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No AccessTechnical Note

Discrete Adjoint Formulation for Continuum Sensitivity Analysis

Published Online:11 Nov 2015https://doi.org/10.2514/1.J053827
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References

  • [1] Dems K. and Mroz Z., “Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis. Part 2 – Structure Shape Variation,” International Journal of Solids and Structures, Vol. 53, No. 11, 1984, pp. 527–552. doi:https://doi.org/10.1016/0020-7683(84)90026-X CrossrefGoogle Scholar

  • [2] Dems K. and Haftka R. T., “Two Approaches to Sensitivity Analysis for Shape Variation of Structures,” Mechanics of Structures and Machines, Vol. 16, No. 4, 1988, pp. 501–522. doi:https://doi.org/10.1080/08905458808960274 CrossrefGoogle Scholar

  • [3] Arora J. S., “An Exposition of the Material Derivatives Approach for Structural Shape Sensitivity Analysis,” Computer Methods in Applied Mechanics and Engineering, Vol. 105, No. 1, 1993, pp. 41–62. doi:https://doi.org/10.1016/0045-7825(93)90115-E CrossrefGoogle Scholar

  • [4] Choi K. K. and Kim N.-H., Structural Sensitivity Analysis and Optimization, Springer, New York, 2005. CrossrefGoogle Scholar

  • [5] Borggaard J. and Burns J., “A PDE Sensitivity Equation Method for Optimal Aerodynamic Design,” Journal of Computational Physics, Vol. 136, No. 2, 1997, pp. 366–384. doi:https://doi.org/10.1006/jcph.1997.5743 CrossrefGoogle Scholar

  • [6] Stanley L. G. D. and Stewart D., Design Sensitivity Analysis: Computational Issues of Sensitivity Equation Methods, Academic Press, Philadelphia, 2002. CrossrefGoogle Scholar

  • [7] Duvigneau R. and Pelletier D., “On Accurate Boundary Conditions for a Shape Sensitivity Equation Method,” International Journal for Numerical Methods in Fluids, Vol. 50, No. 2, 2006, pp. 147–164. doi:https://doi.org/10.1002/(ISSN)1097-0363 CrossrefGoogle Scholar

  • [8] Kulkarni M. D., Canfield R. A. and Patil M. J., “Nonintrusive Continuum Sensitivity Analysis for Aerodynamic Shape Optimization,” 15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper  2014-2043, June 2014. LinkGoogle Scholar

  • [9] Liu S. and Canfield R. A., “Boundary Velocity Method for Continuum Shape Sensitivity of Nonlinear Fluid–Structure Interaction Problems,” Journal of Fluids and Structures, Vol. 40, July 2013, pp. 284–301. doi:https://doi.org/10.1016/j.jfluidstructs.2013.05.003 CrossrefGoogle Scholar

  • [10] Cross D. and Canfield R., “Local Continuum Shape Sensitivity with Spatial Gradient Reconstruction,” Structural and Multidisciplinary Optimization, Vol. 50, No. 11, 2014, pp. 975–1000. doi:https://doi.org/10.1007/s00158-014-1092-0 CrossrefGoogle Scholar

  • [11] Kulkarni M. D., Canfield R. A., Patil M. J. and Alyanak E. J., “Integration of Geometric Sensitivity and Spatial Gradient Reconstruction for Aeroelastic Shape Optimization,” 10th AIAA Multidisciplinary Design Optimization Conference, AIAA Paper  2014-0470, Jan. 2014. LinkGoogle Scholar

  • [12] Lozano C. and Ponsin J., “Remarks on the Numerical Solution of the Adjoint Quasi-One-Dimensional Euler Equations,” International Journal for Numerical Methods in Fluids, Vol. 69, No. 5, 2012, pp. 966–982. doi:https://doi.org/10.1002/fld.v69.5 CrossrefGoogle Scholar

  • [13] Duivesteijn G. F., Bijl H., Koren B. and van Brummelen E. H., “On the Adjoint Solution of the Quasi-1D Euler Equations: The Effect of Boundary Conditions and the Numerical Flux Function,” International Journal for Numerical Methods in Fluids, Vol. 47, Nos. 8–9, 2005, pp. 987–993. doi:https://doi.org/10.1002/fld.922 CrossrefGoogle Scholar

  • [14] Liu S. and Canfield R. A., “Equivalence of Continuum and Discrete Analytic Sensitivity Methods for Nonlinear Differential Equations,” Structural and Multidisciplinary Optimization, Vol. 48, No. 11, Dec. 2013, pp. 1173–1188. doi:https://doi.org/10.1007/s00158-013-0951-4 CrossrefGoogle Scholar

  • [15] Wickert D. P., Canfield R. A. and Reddy J. N., “Least-Squares Continuous Sensitivity Shape Optimization for Structural Elasticity Applications,” AIAA Journal, Vol. 48, No. 12, 2010, pp. 2752–2762. doi:https://doi.org/10.2514/1.44349 LinkGoogle Scholar

  • [16] Cross D. M. and Canfield R. A., “Continuum Shape Sensitivity with Spatial Gradient Reconstruction of Nonlinear Aeroelastic Gust Response,” 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, AIAA Paper  2012-5597, Sept. 2012. LinkGoogle Scholar

  • [17] Borggaard J. and Burns J., “A Sensitivity Equation Approach to Shape Optimization in Fluid Flows,” NASA CR 191598, 1994. Google Scholar

  • [18] Arora J. S. and Haug E. J., “Methods of Design Sensitivity Analysis in Structural Optimization,” AIAA Journal, Vol. 17, No. 9, 1979, pp. 970–974. doi:https://doi.org/10.2514/3.61260 LinkGoogle Scholar

  • [19] Yang R. and Botkin M., “Comparison Between the Variational and Implicit Differentiation Approaches to Shape Design Sensitivities,” AIAA Journal, Vol. 24, No. 11, 1986, pp. 1027–1032. doi:https://doi.org/10.2514/3.9380 LinkGoogle Scholar

  • [20] Kulkarni M. D., Canfield R. A. and Patil M. J., “Discrete Adjoint Formulation for Continuum Sensitivity Analysis,” 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper  2015-0138, Jan. 2015. LinkGoogle Scholar

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