Finite element analysis of free material optimization problem

Jan Mach

Applications of Mathematics (2004)

  • Volume: 49, Issue: 4, page 285-307
  • ISSN: 0862-7940

Abstract

top
Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.

How to cite

top

Mach, Jan. "Finite element analysis of free material optimization problem." Applications of Mathematics 49.4 (2004): 285-307. <http://eudml.org/doc/33186>.

@article{Mach2004,
abstract = {Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.},
author = {Mach, Jan},
journal = {Applications of Mathematics},
keywords = {structural optimization; material optimization; topology optimization; finite elements; structural optimization; topology optimization; finite elements},
language = {eng},
number = {4},
pages = {285-307},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite element analysis of free material optimization problem},
url = {http://eudml.org/doc/33186},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Mach, Jan
TI - Finite element analysis of free material optimization problem
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 4
SP - 285
EP - 307
AB - Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.
LA - eng
KW - structural optimization; material optimization; topology optimization; finite elements; structural optimization; topology optimization; finite elements
UR - http://eudml.org/doc/33186
ER -

References

top
  1. 10.1016/S0045-7825(00)00284-X, Comput. Methods Appl. Mech. Engrg. 190 (2001), 3565–3579. (2001) MR1819157DOI10.1016/S0045-7825(00)00284-X
  2. 10.1137/S1052623497327994, SIAM J.  Optim. 9 (1999), 813–832. (1999) MR1724765DOI10.1137/S1052623497327994
  3. Optimization of Structural Topology, Shape and Material, Springer-Verlag, Heidelberg-Berlin, 1995. (1995) MR1350791
  4. 10.1007/BF01743387, Structural Optimization 6 (1993), 268–270. (1993) DOI10.1007/BF01743387
  5. 10.1002/nme.1620380705, Internat. J.  Numer. Methods Engrg. 38 (1995), 1149–1170. (1995) MR1325337DOI10.1002/nme.1620380705
  6. 10.1115/1.2901581, J.  Appl. Mech. 61 (1994), 930–937. (1994) MR1327483DOI10.1115/1.2901581
  7. Optimization of structures and material properties for solids composed of softening material, Int. J.  Solids Struct. 33 (1995), 1179–1813. (1995) 
  8. Mechanics of Continuum, NČSAV, Praha, 1959. (Czech) (1959) 
  9. Lectures on Optimization, Springer-Verlag, Berlin-Heidelberg-New York, 1978. (1978) Zbl0409.90050
  10. The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam-New York-Oxford, 1978. (1978) Zbl0383.65058MR0520174
  11. Convex Analysis and Variational Problems, North-Holland, Amsterdam-Oxford, 1976. (1976) MR0463994
  12. Measure Theory and Fine Properties of Functions, CRC  Press, London, 1992. (1992) MR1158660
  13. Finite element analysis for unilateral problems with obstacles on the boundary, Apl. Mat. 22 (1977), 180–188. (1977) Zbl0434.65083MR0440956
  14. Finite Element Approximation for Optimal Shape, Material, and Topology Design, John Wiley & Sons, Chichester, 1996. (1996) MR1419500
  15. Free Material Optimization, Doc. Math. J.  DMV, Extra Volume ICM III (1998), 707–716. (1998) MR1648200
  16. Les méthodes directes en théorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
  17. Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier, Amsterdam-Oxford-New York, 1981. (1981) MR0600655
  18. 10.1090/qam/1622499, Quart. Appl. Math. 56 (1998), 309–325. (1998) MR1622499DOI10.1090/qam/1622499
  19. 10.1007/BF01743590, Structural Optimization 5 (1993), 265–267. (1993) DOI10.1007/BF01743590
  20. 10.1007/BF02614328, Math. Program. Series  B 79 (1997), 445–466. (1997) MR1464778DOI10.1007/BF02614328

NotesEmbed ?

top

You must be logged in to post comments.