Abstract
Almost any machine part is dynamically loaded and fails in most cases by fatigue. Nevertheless many authors recommend just a static shape optimization based on the minimization of maximum stress to improve the lifetime. In this paper a more detailed description of fatigue within continuum damage mechanics (CDM) considering the loading history is introduced. On this basis, two new cost functions are determined for shape optimization of dynamically loaded machine parts. An optimization procedure is built up using the methods of mathematical programming (MP). The optimized parts show a remarkably increased lifetime in numerical results as well as in experiments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fanni, M.; Schnack, E.; Grunwald J. 1994: Lifetime maximixation through shape optimization of dynamically loaded machine parts.Int. J. Eng. Analysis & Design 1, 25–41
Fanni, M. 1993:Formoptimierung dynamisch belasteter Bauteile. Dissertation, University of Karlsruhe
Grunwald, J.; Schnack, E. 1995: Models for shape optimization of dynamically loaded machine parts. In: Olhoff, N.; Rozvany, G.I.N. (eds.)WCSMO — 1. First World Congress on Structural and Multidisciplinary Optimization (held in Goslar May 28 to June 2, 1995), pp. 307–314. Oxford: Pergamon
Grunwald, J. 1996:A fatigue model for shape optimization based on continuum damage mechanics. Dissertation, University of Karlsruhe
Kachanov, L.M. 1986:Introduction to continuum damage mechanics. Dordrecht: Martinus Nijhoff
Lemaitre, J.; Chaboche, J.L. 1990:Mechanics of solid materials. Cambridge University Press
Lemaitre, J.; Doghri, J. 1994: Damage 90. A postprocessor for crack initiation.Comp. Meth. Appl. Mech. Eng 115, 197–232
Lemaitre, J. 1992:A course on damage mechanics. Berlin, Heidelberg, New York: Springer
Marquis, D.; Lemaitre, J. 1989: Modelling complex behavior of Metals by state kinetic coupling theory.J. Eng. Mater. Tech. 114, 250–254
Schittkowski, K. 1981: The nonlinear programming method of Wilson, Han and Powell with an augmented Lagrangian type line search function. Part 1: Convergence analysis; Part 2: An efficient implementation with linear least squares subproblems.Numerische Mathematik 38, 83–127
Schittkowski, K. 1984/85: NLPQL. A Fortran subroutine solving constrained nonlinear programming problems.Annals of Operation Research 5, 485–500
Schnack, E. 1979: An optimization procedure for stress concentrations by the finite element technique.Int. J. Num. Meth. Eng. 14 1, 115–124
Schnack, E.; Iancu G. 1989: Shape design of elastostatic structures based on local perturbation analysis.Struct. Optim. 1, 117–125
Schnack, E.; Spörl, U.; Iancu, G. 1988: Gradientless shape optimization with FEM.VDI Forschungsheft, VDI Verlag 647/88
Taylor, G.I. 1938: Plastic strain in metals.J. Inst. Met., 62–307
Zienkiewicz, O.C.; Zhu, J.Z. 1987: A simple error estimator and adaptive procedure for practical engineering analysis.Int. J. Num. Meth. Eng. 24, 337–357.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Grunwald, J., Schnack, E. A fatigue model for shape optimization. Structural Optimization 14, 36–44 (1997). https://doi.org/10.1007/BF01197556
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01197556