Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications

Authors : Roland Herzog, Christian Meyer, Gerd Wachsmuth

Published in: Trends in PDE Constrained Optimization

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. The forward system is reformulated such that it involves the plastic multiplier and a complementarity condition. In order to derive necessary optimality conditions, a family of regularized optimal control problems is analyzed. C-stationarity type conditions are obtained by passing to the limit with the regularization. Numerical results are presented.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Optimal Control of Allen-Cahn Systems
next chapter One-Shot Approaches to Design Optimzation
Literature
1.
V. Barbu, Optimal Control of Variational Inequalities. Research Notes in Mathematics, vol. 100. (Pitman, Boston, 1984)
2.
T. Betz, C. Meyer, Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening. To appear in ESAIM J. Control Optim. Calc. Var.
3.
J.C. de los Reyes, R. Herzog, C. Meyer, Optimal control of static elastoplasticity in primal formulation. Technical report SPP1253-151, Priority Program 1253, German Research Foundation, 2013
4.
P. Grisvard, Elliptic Problems in Nonsmooth Domains (Pitman, Boston, 1985)MATH
5.
K. Gröger, Initial value problems for elastoplastic and elastoviscoplastic systems, in Nonlinear Analysis, Function Spaces and Applications (Proceedings of Spring School, Horni Bradlo, 1978) (Teubner, Leipzig, 1979), pp. 95–127
6.
K. Gröger, A W 1, p -estimate for solutions to mixed boundary value problems for second order elliptic differential equations. Mathematische Annalen 283, 679–687 (1989). doi:10.1007/BF01442860CrossRefMATHMathSciNet
7.
R. Haller-Dintelmann, C. Meyer, J. Rehberg, A. Schiela, Hölder continuity and optimal control for nonsmooth elliptic problems. Appl. Math. Optim. 60(3), 397–428 (2009). doi:10.1007/s00245-009-9077-xCrossRefMATHMathSciNet
8.
9.
R. Herzog, C. Meyer, Optimal control of static plasticity with linear kinematic hardening. J. Appl. Math. Mech. 91(10), 777–794 (2011). doi:10.1002/zamm.200900378MATHMathSciNet
10.
R. Herzog, C. Meyer, G. Wachsmuth, Integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions. J. Math. Anal. Appl. 382(2), 802–813 (2011). doi:10.1016/j.jmaa.2011.04.074CrossRefMATHMathSciNet
11.
R. Herzog, C. Meyer, G. Wachsmuth, Existence and regularity of the plastic multiplier in static and quasistatic plasticity. GAMM Rep. 34(1), 39–44 (2011). doi:10.1002/gamm.201110006CrossRefMATHMathSciNet
12.
R. Herzog, C. Meyer, G. Wachsmuth, C-stationarity for optimal control of static plasticity with linear kinematic hardening. SIAM J. Control Optim. 50(5), 3052–3082 (2012). doi:10.1137/100809325CrossRefMATHMathSciNet
13.
R. Herzog, C. Meyer, G. Wachsmuth, B- and strong stationarity for optimal control of static plasticity with hardening. SIAM J. Optim. 23(1), 321–352 (2013). doi:10.1137/110821147CrossRefMATHMathSciNet
14.
M. Hintermüller, I. Kopacka, Mathematical programs with complementarity constraints in function space: C- and strong stationarity and a path-following algorithm. SIAM J. Optim. 20(2), 868–902 (2009). ISSN 1052-6234. doi:10.1137/080720681
15.
T. Hoheisel, C. Kanzow, A. Schwartz, Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints. Math. Program. 137(1–2), 257–288 (2013). doi:10.1007/s10107-011-0488-5CrossRefMATHMathSciNet
16.
17.
A. Logg, K.-A. Mardal, G. N. Wells et al., Automated Solution of Differential Equations by the Finite Element Method (Springer, Berlin/New York, 2012). ISBN 978-3-642-23098-1. doi:10.1007/978-3-642-23099-8CrossRefMATH
18.
C. Meyer, O. Thoma, A priori finite element error analysis for optimal control of the obstacle problem. SIAM J. Numer. Anal. 51(1), 605–628 (2013)CrossRefMATHMathSciNet
19.
20.
21.
H. Scheel, S. Scholtes, Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Math. Oper. Res. 25(1), 1–22 (2000). doi:10.1287/moor.25.1.1.15213CrossRefMATHMathSciNet
22.
A. Schiela, D. Wachsmuth, Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints. ESAIM Math. Model. Numer. Anal. 47(3), 771–787 (2013). doi:10.1051/m2an/2012049CrossRefMATHMathSciNet
23.
G. Wachsmuth, Optimal control of quasistatic plasticity – An MPCC in function space. PhD Thesis, Chemnitz University of Technology, 2011
24.
G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, Part I: existence and discretization in time. SIAM J. Control Optim. 50(5), 2836–2861 (2012). doi:10.1137/110839187MATHMathSciNet
25.
G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, Part II: regularization and differentiability. Technical report, TU Chemnitz, 2012
26.
G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, Part III: optimality conditions. Technical report, TU Chemnitz, 2012
27.
G. Wachsmuth, Differentiability of implicit functions. J. Math. Anal. Appl. 414(1), 259–272 (2014), doi: 10.1016/j.jmaa.2014.01.007CrossRefMathSciNet
28.
G. Wachsmuth, Strong stationarity for optimal control of the obstacle problem with control constraints. To appear SIAM J. Optim.
Metadata
Title
Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications
Authors
Roland Herzog
Christian Meyer
Gerd Wachsmuth
Copyright Year
2014
Book
Trends in PDE Constrained Optimization

Print ISBN: 978-3-319-05082-9

Electronic ISBN: 978-3-319-05083-6

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-05083-6_4