Hybrid equilibrium plate elements of high degree

• Autorzy: Maunder E. A. W.
• Konferencja: International Workshop on the Trefftz Method (3 ; 16-18.09. 2002 ; Exeter, England)
• Języki publikacji: EN

Abstrakty

EN

This paper concerns the modelling of plate bending problems governed by Reissner-Mindlin theory when hybrid equilibrium elements of high polynomial degree are used. The fields of statically admissible stress-resultants are categorised into three types according to the nature of their incompatibilities, i.e. pure Trefftz or strongly compatible, weakly compatible, and hyperstatic or strongly incompatible. The effects of this categorisation are reflected in the element formulation. Incompatibilities are quantified in terms of local discontinuities which also account for transverse twist terms. The construction of bases for the three corresponding subspaces of stress-resultants by numerical and/or algebraic means is reviewed. The potential use of a reformulated element is considered in the context of glass plate structures where residual or hyperstatic stresses play an important role.

Słowa kluczowe

EN

Reissner-Mindlin theory; hybrid; hybrid equilibrium

PL

teoria Reissner'a-Mindlina; równowaga hybrydowa; hybryd

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 4
• Strony: 531--543
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Maunder E. A. W.

• Department of Engineering, School of Engineering and Computer Science, University of Exeter, Exeter, EX4 4QF, England

Bibliografia

• [1] J.P. Moitinho de Almeida, J. A. Teixeira de Freitas. Alternative approach to the formulation of hybrid equilibrium finite elements. Computers and Structures, 40(4): 1043-1047, 1991.
• [2] J. Jirousek, A. Wroblewski. T-elements: state of the art and future trends. Arch. Camp. Meth. Engrg., 3/ 4: 323-434, 1996.
• [3] J. Jirousek, A. Wroblewski, Q.H. Qin, X.Q. He. A family of quadrilateral hybrid-Trefftz p-elements for thick plate analysis. Camp. Meth. Appl. Mech. Engrg., 127: 315-344, 1995.
• [4] O.J.B.A. Pereira, J.P.M . Almeida, E.A.W. Maunder. Adaptive methods for hybrid equilibrium finite element models. Camp. Meth. Appl. Mech. Eng, 176: 19-39, 1999.
• [5] G.A.O. Davies. Virtual work in structural analysis. Wiley, Chichester, 1982.
• [6] E.A.W. Maunder, J.P. Moitinho de Almeida, A.C.A. Ramsay. A general formulation of equilibrium macro-elements with control of spurious kinematic modes. Int. J. Num Meth. Eng., 39: 3175-3194, 1996.
• [7] C.M. Wang, J.N. Reddy, K.H. Lee. Shear deformable beams and plates - Relationships with classical solutions. Elsevier, Amsterdam, 2000.
• [8] B. Haggblad, K.-J. Bathe. Specifications of boundary conditions for Reissner-Mindlin plate bending finite elements. Int. J. Num. Meth. Eng, 30: 981-1011, 1990.
• [9] E.A.W. Maunder, J.P.B.M. Almeida. A triangular hybrid equilibrium plate element of general degree. 2003. Submitted for publication.
• [10] G.H. Golub, C.F. Van Loan. Matrix computations. Johns Hopkins University Press, Baltimore, 3 edition, 1996.
• [11] T.F. Coleman, A. Pothen. The nullspace problem I: Complexity. SIAM J. Alg. Disc. Meth., 7: 527-537, 1986.
• [12] T.F. Coleman, A. Pothen. The nullspace problem II: Algorithms. SIAM J. Alg. Disc. Meth., 8: 544-563, 1987.
• [13] E.A.W. Maunder. A Trefftz patch recovery method for smooth stress resultants and applications to Reissner-Mindlin equilibrium plate models. GAMES, 8: 409-424, 2001.
• [14] R.D. Milne. Applied functional analysis. Pitman, London, 1980.
• [15] J.C. Maxwell. On the equilibrium of elastic solids. Trans. Roy. Soc. Edinburgh, 20, 1850. reprinted in W.D.Niven, ed., The Scientific Papers of James Clerk Maxwell. Dover, New York, 1965.
• [16] Institution of Structural Engineers Report, London. The structural use of glass in buildings, 1999.