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Defects of Mindlin Plate and Degenerated Shell Elements

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Static and Dynamic Analyses of Plates and Shells

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Abstract

As mentioned in Chap. 2, in most cases, closed form analytical solutions to all but the simplest type of continuum problems are very difficult or even impossible to obtain. Therefore, the discretisation of continuum problems is necessary to obtain numerical solutions for practical purposes. There have been several general techniques directly applicable to the differential equations governing the problems. Such methods include finite difference approximations, various weighted residual procedures, or approximate techniques of determining the stationarity of properly defined “functionals”. However, for the last two decades, the most powerful discretisation tool has been widely acknowledged to be the finite element method which is based on variational principles (or virtual work principles). The method can also be derived from weighted residual procedures.

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References

  1. Ahmad S (1969) Curved finite elements in the analysis of solid, shell and plate. PhD thesis, University College of Swansea, C/PH/7/69

    Google Scholar 

  2. Mindlin RD (1951) Influence of rotatory inertia and shear in flexural motion of isotropic, elastic plates. J Appl Mech 18: 1031–1036

    Google Scholar 

  3. Gallagher RH (1976) Problems and progress in thin shell finite element analysis. In: Ashwell DG, Gallagher RH (eds) Finite elements for thin shells and curved members. John Wiley & Sons, pp 1–14

    Google Scholar 

  4. Zienkiewicz OC (1977) The finite element method, 3rd edn. McGraw-Hill, New York

    MATH  Google Scholar 

  5. Gallagher RH (1975) Shell elements. In: Robinson J (ed) Proceedings of world congress on finite element methods in structural mechanics. Bournemouth, Dorset, England, October 1975, pp El-E35

    Google Scholar 

  6. Ahmad S, Irons BM, Zienkiewicz OC (1970) Analysis of thick and thin shell structures by curved finite elements. Intl J Numer Meth Engng 2: 419–451

    Article  Google Scholar 

  7. Irons BM, Ahmad S (1980) Techniques of finite elements. Ellis Horwood, Chichester

    Google Scholar 

  8. Parisch H (1979) A critical survey of the 9-node degenerated shell element with special emphasis on thin shell application and reduced integration. Comp Meth Appl Mech Engng 20: 323–350

    Article  MATH  Google Scholar 

  9. Zienkiewicz OC, Taylor RL, Too JM (1971) Reduced integration techniques in general analysis of plates and shells. Intl J Numer Meth Engng 3: 275–290

    Article  MATH  Google Scholar 

  10. Zienkiewicz OC, Hinton E (1976) Reduced integration, function smoothing and non-conformity in finite element analysis (with special reference to thick plates). J Franklin Inst 302: 443–461

    Article  MATH  Google Scholar 

  11. Hughes TJR, Cohen M, Haroun M (1978) Reduced and selective integration techniques in the finite element analysis of plates. Nucl Engng Design 46: 203–222

    Article  Google Scholar 

  12. Figueiras JA (1983) Ultimate load analysis of anisotropic and reinforced concrete plates and shells. PhD thesis, University College of Swansea, C/Ph/72/83

    Google Scholar 

  13. Malkus DS, Hughes TJR (1978) Mixed finite element methods–reduced and selective integration techniques: a unification of concepts. Comp Meth Appl Mech Engng 15: 63–81

    Article  MATH  Google Scholar 

  14. Hughes TJR, Tezduyar TE (1981) Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. J Appl Mech 48: 587–596

    Article  MATH  Google Scholar 

  15. Hughes TJR, Liu WK (1981) Nonlinear finite element analysis of shells: Parts I and II: three dimensional and two dimensional shells. Comp Meth Appl Mech Engng 26:331–362, 1981; 27: 167–181

    Article  Google Scholar 

  16. Bathe KJ, Dvorkin EN (1985) A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. Intl J Numer Meth Engng 21: 367–383

    Article  MATH  Google Scholar 

  17. Fried I (1973) Triangular nine-degrees-of-freedom, C(0) plate bending element of quadratic accuracy. Q Appl Mech 31: 303–312

    MATH  Google Scholar 

  18. Fried I (1973) Shear in C(0) and C(1) bending finite elements. J Solids Struct 9: 449–460

    Article  MathSciNet  Google Scholar 

  19. Fried I (1974) Residual energy balancing technique in the generation of plate bending finite element. Comp Struct 4: 771–778

    Article  MathSciNet  Google Scholar 

  20. Belytschko T, Ong JS-J, Liu WK (1984) A consistent control of spurious singles modes in the 9-node Lagrange element for the Laplace and Mindlin plate equations. Comp Meth Appl Mech Engng 44: 269–295

    Article  MATH  Google Scholar 

  21. Dvorkin EN, Bathe KJ (1984) A continuum mechanics based four-node shell element for general nonlinear analysis. Engng Comput 1: 77–88

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, University College of Swansea, SA2 8PP, Swansea, Wales, UK

    Hou-Cheng Huang Ph.D

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  1. Hou-Cheng Huang Ph.D
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© 1989 Springer-Verlag Berlin Heidelberg

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Huang, HC. (1989). Defects of Mindlin Plate and Degenerated Shell Elements. In: Static and Dynamic Analyses of Plates and Shells. Springer, London. https://doi.org/10.1007/978-1-4471-1669-1_3

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  • DOI: https://doi.org/10.1007/978-1-4471-1669-1_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1671-4

  • Online ISBN: 978-1-4471-1669-1

  • eBook Packages: Springer Book Archive

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