Mechanical Field

  • Manfred KaltenbacherEmail author


Let us consider a solid body with prescribed volume force and support at equilibrium, which means that the sum of all forces as well as the sum of all moments are zero.


  1. 1.
    T. Belytschko, W.K. Lui, B. Moran, Nonlinear Finite Elements for Continua and Structures (Wiley, New York, 2000)zbMATHGoogle Scholar
  2. 2.
    P. Wriggers, Nichtlineare Finite-Element-Methoden (Springer, 2001)Google Scholar
  3. 3.
    H. Parkus, Mechanik der Festen Körper (Springer, 1986)Google Scholar
  4. 4.
    F. Ziegler, Mechanics of Solids and Fluids (Springer, New York, 1995)CrossRefGoogle Scholar
  5. 5.
    K.J. Bathe, Finite Element Procedures (Prentice Hall, 1996)Google Scholar
  6. 6.
    T.J.R. Hughes, The Finite Element Method, 1st edn. (Prentice-Hall, New Jersey, 1987)zbMATHGoogle Scholar
  7. 7.
    D. Braess, Finite Elemente (Springer, Berlin, 2003) (3. korregierte Auflage)Google Scholar
  8. 8.
    D. Braess, Nonstandard Mixed Methods. Lecture at Radon Institute of Computational and Applied Mathematics (Linz, Austria, 2005)Google Scholar
  9. 9.
    E.L. Wilson, R.L. Taylor, W.P. Doherty, J. Ghaboussi, Incompatible Displacement Modes. Numerical and Computer Methods in Structural Mechanics (Academic Press, Orlando, 1973), pp. 43–57Google Scholar
  10. 10.
    R.L. Taylor, P.J. Beresford, E.L. Wilson, A non-conforming element for stress analysis. Int. J. Numer. Methods Eng. 10, 1211–1219 (1976)CrossRefzbMATHGoogle Scholar
  11. 11.
    O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method (Heinemann, Butterworth, 2003)Google Scholar
  12. 12.
    A. Ibrahimbegovic, E.L. Wilson, A modified method of incompatible modes. Commun. Appl. Numer. Methods 7, 187–194 (1991)CrossRefzbMATHGoogle Scholar
  13. 13.
    M. Bischoff, I. Romero, A generalization of the method of incompatible modes. Int. J. Numer. Methods Eng. 69, 1851–1868 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    J.C. Simo, M.S. Rifai, A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods Eng. 29, 1595–1638 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    D. Andelfinger, E. Ramm, EAS-elements for two-dimensional, three-dimensional, plate and schell structures and their equivalence to HR-elements. Int. J. Numer. Methods Eng. 36, 1311–1337 (1993)CrossRefzbMATHGoogle Scholar
  16. 16.
    J.M. Cesar de Sa, R.M.N. Jorge, New enhanced strain elements for incompressible problems. Int. J. Numer. Methods Eng. 44, 229–248 (1999)CrossRefzbMATHGoogle Scholar
  17. 17.
    D.N. Arnold, F. Brezzi, Some new elements for the Reissner-Mindlin plate model, in Boundary Value Problems for Partial Differential Equations and Applications, ed. by J.-L. Lions, C. Baiocchi (Masson, Paris, 1993), pp. 287–292Google Scholar
  18. 18.
    D. Chapelle, R. Stenberg, An optimal low-order locking-free finite element method for Mindlin-Reissner plates. Math. Models Methods Appl. Sci. 8, 407–430 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    D. Braess, Finite Elements (Cambridge University Press, Cambridge, 2001)zbMATHGoogle Scholar
  20. 20.
    S. Reese, A large deformation solid-shell concept based on reduced integration with hourglass instability. Int. J. Numer. Methods Eng. 69, 1671–1716 (2006)CrossRefMathSciNetGoogle Scholar
  21. 21.
    D. Braess, M. Kaltenbacher, Efficient 3d-finite-element-formulation for thin mechanical and piezoelectric structures. Int. J. Numer. Methods Eng. 73(2), 147–161 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    T.J.R. Hughes, T.E. Tezduyar, Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. J. Appl. Mech., ASME 48(3), 587–596 (1981)CrossRefzbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of Mechanics and MechatronicsVienna University of TechnologyViennaAustria

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