Finite Element Method for Membranes (2-D Solids)

  • Maria Augusta Neto
  • Ana Amaro
  • Luis Roseiro
  • José Cirne
  • Rogério Leal


The development of finite element equations for the stress analysis of two dimensional structures subjected to external loads that are applied within their 2-D geometrical plane will be presented in this chapter. The basic concepts, procedures and formulations can also be found in many existing textbooks [1–4]. The element developed is called membrane or 2D solid element. The finite element solution will solve only the selected mathematical model and that all assumptions in this model will be reflected in the predicted response. Thus, the choice of an appropriate mathematical model is crucial and completely determines the insight into the physical problem that we can obtain by this kind of analysis.


Shape Function Triangular Element Finite Element Solution Rectangular Element Rigid Body Mode 
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  1. 1.
    Reddy JN (1993) Finite element method. Wiley, New YorkGoogle Scholar
  2. 2.
    Bathe K-J (1996) Finite element procedures. Prentice Hall, Englewood CliffsGoogle Scholar
  3. 3.
    Zienkiewicz OC, Taylor RL (2000) The finite element method. Butterworth-Heinemann, BostonzbMATHGoogle Scholar
  4. 4.
    Brenner S, Scott LR (2008) The mathematical theory of finite element method. Springer, New YorkCrossRefGoogle Scholar
  5. 5.
    Eisenberg MA, Malvern LE (1973) On finite element integration in natural coordinates. Int J Nume Methods Eng 7:574–575CrossRefzbMATHGoogle Scholar
  6. 6.
    Argyris JH, Fried I, Scharpf DW (1968) The TET 20 and TEA 8 elements for the matrix displacement method. Aero J 72:618–625Google Scholar
  7. 7.
    Piltner R, Taylor RL (2000) Triangular finite elements with rotational degrees of freedom and enhanced strain modes. Comput Struct 75(4):361–368CrossRefGoogle Scholar
  8. 8.
    Liu GR, Quek SS (2003) The finite element method: a practical course. Butterworth-Heinemann, Amsterdam/BurlingtonGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Maria Augusta Neto
    • 1
  • Ana Amaro
    • 1
  • Luis Roseiro
    • 2
  • José Cirne
    • 3
  • Rogério Leal
    • 3
  1. 1.CEMUC - Centre for Mechanical EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.Department of Mechanical EngineeringPolytechnic Institute of CoimbraCoimbraPortugal
  3. 3.Department of Mechanical EngineeringUniversity of CoimbraCoimbraPortugal

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