CIRCULAR PLATE UNDER UNIFORM PRESSURE AND A BENDING MOMENT



Loads and boundary conditions



Mechanical and geometrical characteristics



Loading case



where









Comparison with existing results

Influence of material damage


[1] Hachemi, A. and Weichert, D.: Numerical shakedown analysis of damaged structures. Comput. Methods Appl. Mech. Engrg. 160, 57-70 (1998).
[2] König, J.A.: Shakedown theory of plates. Arch. Mech. Stos. 5, 623-637 (1969).
[3] Morelle, P.: Analyse duale de líadaptation plastique des structures par la méthode des éléments finis et la programmation mathématique. Ph.D. Thesis, Université de Liège (1989).

CIRCULAR PLATE UNDER UNIFORM PRESSURE AND VARIABLE TEMPERATURE



Loads and boundary conditions



Mechanical and geometrical characteristics



Loading case



where









Comparison with existing results

Influence of material damage


[1] Hachemi, A. and Weichert, D.: Numerical shakedown analysis of damaged structures. Comput. Methods Appl. Mech. Engrg. 160, 57-70 (1998).
[2] Gokhfeld, D.A. and Cherniavsky, O. F.: Limit analysis of structures at thermal cycling. Sijthoff and Noordhoff, Leyden (1980).

CYLINDRICAL SHELL UNDER INTERNAL PRESSURE AND VARIABLE TEMPERATURE



Loads and boundary conditions



Mechanical and geometrical characteristics



Loading case



where





Perfectly plastic behaviour




Influence of kinematical hardening


[1] Hachemi, A.: Contribution à líanalyse de líadaptation des structures inélastiques avec prise en compte de líendommagement. Ph. D. thesis, Université des Sciences et Technologies de Lille (1994).

CYLINDRICAL SHELL UNDER INTERNAL PRESSURE AND A BENDING MOMENT



Loads and boundary conditions



Mechanical and geometrical characteristics



Loading case



where









Influence of material damage

(Comparison with an incremental method)


[1] Hachemi, A. and Weichert, D.: Numerical shakedown analysis of damaged structures. Comput. Methods Appl. Mech. Engrg. 160, 57-70 (1998).

CYLINDRICAL SHELL UNDER INTERNAL PRESSURE



Loads and boundary conditions



Mechanical and geometrical characteristics



Loading case



with






Influence of geometrical nonlinearities

and ductile damage


[1] Weichert, D. and Hachemi, A.: Influence of geometrical nonlinearities on the shakedown of damaged structures. Int. J. Plasticity 14, 891-907 (1998).

CYLINDRICAL SHELL UNDER INTERNAL PRESSURE AND A BENDING MOMENT



Loads and boundary conditions



Mechanical and geometrical characteristics



Loading case



where






Influence of geometrical nonlinearities

and ductile damage


[1] Weichert, D. and Hachemi, A.: Influence of geometrical nonlinearities on the shakedown of damaged structures. Int. J. Plasticity 14, 891-907 (1998).

CONICAL SHELL UNDER INTERNAL PRESSURE AND AN AXIAL RING LOAD



Loads and boundary conditions



Mechanical and geometrical characteristics



Loading case



where






Influence of geometrical nonlinearities

and ductile damage


[1] Weichert, D. and Hachemi, A.: Influence of geometrical nonlinearities on the shakedown of damaged structures. Int. J. Plasticity 14, 891-907 (1998).

FIBER-REINFORCED COMPOSITES



Considered composite



Mechanical characteristics



Loading case





Quadratic arrangement




Hexagonal arrangement


Variation of macroscopic stress with fiber volume fraction

[1] Du, Z.Z., McMeeking, R.M. and Schmauder, S.: Transverse yielding and matrix flow past the fibers in metal matrix composites. Mech. Mat. 21: 159167 (1995).
[2] Ponter, A.R.S., Carter, K.F. and Duggan, J.M.: Shakedown limits for a metal matrix composite. Private Communication (1998).
[3] Schwabe, F.:. Einspieluntersuchungen von Verbundwerkstoffen mit periodischer Mikrostruktur. Ph. D. thesis, RWTH Aachen (2000).