Abstract
This paper presents a hierarchical neighbourhood search method for solving topology optimization problems defined on discretized linearly elastic continuum structures. The design of the structure is represented by binary design variables indicating material or void in the various finite elements.
Two different designs are called neighbours if they differ in only one single element, in which one of them has material while the other has void. The proposed neighbourhood search method repeatedly jumps to the “best” neighbour of the current design until a local optimum has been found, where no further improvement can be made. The “engine” of the method is an efficient exploitation of the fact that if only one element is changed (from material to void or from void to material) then the new global stiffness matrix is just a low-rank modification of the old one. To further speed up the process, the method is implemented in a hierarchical way. Starting from a coarse finite element mesh, the neighbourhood search is repeatedly applied on finer and finer meshes.
Numerical results are presented for minimum-weight problems with constraints on respectively compliance, strain energy densities in all non-void elements, and von Mises stresses in all non-void elements.
Similar content being viewed by others
References
Bend Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202
BendSig Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654
TopOpt Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Berlin Heidelberg New York
Cook Cook RD, Malkus DS, Plesha ME (1989) Concepts and appplications of finite element analysis. Wiley, New York
Olhoff Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54:331–390
Matrix Golub GH, Van Loan CF (1983) Matrix computations. North Oxford Academic, Oxford
Rozvany Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4:250–252
StolpeSvanberg Stolpe M, Svanberg K (2001) An alternative interpolation model for minimum compliance topology optimization. Struct Multidisc Optim 22(2):116–124
LinStSv Stolpe M, Svanberg K (2003) Modelling topology optimization problems as linear mixed 0-1 programs. Int J Numer Methods Eng 57:723–739
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Svanberg, K., Werme, M. A hierarchical neighbourhood search method for topology optimization. Struct Multidisc Optim 29, 325–340 (2005). https://doi.org/10.1007/s00158-004-0493-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-004-0493-x