled structures, 43:107–133
Haftka RT, Gürdal Z (1992) Elements of Structural Optimization, 3rd edn. Kluwer, Dordrecht
Jones RM (1975) Mechanics of composite materials. McGraw–Hill, New York
Markine VL, Toropov VV (2002) Use of high- and low-fidelity models in approximations for design optimization. AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 9th, Atlanta, Georgia, USA, September 4–6 2002, AIAA paper 2002-5651
Polynkine AA, Van Keulen F, Toropov VV (1995) Optimization of geometrically nonlinear thin-walled structures using multipoint approximation method. Struct Optim 9:105–112
Polynkine AA, Van Keulen F, Toropov VV (1996) Optimization of geometrically non-linear structures based on a multi-point approximation method and adaptively. Eng Comput 13(2–4):76–97
Toropov VV, Filatov AA, Polynkine AA (1993) Multiparameter structural optimization using FEM and multi-point explicit approximations. Struct Optim 6:7–14
Toropov VV, Markine VL (1996) The use of simplified numerical models as mid-range approximations. AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 6th, Bellevue WA, September 4–6 1996, Part 2, (1-56347-218-X) pp 952–958
Toropov VV, Van Keulen F, Markine VL, Alvarez LF (1999) Multipoint approximations based on response surface fitting: a summary of recent developments. In: Toropov VV (ed) Proceeding of the 1st ASMO UK/ISSMO Conference on Engineering Design Optimization, Ilkley, West Yorkshire, UK, July 8–9 1999, pp 371–381. ISBN 0-86176-650-4
Van Keulen F, De Boer H (1998) Refined semi-analytical design sensitivities for buckling. Paper AIAA-98-4761
Venkataraman S, Haftka RT, Johnson TF (1998) Design of shells structures for buckling using correction response surface approximations. AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 7th, St. Louis, MO, Sept. 2–4 1998, Collection of Technical Papers. Pt. 2 (A98-39701 10-31), Reston, VA, American Institute of Aeronautics and Astronautics, pp 1131–1144
Vitali R, Haftka RT, Bhavani VS (1998) Correction response surface approximations for stress intensity factors of a composite stiffened plate. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference, Paper AIAA-98-2047, Proceeding, Long Beach, Florida, pp 2917–2922
Vitali R, Haftka RT, Sankar BV (2002) Multi-fidelity design of stiffened composite panel with a crack. Struct Multidisc Optim 23:347–356
Vitali R, Park O, Haftka RT, Sankar BV (1997) Structural optimization of a hat stiffened panel by response surface techniques. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference, Paper AIAA-97-1151, Proceedings, Kissimmee, Florida, Vol. 4, pp 2983–2993
Vitali R, Sankar V (1999) Correction response surface design of stiffned composite panel with a crack. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference, Paper AIAA-99-1313, Proceedings, St. Louis, Missouri
Whitney JM (1987) Structural analysis of laminated anisotropic plates. Technomic, PA
Zadeh PM, Toropov VV (2002) Multi-fidelity multidisciplinary design optimization based on collaborative optimization framework, AIAA-2002-5504 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia, Sep. 4–6 2002
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Goldfeld, Y., Vervenne, K., Arbocz, J. et al. Multi-fidelity optimization of laminated conical shells for buckling. Struct Multidisc Optim 30, 128–141 (2005). https://doi.org/10.1007/s00158-004-0506-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-004-0506-9