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Articles

Challenges and solutions to arc-length controlled structural shape design problems

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Pages 4088-4119 | Received 13 Nov 2020, Accepted 29 Jun 2021, Published online: 28 Jul 2021

References

  • Bashir-Ahmed, M., and S. U. Xiao-zu. 2004. Arc-length technique for nonlinear finite element analysis. Journal of Zhejiang University SCIENCE 5 (5):618–28.
  • Bhattacharyya, A., C. Conlan-Smith, and K. A. James. 2019. Design of a bi-stable airfoil with tailored snap-through response using topology optimization. Computer-Aided Design 108:42–55. doi:10.1016/j.cad.2018.11.001.
  • Bruns, T. E., and O. Sigmund. 2004. Toward the topology design of mechanisms that exhibit snap-through behavior. Computer Methods in Applied Mechanics and Engineering 193 (36–38):3973–4000. doi:10.1016/j.cma.2004.02.017.
  • Bruns, T. E., O. Sigmund, and D. A. Tortorelli. 2002. Numerical methods for the topology optimization of structures that exhibit snap-through. International Journal for Numerical Methods in Engineering 55 (10):1215–37. doi:10.1002/nme.544.
  • Crisfield, M. A. 1981. A fast incremental/iterative solution procedure that handles snap-through. Computers & Structures 13 (1–3):55–62. doi:10.1016/0045-7949(81)90108-5.
  • DaDeppo, D., and E. Schmidt. 1975. Instability of clamped-hinged circular arches subjected to a point load. Journal of Applied Mechanics 42 (4):894–6. doi:10.1115/1.3423734.
  • Deng, H., L. Cheng, X. Liang, D. Hayduke, and A. C. To. 2020. Topology optimization for energy dissipation design of lattice structures through snap-through behavior. Computer Methods in Applied Mechanics and Engineering 358:112641. doi:10.1016/j.cma.2019.112641.
  • Hisada, T. 1995. Recent progress in nonlinear FEM-based sensitivity analysis. JSME International Journal 38 (3):430–3.
  • Keller, H. B. 1979. Constructive methods for bifurcation and nonlinear eigenvalue problems. In Computing methods in applied sciences and engineering, 1977, ed. I. R. Glowinski, J. L. Lions, and I. Laboria, 241–51. Berlin, Heidelberg: Springer Berlin Heidelberg.
  • Kok, S., and D. N. Wilke. 2015. Optimizing snap-through structures by using gradient-only algorithms. In 11th World Congress on Structural and Multidisciplinary Optimisation, 7–12, Sydney, Australia.
  • Kraft, D. 1988. A software package for sequential quadratic programming. Tech. Rep., DLR German Aerospace Center Institute for Flight Mechanics, Koln, Germany.
  • Leahu-Aluas, I., and F. Abed-Meraim. 2011. A proposed set of popular limit-point buckling benchmark problems. Structural Engineering and Mechanics 38 (6):767–802. doi:10.12989/sem.2011.38.6.767.
  • Olhoff, N., and E. Lund. 1995. Finite element based engineering design sensitivity analysis and optimization. PhD diss., Aalborg University.
  • Parente, J., and L. E. Vaz. 2003. On evaluation of shape sensitivities of non-linear critical loads. International Journal for Numerical Methods in Engineering 56 (6):809–46. doi:10.1002/nme.587.
  • Pian, T. H., and K. Sumihara. 1984. Rational approach for assumed stress finite elements. International Journal for Numerical Methods in Engineering 20 (9):1685–95. doi:10.1002/nme.1620200911.
  • Rheinboldt, W. C. 1978. Numerical methods for a class of finite dimensional bifurcation problems. SIAM Journal on Numerical Analysis 15 (1):1–11. doi:10.1137/0715001.
  • Riks, E. 1972. The application of newton’s method to the problem of elastic stability. Journal of Applied Mechanics 39 (4):1060–5. doi:10.1115/1.3422829.
  • Ritto-Corrêa, M., and D. Camotim. 2008. On the arc-length and other quadratic control methods: Established, less known and new implementation procedures. Computers & Structures 86 (11–12):1353–68. doi:10.1016/j.compstruc.2007.08.003.
  • Ryu, Y. S., M. Haririan, C. C. Wu, and J. S. Arora. 1985. Structural design sensitivity analysis of nonlinear response. Computers & Structures 21 (1–2):245–55. doi:10.1016/0045-7949(85)90247-0.
  • Sekimoto, T., and H. Noguchi. 2001. Homologous topology optimization in large displacement and buckling problems. JSME International Journal Series A 44 (4):616–22. doi:10.1299/jsmea.44.616.
  • Snyman, J. A., and D. N. Wilke. 2018. Practical mathematical optimization. 2nd ed. Springer International Publishing.
  • Wilke, D. 2010. Approaches to accommodate remeshing in shape optimization. PhD diss., University of Pretoria.
  • Wilke, D. 2011. Modified subgradient methods for remeshing based structural shape optimization. In Proceedings of the 13th International Conference on Civil, Structural and Environmental Engineering Computing. Crete, Greece.
  • Wilke, D. 2012. Structural shape optimization using shors r-algorithm. In Third International Conference on Engineering Optimization. Rio de Janeiro, Brazil.
  • Wilke, D., S. Kok, and A. Groenwold. 2013. Relaxed error control in shape optimization that utilizes remeshing. International Journal for Numerical Methods in Engineering 94 (3):273–89. doi:10.1002/nme.4445.
  • Wilke, D., J. Snyman, S. Kok, and A. Groenwold. 2013. Gradient-only approaches to avoid spurious local minima in unconstrained optimization. Optimization and Engineering 14 (2):275–304. doi:10.1007/s11081-011-9178-7.
  • Wilke, D. N., and S. Kok. 2014. Numerical sensitivity computation for discontinuous gradient-only optimization problems using the complex-step method. Proceedings of the Tenth World Congress on Computational Mechanics (WCCM 2012) 1:3665–76.
  • Wilke, D. N., S. Kok, and A. A. Groenwold. 2010. The application of gradient-only optimization methods for problems discretized using non-constant methods. Structural and Multidisciplinary Optimization 40 (1–6):433–51. doi:10.1007/s00158-009-0389-x.

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