Abstract
In this paper we present a formulation of the wellknown structural topology optimization problem that accounts for the presence of loads capable of causing permanent damage to the structure. Damage is represented in the form of an internal variable model which is standard in continuum damage mechanics. Here we employ an interpretation of this model as an optimum remodeling problem for maximal compliance over all damage distributions, making also the analysis of the damage model a study in structural optimization. The damage criterion can be included in the optimal design model in a number of ways. We present results for finding the optimal topology of the reinforcement of an existing design with the goal of minimizing damage. Also, we treat the problem of finding the topology of a structure where we seek maximal stiffness under service loads with a constraint on the amount of damage which occurs under a separate set of damage loads.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Achtziger, W.; Bendsøe, M.P.; Taylor, J.E. 1998: Bounds on the effect of progressive structural degradation.J. Mech. Phys. Solids,46, 1055–1087
Allaire, G.: Aubry, S.; Jouve, F. 1997: Simulation numerique de l'endommagement a l'aide du modele Francfort-Marigo.Proc. Congres National d'Analyse Numerique, Imbourg, France
Allaire, G.; Francfort, G.A. 1993: A numerical algorithm for topology and shape optimization. In Bendsøe, M.P.; Mota Soares C.A. (eds.)Topology optimization of structures, pp. 239–248. Dordrecht: Kluwer
Allaire, G.; Kohn, R.V. 1993a: Explicit bounds on the elastic energy of a two-phase composite in two space dimensions.Q. Appl. Math. 51, 675–699
Allaire, G.; Kohn, R.V. 1993b: Optimal design for minimum weight and compliance in plane stress using extremal microstructures.Euro. J. Mech. A12, 839–878
Bendsøe, M.P. 1995:Optimization of structural topology, shape and material. Berlin, Heidelberg, New York: Springer
Francfort, G.A.; Marigo, J.-J. 1993: Stable damage evolution in a brittle continuous medium.Eur. J. Mech. A/Solids 12, 149–189
Jog, C.; Haber, R.B.; Bendsøe, M.P. 1994: Topology design with optimized, self-adaptive materials.Int. J. Num. Meth. Engng. 37, 1323–1350
Krajcinovic, D. 1996:Damage mechanics. Amsterdam: Elsevier Science
Lemaitre, J. 1996:A course on damage mechanics, 2-nd edition. Berlin, Heidelberg, New York: Springer
Lemaitre, J.; Chaboche, J.L. 1990:Mechanics of solid materials. Cambridge: Cambridge University Press
Michelaris, P.; Tortorelli, D.A.; Vidal, C. 1994: Tangent operators and sensitivity formulations for transient nonlinear coupled problems with applications to elasto-plasticity.Int. J. Num. Meth. Engng. 37, 2471–2500
Min, S.; Kikuchi, N.; Park, Y.C.; Kim, S.; Chang, S. 1997: Optimal reinforcement design of structures under impact loads. In: Gutkowski, W.; Mroz, Z. (eds.)Proc. 2-nd World Cong. of Structural and Multidisciplinary Optimization, pp. 583–588. Warsaw: Inst. of Fundamental Technological Research
Mlejnik, H.P.; Schirrmacher, R. 1993: An engineering approach to optimal material distribution and shape finding.Comp. Meth. Appl. Mech. Engng. 106, 1–26
Olhoff, N.; Taylor, J.E. 1979: On optimal structural remodeling.JOTA 27, 571–582
Pedersen, P. 1989: On optimal orientation of orthotropic materials.Struct. Optim. 1, 101–106
Rozvany, G.I.N.; Zhou, M.; Sigmund, O. 1994: Topology optimization in structural design. In: Adeli, H. (ed.)Advances in design optimization, pp. 340–399. London: Chapman and Hall
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bendsøe, M.P., Díaz, A.R. A method for treating damage related criteria in optimal topology design of continuum structures. Structural Optimization 16, 108–115 (1998). https://doi.org/10.1007/BF01202821
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01202821