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Field-consistency — toward a science of constrained multi-strain-field finite element formulations

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Abstract

The finite element method has progressed rapidly from simple engineering principles through rigorous mathematical formaisations to become a body of engineering knowledge incorporating well-defined conceptual schemes and operational procedures. The current practice however leads to a series of difficulties which are actually inter-related. In this paper, we describe an additional conceptual scheme called ‘field-consistency’, and demonstrate new methodology and terminology that helps to clear up this area of the finite element method that had remained difficult to understand for some time. The new procedure also enhances the predictive capabilities of error analyses of the method, giving it some of the self-criticality needed for a ‘falsifiable’ scientific basis. This paper is also in a limited sense, an essay on how the processes of the method of science are seen to work in this area of engineering know-how.

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References

  • Argyris J H 1960Energy theorems and structural analysis (London: Butterworths) (reprinted fromAircr. Eng. 1954–55)

    Google Scholar 

  • Barlow J 1976Int. J. Numer. Methods Eng. 10: 243–251

    Article  MATH  Google Scholar 

  • Belytschko T, Tsay C S, Liu W K 1981Comput. Struct. 29: 313–327

    MATH  MathSciNet  Google Scholar 

  • Cook R D 1977Int. J. Numer. Methods Eng. 11: 1334–1339

    Article  Google Scholar 

  • Crisfield M A 1984Comput. Struct. 18: 833–852

    Article  MATH  Google Scholar 

  • Fried I 1974Comput. Struct. 8: 771–778

    Article  Google Scholar 

  • Hinton E, Campbell J S 1974Int. J. Numer. Methods Eng. 8: 461–480

    Article  MATH  MathSciNet  Google Scholar 

  • Hughes T J R, Taylor R L, Kanoknukulchal W 1977Int. J. Numer. Methods Eng. 11: 1529–1543

    Article  MATH  Google Scholar 

  • Hughes T J R, Tezduyar T E 1981J. Appl. Mech. 48: 587–596

    Article  MATH  Google Scholar 

  • Kuhn T S 1962The structure of scientific revolutions (Chicago: University Press)

    Google Scholar 

  • Medawar P B 1979Advice to a young scientist (New York: Harper and Row)

    Google Scholar 

  • Mindlin R D 1951J. Appl. Mech. 18: 31–38

    MATH  Google Scholar 

  • Mohr G A 1980Comput. Struct. 11: 565–571

    Article  MATH  MathSciNet  Google Scholar 

  • Oleson J F 1983Comput. Struct. 17: 157–159

    Article  Google Scholar 

  • Pian T H H 1964AIAA J. 2: 1333–1336

    Article  Google Scholar 

  • Popper K R 1972Conjectures and refutations — the growth of scientific knowledge 4th edn (London & Henley: Routledge and Kegan Paul)

    Google Scholar 

  • Prathap G 1984a A field consistent 8-node brick element, DFVLR IB 131-84/34, Institute of Structural Mechanics, Braunschweig, W Germany

  • Prathap G 1984b Field-consistent representation of incompressible strain states in a brick element, DFVLR IB 131-84/35, Institute of Structural Mechanics, Braunschweig, W Germany

  • Prathap G 1984c Field consistent finite element formulations, DFVLR IB 131-84/33, Institute of Structural Mechanics, Braunschweig, W Germany

  • Prathap G 1984dAnalysis of structures (eds) K A V Pandalai and B R Somashekar (Bangalore: Natl. Aeronaut. Lab.)

    Google Scholar 

  • Prathap G 1984eComput. Struct. 18: 789–794

    Article  MATH  Google Scholar 

  • Prathap G 1985aInt. J. Numer. Methods Eng. 21: 389–407

    Article  MATH  Google Scholar 

  • Prathap G 1985bInt. J. Numer. Methods Eng. 21: 825–835

    Article  MATH  Google Scholar 

  • Prathap G 1985cInt. J. Numer. Methods. Eng. 21: 1149–1156

    Article  MATH  Google Scholar 

  • Prathap G 1985dComput. Struct. 21: 995–999

    Article  Google Scholar 

  • Prathap G 1985eInt. J. Numer. Methods Eng. 21: 1001–1012

    Article  MATH  Google Scholar 

  • Prathap G, Bhashyam G R 1982Int. J. Numer. Methods Eng. 18: 195–210

    Article  MATH  Google Scholar 

  • Prathap G, Ramesh Babu C 1985a An isoparametric quadratic thick curved beam element, NAL TM ST 8505 (also,Int. J. Numer. Methods Eng., 1986, 23: 1583–1600)

  • Prathap G, Ramesh Babu C 1985b A field-consistent three-noded curved axisymmetric shell element, NAL TM ST 8502 (also,Int. J. Numer. Methods Eng., 1986, 23: 711–723)

    Google Scholar 

  • Prathap G, Ramesh Babu C 1985c Field consistency and violent stress oscillations in the finite element method, NAL TM ST 8506 (also,Int. J. Numer. Methods Eng., in press)

  • Prathap G, Subramanian G Ramesh Babu C 1985 Stress oscillations in plane stress modelling of flexure — a field-consistency approach, NAL TM ST 8507

  • Prathap G, Viswanath S 1982Comput. Struct. 15: 491

    Article  Google Scholar 

  • Prathap G, Viswanath S 1983Int. J. Numer. Methods Eng. 19: 831–840

    Article  MATH  Google Scholar 

  • Ramesh Babu C, Prathap G 1985a A field-consistent two-noded curved axisymmetric shell element, NAL TM ST 8501 (also,Int. J. Numer. Methods Eng., 1986, 23: 1245–1261)

  • Ramesh Babu C, Prathap G 1985b A linear thick curved beam element, NAL TM ST 8504 (also,Int. J. Numer. Methods Eng., 1986, 23: 1313–1328)

  • Somashekar B R 1983Comput. Struct. 17: 403–406

    Article  Google Scholar 

  • Turner M J, Clough R W, Martin H C, Topp L J 1956J. Aerosp. Sci. 23: 805–823

    Google Scholar 

  • Viswanath S, Prathap G 1983Int. J. Numer. Methods Eng. 19: 305–309

    Article  MATH  Google Scholar 

  • Walz J E, Fulton R E, Cyrus N J, Eppink R T 1970 Accuracy of finite element approximations to structural problems, NASA TN-D 5728

  • Zienkiewicz O C 1977The finite element method (New Delhi: Tata McGraw Hill)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Structural Sciences Division, National Aeronautical Laboratory, 560 017, Bangalore, India

    G Prathap

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  1. G Prathap
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Prathap, G. Field-consistency — toward a science of constrained multi-strain-field finite element formulations. Sadhana 9, 319–343 (1986). https://doi.org/10.1007/BF02811972

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  • DOI: https://doi.org/10.1007/BF02811972

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