Contact shape optimization based on the reciprocal variational formulation

Jaroslav Haslinger

Applications of Mathematics (1999)

  • Volume: 44, Issue: 5, page 321-358
  • ISSN: 0862-7940

Abstract

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The paper deals with a class of optimal shape design problems for elastic bodies unilaterally supported by a rigid foundation. Cost and constraint functionals defining the problem depend on contact stresses, i.e. their control is of primal interest. To this end, the so-called reciprocal variational formulation of contact problems making it possible to approximate directly the contact stresses is used. The existence and approximation results are established. The sensitivity analysis is carried out.

How to cite

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Haslinger, Jaroslav. "Contact shape optimization based on the reciprocal variational formulation." Applications of Mathematics 44.5 (1999): 321-358. <http://eudml.org/doc/33037>.

@article{Haslinger1999,
abstract = {The paper deals with a class of optimal shape design problems for elastic bodies unilaterally supported by a rigid foundation. Cost and constraint functionals defining the problem depend on contact stresses, i.e. their control is of primal interest. To this end, the so-called reciprocal variational formulation of contact problems making it possible to approximate directly the contact stresses is used. The existence and approximation results are established. The sensitivity analysis is carried out.},
author = {Haslinger, Jaroslav},
journal = {Applications of Mathematics},
keywords = {shape optimization; contact problems; reciprocal variational formulation; sensitivity analysis; optimal shape design; unilateral contact; elasticity},
language = {eng},
number = {5},
pages = {321-358},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Contact shape optimization based on the reciprocal variational formulation},
url = {http://eudml.org/doc/33037},
volume = {44},
year = {1999},
}

TY - JOUR
AU - Haslinger, Jaroslav
TI - Contact shape optimization based on the reciprocal variational formulation
JO - Applications of Mathematics
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 5
SP - 321
EP - 358
AB - The paper deals with a class of optimal shape design problems for elastic bodies unilaterally supported by a rigid foundation. Cost and constraint functionals defining the problem depend on contact stresses, i.e. their control is of primal interest. To this end, the so-called reciprocal variational formulation of contact problems making it possible to approximate directly the contact stresses is used. The existence and approximation results are established. The sensitivity analysis is carried out.
LA - eng
KW - shape optimization; contact problems; reciprocal variational formulation; sensitivity analysis; optimal shape design; unilateral contact; elasticity
UR - http://eudml.org/doc/33037
ER -

References

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  1. Optimal design for elastic bodies in contact, Optimization of Distributed-Parameter Structures, Haug, E. J. and Céa, J. (eds.), Sijthoff and Noordhoff aan den Rijn, Holland, 1981, pp. 1553–1599. (1981) 
  2. 10.1080/01630568508816186, Numer. Funct. Anal. and Optimiz. 7 (1984), 145–156. (1984) MR0767379DOI10.1080/01630568508816186
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  4. Numerical Solution of Variational Inequalities, Springer Series in Applied Mathematical Sciences 66, Springer-Verlag, New York, 1988. (1988) 
  5. Shape optimization in unilateral contact problems using generalized reciprocal energy as objective functional, Nonlinear Analysis, Methods & Appl. 21 (1993), 815–834. (1993) MR1249662
  6. Finite Element Approximation for Optimal Shape Design: Theory and Applications, J. Wiley, Chichester-New York, 1988. (1988) MR0982710
  7. Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd Edition, J. Wiley, Chichester-New York, 1996. (1996) MR1419500
  8. Approximation of contact problems with friction by reciprocal variational formulation, Proc. Roy. Soc. Edingburgh 98A (1984), 365–383. (1984) MR0768357
  9. Contact Problems in Elasticity: A study of variational inequalities and finite element methods, SIAM, Philadelphia, 1988. (1988) MR0961258
  10. 10.1007/BF01743581, Struct. Opt. 5 (1993), 213–216. (1993) DOI10.1007/BF01743581
  11. Optimal Shape Design for Elliptic Systems, Springer series in Computational Physics, Springer-Verlag, New York, 1984. (1984) Zbl0534.49001MR0725856
  12. Introduction to Shape Optimization, Springer-Verlag, 1992. (1992) MR1215733

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