Open Access
Volume 28, 2022
Article Number 47
Number of page(s) 40
Published online 07 July 2022
  1. G. Allaire, Shape optimization by the homogenization method. Vol. 146 of Applied Mathematical Sciences. Springer-Verlag, New York (2002). [CrossRef] [Google Scholar]
  2. S. Almi and U. Stefanelli, Topology optimization for incremental elastoplasticity: a phase-field approach. SIAM J. Control Optim. 59 (2021) 339–364. [CrossRef] [MathSciNet] [Google Scholar]
  3. M.P. Bendsoe and O. Sigmund, Topology optimization. Theory, methods and applications. Springer-Verlag, Berlin (2003). [Google Scholar]
  4. L. Blank, H. Garcke, C. Hecht and C. Rupprecht, Sharp interface limit for a phase field model in structural optimization. SIAM J. Control Optim. 54 (2016) 1558–1584. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Blank, H. Garcke, M.H. Farshbaf-Shaker and V. Styles, Relating phase field and sharp interface approaches to structural topology optimization. ESAIM: COCV 20 (2014) 1025–1058. [CrossRef] [EDP Sciences] [Google Scholar]
  6. M. Boissier, J. Deaton, P. Beran and N. Vermaak, Elastoplastic topology optimization and cyclically loaded structures via direct methods for shakedown. Struct. Multidisc. Optim. 64 (2021) 189–217. [CrossRef] [Google Scholar]
  7. B. Bourdin and A. Chambolle, Design-dependent loads in topology optimization. ESAIM: COCV 9 (2003) 19–48. [CrossRef] [EDP Sciences] [Google Scholar]
  8. M. Burger and R. Stainko, Phase-field relaxation of topology optimization with local stress constraints. SIAM J. Control Optim. 45 (2006) 1447–1466. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Carraturo, E. Rocca, E. Bonetti, D. Homberg, A. Reali and F. Auricchio, Graded-material design based on phase-field and topology optimization. Comput. Mech. 64 (2019) 1589–1600. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.C. de los Reyes, R. Herzog and C. Meyer, Optimal control of static elastoplasticity in primal formulation. SIAM J. Control Optim. 54 (2016) 3016–3039. [CrossRef] [MathSciNet] [Google Scholar]
  11. K. Gröger, A W1,p-estimate for solutions to mixed boundary value problems for second order elliptic differential equations. Math. Ann. 283 (1989) 679–687. [Google Scholar]
  12. W. Han and B.D. Reddy, Plasticity, Interdisciplinary Applied Mathematics. Springer, New York (2013). [CrossRef] [Google Scholar]
  13. J. Haslinger and P. Neittaanmöaki, On the existence of optimal shapes in contact problems-perfectly plastic bodies. Comput. Mech. 1 (1986) 293–299. [Google Scholar]
  14. J. Haslinger, P. Neittaanmaöki and T. Tiihonen, Shape optimization in contact problems. 1. Design of an elastic body. 2. Design of an elastic perfectly plastic body. Analysis and Optimization of Systems, Springer (1986) 29–39. [CrossRef] [Google Scholar]
  15. R. Herzog, C. Meyer and G. Wachsmuth, Integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions. J. Math. Anal. Appl. 382 (2011) 802–813. [Google Scholar]
  16. R. Herzog, C. Meyer and G. Wachsmuth, C-stationarity for optimal control of static plasticity with linear kinematic hardening. SIAM J. Control Optim. 50 (2012) 3052–3082. [CrossRef] [MathSciNet] [Google Scholar]
  17. I. Hlavacek, Shape optimization of elastoplastic bodies obeying Hencky's law. Appl. Mater. 31 (1986) 486–499. [Google Scholar]
  18. I. Hlavâcek, Shape optimization of an elastic-perfectly plastic body. Appl. Mater. 32 (1987) 381–400. [Google Scholar]
  19. I. Hlavâcek, Shape optimization of elastoplastic axisymmetric bodies. Appl. Math. 36 (1991) 469–491. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. Karkauskas, Optimization of elastic-plastic geometrically non-linear lightweight structures under stiffness and stability constraints. J. Civil Eng. Manag. 10 (2004) 97–106. [Google Scholar]
  21. M. Khanzadi and M. Tavakkoli, Optimal plastic design of frames using evolutionary structural optimization. Int. J. Civil Eng. 9 (2011) 175–170. [Google Scholar]
  22. P. KrejCi, Evolution variational inequalities and multidimensional hysteresis operators. Technical Report 432, Weierstrass Institute for Applied Analysis and Stochastics (WIAS) (1998). [Google Scholar]
  23. A. Maury, G. Allaire and F. Jouve, Elasto-plastic shape optimization using the level set method. SIAM J. Control Optim. 56 (2018) 556–581. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Mielke, Evolution in rate-independent systems. In Vol. 2 of Handbook of Differential Equations, Evolutionary Equations. Edited by C. Dafermos and E. Feireisl. Elsevier (2005) 461–559. [CrossRef] [Google Scholar]
  25. A. Mielke and T. Roubföek, Rate-independent systems. Vol. 193 of Applied Mathematical Sciences. Springer, New York (2015). Theory and application. [CrossRef] [Google Scholar]
  26. A. Mielke, T. Roubföek and U. Stefanelli, T-limits and relaxations for rate-independent evolutionary problems. Calc. Var. Partial Differ. Equ. 31 (2008) 387–416. [CrossRef] [Google Scholar]
  27. L. Modica and S. Mortola, Un esempio di T--convergenza. Boll. Un. Mat. Ital. B 14 (1977) 285–299. [MathSciNet] [Google Scholar]
  28. C.B.W. Pedersen, Topology optimization of 2D-frame structures with path-dependent response. Internat. J. Numer. Methods Eng. 57 (2003) 1471–1501. [CrossRef] [Google Scholar]
  29. P. Penzler, M. Rumpf and B. Wirth, A phase-field model for compliance shape optimization in nonlinear elasticity. ESAIM: COCV 18 (2012) 229–258. [CrossRef] [EDP Sciences] [Google Scholar]
  30. F. Rindler, Optimal control for nonconvex rate-independent evolution processes. SIAM J. Control Optim. 47 (2008) 2773–2794. [Google Scholar]
  31. F. Rindler, Approximation of rate-independent optimal control problems. SIAM J. Numer. Anal. 47 (2009) 3884–3909. [Google Scholar]
  32. J. Sokolowski and J.-P. Zolesio, Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer Ser. Comput. Math. 16. Springer-Verlag, Berlin (1992). [CrossRef] [Google Scholar]
  33. G. Wachsmuth, Optimal control of quasi-static plasticity with linear kinematic hardening, Part I: Existence and discretization in time. SIAM J. Control Optim. 50 (2012) 2836–2861 + loose erratum. [CrossRef] [MathSciNet] [Google Scholar]
  34. G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening II: regularization and differentiability. Z. Anal. Anwend. 34 (2015) 391–418. [CrossRef] [MathSciNet] [Google Scholar]
  35. G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening III: optimality conditions. Z. Anal. Anwend. 35 (2016) 81–118. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.