Limit Analysis of FGM Circular Plates Subjected to Arbitrary Rotational Symmetric Loads
The limit load carrying capacity of functionally
graded materials (FGM) circular plates subjected to an arbitrary
rotationally symmetric loading has been computed. It is provided that
the plate material behaves rigid perfectly plastic and obeys either the
Square or the Tresca yield criterion. To this end the upper and lower
bound principles of limit analysis are employed to determine the
exact value for the limiting load. The correctness of the result are
verified and finally limiting loads for two examples namely; through
radius and through thickness FGM circular plates with simply
supported edges are calculated, respectively and moreover, the values
of critical loading factor are determined.
[1] W. Prager, "An introduction to plasticity" Reading, MA: Addison-
Wesley; 1959.
[2] M. R. Horne, "Plastic theory of structures". Cambridge, MA: MIT;
1971.
[3] E. H. Mansfield, "Studies in collapse analysis of rigid-plastic plates with
a square yield diagram", Proc. R. Soc. A; pp.241:311-38, 1958.
[4] P.G. Hodge, "Limit analysis of rotationally symmetric plates and shells",
Englewood Cliffs, NJ: Prentice-Hall; 1963.
[5] M.A. Save, "Massonnet CE. Plastic analysis and design of plates, shells
and disks. Amsterdam", North-Holland; 1972.
[6] Z. Sobotka, "Theory of plasticity and limit design of plates",
Amsterdam: Elsevier; 1989.
[7] M. Ghorashi, "Limit analysis of circular plates subjected to arbitrary
rotational symmetric loadings", Int. J. Mech. Sci.; vol. 36, no. 2, pp.87-
94,1994.
[8] M. Ghorashi, M. Daneshpazhooh, "Limit analysis of variable thickness
circular plates", Comp. and Struct.; vol. 79, no 2, pp.461-468, 2001.
[9] M. Guowei, I. Shoji, M. Yutaka, D. Hideaki, "Plastic limit analysis of
circular plates with respect to unified yield criterions", Int. J. Mech. Sci.;
vol. 40, no. 10,pp. 963-976, 1998.
[10] T. Hirai, "Functionally gradient materials", In: Brook RJ, editor.
Processing of ceramics, Part 2. Mat. Sci. and Tech., Weinheim,
Germany: VCH Verlagsgesellschaft mbH;; vol.17B, pp. 292-34, 1996.
[11] S. Suresh, A. Mortensen "Functionally graded materials", London: The
Institute of Materials, IOM Communications Ltd.; 1998.
[12] G.H. Paulino, Z.H. Jin, R.H. Jr. Dodds "Failure of functionally graded
materials", In: B. Karihaloo, W.G. Knauss, editors. Comprehensive
Struct. Integ., vol.2, Oxford: Elsevier Science Limited; 2002, ch. 13.
[13] S. Suresh, and A. Mortensen, "Fundamentals of Functionally Graded
Materials", IOC Communications Ltd, London, 1998.
[14] R. L. Williamson, B. H. Rabin, and Drake, "Finite element analysis of
thermal residual stresses at graded ceramic-metal interfaces", I. Model
description and geometrical effects, J. T. J. Appl. Phys., vol. 74, pp.
1310-1320, 1993
[15] A. Mortensen, and S. Suresh, "Functionally graded metals and metalceramic
composites: Part 1", Processing, S. Int. Mater. Rev., vol. 40, pp.
239-265, 1995.
[16] S. Suresh, and A. Mortensen, "Functionally graded metals and metalceramic
composites: Part 2", Thermomechanical Behaviour,A. Int.
Mater. Rev., vol. 42, pp. 85-116, 1997.
[17] I. Tamura, Y. Tomota, H. Ozawa "Strength and ductility of Fe-Ni-C
alloys composed of austenite and martensite with various strength", In:
Proc. of the Third Int. Conf. on Strength of Metals and Alloys, vol. 1.
Cambridge: Institute of Metals; pp. 611-5, 1973.
[18] M. H. Kargarnovin and M. Ghorashi, "Limit analysis of a circular plate
subjected to an arbitrary rotational symmetric loading", Proc. 3rd Int.
Conf. on Computational Plasticity, Barcelona;:pp.2149-2159, 1992
[19] Z. H. Jin R.H. Doddas Jr, "Crack growth resistance behavior of a
functionally graded material: computational studies", Engineering
Fracture Mechanics; vol. 71, pp.1651-1672, 2004.
[1] W. Prager, "An introduction to plasticity" Reading, MA: Addison-
Wesley; 1959.
[2] M. R. Horne, "Plastic theory of structures". Cambridge, MA: MIT;
1971.
[3] E. H. Mansfield, "Studies in collapse analysis of rigid-plastic plates with
a square yield diagram", Proc. R. Soc. A; pp.241:311-38, 1958.
[4] P.G. Hodge, "Limit analysis of rotationally symmetric plates and shells",
Englewood Cliffs, NJ: Prentice-Hall; 1963.
[5] M.A. Save, "Massonnet CE. Plastic analysis and design of plates, shells
and disks. Amsterdam", North-Holland; 1972.
[6] Z. Sobotka, "Theory of plasticity and limit design of plates",
Amsterdam: Elsevier; 1989.
[7] M. Ghorashi, "Limit analysis of circular plates subjected to arbitrary
rotational symmetric loadings", Int. J. Mech. Sci.; vol. 36, no. 2, pp.87-
94,1994.
[8] M. Ghorashi, M. Daneshpazhooh, "Limit analysis of variable thickness
circular plates", Comp. and Struct.; vol. 79, no 2, pp.461-468, 2001.
[9] M. Guowei, I. Shoji, M. Yutaka, D. Hideaki, "Plastic limit analysis of
circular plates with respect to unified yield criterions", Int. J. Mech. Sci.;
vol. 40, no. 10,pp. 963-976, 1998.
[10] T. Hirai, "Functionally gradient materials", In: Brook RJ, editor.
Processing of ceramics, Part 2. Mat. Sci. and Tech., Weinheim,
Germany: VCH Verlagsgesellschaft mbH;; vol.17B, pp. 292-34, 1996.
[11] S. Suresh, A. Mortensen "Functionally graded materials", London: The
Institute of Materials, IOM Communications Ltd.; 1998.
[12] G.H. Paulino, Z.H. Jin, R.H. Jr. Dodds "Failure of functionally graded
materials", In: B. Karihaloo, W.G. Knauss, editors. Comprehensive
Struct. Integ., vol.2, Oxford: Elsevier Science Limited; 2002, ch. 13.
[13] S. Suresh, and A. Mortensen, "Fundamentals of Functionally Graded
Materials", IOC Communications Ltd, London, 1998.
[14] R. L. Williamson, B. H. Rabin, and Drake, "Finite element analysis of
thermal residual stresses at graded ceramic-metal interfaces", I. Model
description and geometrical effects, J. T. J. Appl. Phys., vol. 74, pp.
1310-1320, 1993
[15] A. Mortensen, and S. Suresh, "Functionally graded metals and metalceramic
composites: Part 1", Processing, S. Int. Mater. Rev., vol. 40, pp.
239-265, 1995.
[16] S. Suresh, and A. Mortensen, "Functionally graded metals and metalceramic
composites: Part 2", Thermomechanical Behaviour,A. Int.
Mater. Rev., vol. 42, pp. 85-116, 1997.
[17] I. Tamura, Y. Tomota, H. Ozawa "Strength and ductility of Fe-Ni-C
alloys composed of austenite and martensite with various strength", In:
Proc. of the Third Int. Conf. on Strength of Metals and Alloys, vol. 1.
Cambridge: Institute of Metals; pp. 611-5, 1973.
[18] M. H. Kargarnovin and M. Ghorashi, "Limit analysis of a circular plate
subjected to an arbitrary rotational symmetric loading", Proc. 3rd Int.
Conf. on Computational Plasticity, Barcelona;:pp.2149-2159, 1992
[19] Z. H. Jin R.H. Doddas Jr, "Crack growth resistance behavior of a
functionally graded material: computational studies", Engineering
Fracture Mechanics; vol. 71, pp.1651-1672, 2004.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:53528", author = "Kargarnovin M.H. and Faghidian S. A and Arghavani J.", title = "Limit Analysis of FGM Circular Plates Subjected to Arbitrary Rotational Symmetric Loads", abstract = "The limit load carrying capacity of functionally
graded materials (FGM) circular plates subjected to an arbitrary
rotationally symmetric loading has been computed. It is provided that
the plate material behaves rigid perfectly plastic and obeys either the
Square or the Tresca yield criterion. To this end the upper and lower
bound principles of limit analysis are employed to determine the
exact value for the limiting load. The correctness of the result are
verified and finally limiting loads for two examples namely; through
radius and through thickness FGM circular plates with simply
supported edges are calculated, respectively and moreover, the values
of critical loading factor are determined.", keywords = "Circular plate, FGM circular plate, Limit analysis,Lower and Upper bound theorems.", volume = "1", number = "12", pages = "705-6", }