Abstract
Recent results obtained by using the lower-bound theorem of shakedown analysis are presented in this paper together with a new method for solving large-scale problems by using a selective algorithm. Industrially important examples from mechanical and pavement engineering are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aboudi, A.J., Sloan, S.W.: A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion. Computers and Structures 54, 427–441 (1995).
Akoa, F., Hachemi, A., Le Thi Hoai An, Mouhtamid, S., Pham Dinh Tao: Application of lower bound direct method to engineering structures. J. Global Optim. 37, 609–630 (2007).
An Danh Nguyen: Lower-bound shakedown analysis of pavements by using the interior point method. Doctor thesis, RWTH Aachen (2007).
Ansys Release 8.0: Ansys, Inc. Southpointe 275 Technology Drive Canonsburg, PA 15317.
Cloud, R.L., Rodabaugh, E.C.: Approximate analysis of the plastic limit pressures of nozzles in cylindrical shells. Trans. ASME, J. Engrg. Power 4, 171–176 (1968).
Conn, A.R., Gould, N.I.M., Toint, Ph.L.: LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization (Release A). Berlin, Springer-Verlag (1992).
Feige, A.: Das Traglast-Berechnungsverfahren, 2. Aufl.; Verlag Stahleisen, Düsseldorf (1980).
Gokhfeld, D.A., Cherniavsky, O.F.: Limit analysis of structures at thermal cycling. Sijthoff and Noordhoff (1980).
Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985).
Johnson, K.L.: The application of shakedown principles in rolling and sliding contact. Eur. J. Mech. A/Solids 11, 155–172 (1992).
Koiter, W.T.: General theorems for elastic-plastic solids. In: Sneddon, I.N., Hill, R. (eds.), Progress in Solid Mechanics. North-Holland, Amsterdam, pp. 165–221 (1960).
König, J.A.: Shakedown of elastic-plastic structures. Elsevier, Amsterdam (1987).
Le Thi Haoi An, Pham Dinh Tao: The DC (difference of convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23–46 (2005).
Maier, G., Pastor, J., Ponter, A.R.S., Weichert, D.: Direct Methods of Limit and Shakedown Analysis. In: De Borst, R.; Mang, H. A. (eds.), Numerical and computational methods, Chapter 12, Vol. 3. In: Milne, I., Ritchie, R. O.; Karihaloo, B. (eds.), Comprehensive Structural Integrity. Elsevier-Pergamon, Amsterdam (2003).
Martin, G.B.: Plasticity: Fundamentals and General Results. MIT Press, Cambridge, MA (1975).
Melan, E.: Zur Plastizität des räumlichen Kontinuums. Ing. Arch. 9, 116–126 (1938).
Mouhtamid, S.: Anwendung direkter Methoden zur industriellen Berechnung von Grenzlasten mechanischer Komponenten. Doctor thesis, RWTH Aachen (2007).
Nayak G.C., Zienkiewicz O.C.: Conventional form of stress invariants for plasticity. J. Struct. Div., Proc. American Society Civil Engineers 98, 949–954 (1972).
Nguyen An Danh, Hachemi, A., Weichert, D.: Application of the interior-point method to shakedown analysis of pavements. Int. J. Numer. Meth. Engng. 75, 414–439 (2008).
Sharp, R.W., Booker, J.R.: Shakedown of pavements under moving surface loads. J. Transp. Enrg. 110, 1–14 (1984).
Vu, D.K.: Dual limit and shakedown analysis of structures. Doctor thesis, University of Liege Faculty of Applied Sciences (2001).
Wagner, W.: Festigkeitsberechnungen im Apparate- und Rohrleitungsbau. Vogel Buchverlag, Würzburg (1991).
Weichert, D., Maier, G.: Inelastic Behaviour of Structures under Variable Repeated Loads: Direct Analysis methods. CISM Courses and Lectures No. 432, International Centre for Mechanical Sciences, Springer Wien-New York (2002).
Wellinger, K, Dietmann, H.: Festigkeitsberechnung. Alfred Kröner Verlag, Stuttgart (1969).
Wächter, A., Biegler, L.T.: On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Non-linear Programming. IBM Research Report RC 23149 IBM T. J. Watson Research Center March, Yorktown Heights, NY. USA, pp. 1–28 (2004).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Hachemi, A., Mouhtamid, S., Nguyen, A., Weichert, D. (2009). Application of Shakedown Analysis to Large-Scale Problems with Selective Algorithm. In: Dieter, W., Alan, P. (eds) Limit States of Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9634-1_15
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9634-1_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9633-4
Online ISBN: 978-1-4020-9634-1
eBook Packages: EngineeringEngineering (R0)