Abstract
The optimization of shell buckling is performed considering peak normal force and absorbed internal energy in the presence of geometrical imperfections implemented through Karhunen-Loève expansions. Initially, the mass of a shell is minimized in the presence of random initial imperfections by allowing cutouts in the material, subject to constraints on the average peak force and average internal energy. Then, robustness is considered by minimizing the coefficient of variation of the normal peak force while constraining the average peak force and average internal energy. LS-OPT® is used both to generate an experimental design and to perform a Monte Carlo simulation (96 runs) using LS-DYNA® at each of the experimental design points. The effect of imperfections when minimizing the mass is not large, but when considering robustness, however, the optimal design has a substantially increased hole size and increased shell thickness, resulting in a heavier design with maximal robustness within the constraints.
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References
Arbocz J (2000) The effect of imperfect boundary conditions on the collapse behavior of anisotropic shells. Int J Solids Struct 37:6891–6915
Arbocz J, Abramovich H (1979) The initial imperfection databank at the Delft University of Technology. Part 1. Technical Report LR-290, Delft University of Technology, Department of Aerospace Engineering
Arbocz J, Starnes JH (2002) Future directions and challenges in shell stability analysis. Thin Wall Struct 40:729–754
Bushnell D (1985) Computerized Buckling Analysis of Shells. Marthinus Nijhoff, Dordrecht
Elishakoff I (2000) Uncertain buckling: its past, present and future. Int J Solids Struct 37:6869–6889
Ghanem RG, Spanos PD (1991) Stochastic finite elements—a spectral approach. Revised Edition, Dover, 2003. Springer, New York
Le Mâıtre OP, Reagan MT, Najm HN, Ghanem RG, Knio OM (2002) A stochastic projection method for fluid flow. II. Random process. J Comp Phys 181:9–44
Livermore Software Technology Corporation (LSTC) (2004) LS-DYNA manual version 970. Livermore, CA
Livermore Software Technology Corporation (LSTC) (2006) LS-DYNA version 971. Livermore, CA
Phoon KK, Huang SP, Quek ST (2002a) Simulation of second-order processes using Karhunen–Loève expansion. Comput Struct 80(12):1049–1060
Phoon KK, Huang SP, Quek ST (2002b) Implementation of Karhunen–Loève expansion for simulation using a wavelet-Galerkin scheme. Probabilist Eng Mech 17(3):293–303
Phoon KK, Huang HW, Quek ST (2004) Comparison between Karhunen–Loève and wavelet expansions for simulation of Gaussian processes. Comput Struct 82(13–14):985–991
Phoon KK, Huang SP, Quek ST (2005) Simulation of strongly non-Gaussian processes using Karhunen–Loève expansion. Probabilist Eng Mech 20(2):188–198
Rahman S, Xu H (2005) A meshless method for computational stochastic mechanics. Int J Comput Meth Eng Science Mech 6:41–58
Roux WJ, Craig KJ (2006) Validation of structural simulations considering stochastic process variation. Paper 06M-67, SAE Congress, Detroit, USA
Roux WJ, Stander N, Günther F, Müllerschön H (2006) Stochastic analysis of highly nonlinear structures. Int J Numer Meth Eng 65:1221–1242
Schenk CA, Schuëller GI (2003) Buckling analysis of cylindrical shells with random geometrical imperfections. Int J Nonlinear Mech 38:1119–1132
Schenk CA, Schuëller GI (2005) Uncertainty assessment of large finite element systems. Lecture Notes in Applied and Computational Mechanics, Vol.24. Springer, Berlin, Heidelberg
Stander N, Craig KJ (2002) On the robustness of a simple domain reduction scheme for simulation-based optimization. Eng Comput 19(4):431–450
Stander N, Roux WJ, Eggleston TA, Craig KJ (2006) LS-OPT v3.1 User’s manual, Livermore Software Technology Corporation. Livermore, USA
TrueGrid Manual (2005) XYZ Scientific Applications. Livermore, CA
Turk M, Pentland A (1991) Eigenfaces for recognition. J Cognit Neurosci 3(1):71–86
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An erratum to this article can be found at http://dx.doi.org/10.1007/s00158-008-0331-7
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Craig, K.J., Stander, N. Optimization of shell buckling incorporating Karhunen-Loève-based geometrical imperfections. Struct Multidisc Optim 37, 185–194 (2008). https://doi.org/10.1007/s00158-007-0178-3
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DOI: https://doi.org/10.1007/s00158-007-0178-3