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Convergence of the C* family of finite elements and problems associated with forcing continuity of the derivatives at the nodes

  • Bigdeli, B. (School of Mechanical and Manufacturing Engineering, The University of New South Wales) ;
  • Kelly, D.W. (School of Mechanical and Manufacturing Engineering, The University of New South Wales)
  • 발행 : 1999.06.25

초록

A $C^*$-convergence algorithm for finite element analysis has been proposed by Bigdeli and Kelly (1997) and elements for the first three levels applied to planar elasticity have been defined. The fourth level element for the new family is described in this paper and the rate of convergence for the $C^*$-convergence algorithm is investigated numerically. The new family adds derivatives of displacements as nodal variables and the number of nodes and elements can therefore be kept constant during refinement. A problem exists on interfaces where the derivatives are required to be discontinuous. This problem is addressed for curved boundaries and a procedure is suggested to resolve the excessive interelement continuity which occurs.

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참고문헌

  1. Bigdeli, B. and Kelly, D.W. (1996), "C*-convergence and nodal derivatives in the finite element method" , Proc. First Australasian Congress on Applied Mechanics, The Institution of Engineers, Melbourne, Australia, 2, 571-576.
  2. Bigdeli, B. (1996), "An investigation of the C*-convergence in the finite element method", PhD. Thesis, The University of New South Wales, Sydney, Australia.
  3. Bigdeli, B. and Kelly, D.W. (1997), "C*-convergence in the finite element method", Int. J. Numer. Methods Engng., 40, 4405-4425. https://doi.org/10.1002/(SICI)1097-0207(19971215)40:23<4405::AID-NME267>3.0.CO;2-K
  4. Gago, J.P. de S.R. (1982), "A-posteriori error analysis and adaptivity for the finite element method" , PhD. Thesis, Dept. of Civil Eng., University College of Swansea, Swansea, Wales.
  5. MATLAB (1992), High-Performance Numeric Computation and Visualisation Software, User's Guide, The Math Works, Inc., 24 Prime Park Way, Natick, Mass. 01760, USA.
  6. Tsai, S.W. and Hahn, H.T. (1980), "Introduction to composite materials" , Technomic Publishing Co.
  7. STRAND6 (1993) Finite Element Analysis System, Reference Manual and User Guide, G+D Computing Pty Ltd., Level 7, 541 Kent St., Sydney 2000, Australia.
  8. Szabo, B. and Babuska, I. (1991), Finite Element Analysis, Wiley.