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Introduction — The Evolutive Finite Element Method

  • Yu-Qiu Long
  • Song Cen
  • Zhi-Fei Long

Abstract

This chapter is an opening introduction to the entire book, and also an introduction to the evolutive Finite Element Method (FEM). Firstly, a brief review on the features of FEM is given. Then, a close relationship between FEM and variational principle is discussed according to the development history and categories of FEM. Thirdly, some research areas of FEM of significant interest are listed. Finally, the topics of the book are presented. The purpose of the above arrangement is to explain the background and main idea of this book.

Keywords

finite element method variational principle research area advance outline 

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References

  1. [1]
    Courant R (1943) Variational methods for the solution of problems of equilibrium and vibration. Bull Am Math Soc 49: 1–23CrossRefMathSciNetzbMATHGoogle Scholar
  2. [2]
    Turner MJ, Clough RW, Martin HC, Toop LC (1956) Stiffness and deflection analysis of complex structures. J Aeronaut Sci 23(9): 805–823CrossRefzbMATHGoogle Scholar
  3. [3]
    Clough RW (1960) The finite element method in plane stress analysis. In: Proc 2nd Conference on Electronic Computation. Pittsburgh: ASCE, pp 345–377Google Scholar
  4. [4]
    Melosh RJ (1963) Basis for derivation for the direct stiffness method. AIAA Journal 1(7): 1631–1637CrossRefGoogle Scholar
  5. [5]
    Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Oxford: Butterworth-HeinemannzbMATHGoogle Scholar
  6. [6]
    Cook RD, Malkus DS, Plesha ME (1989) Concepts and applications of finite element analysis. 3rd edn. John Wiley & Sons Inc, New YorkzbMATHGoogle Scholar
  7. [7]
    Huebner KH, Thornton EA, Byrom TG (1995) The finite element method for engineers. John Wiley & Sons Inc, New YorkGoogle Scholar
  8. [8]
    Bathe KJ (1996) Finite element procedures. Prentice-Hall Inc, New JerseyGoogle Scholar
  9. [9]
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, ChichesterzbMATHGoogle Scholar
  10. [10]
    Chien WZ (1980) Calculus of variations and finite elements (Vol. 1). Science Press, Beijing (in Chinese)Google Scholar
  11. [11]
    Hu HC (1984) Variational principles of theory of elasticity with applications. Science Press, BeijingGoogle Scholar
  12. [12]
    Long YQ (1978, 1991) Introduction to finite element method. 1st edn, 2nd edn. Higher Education Press, Beijing (in Chinese)Google Scholar
  13. [13]
    Long YQ (1992) Introduction to new finite element method. Tsinghua University Press, Beijing (in Chinese)Google Scholar
  14. [14]
    Long ZF, Cen S (2001) New monograph of finite element method: principle, programming, developments. China Hydraulic and Water-power Press, Beijing (in Chinese)Google Scholar
  15. [15]
    Hu HC (1955) On some variational principles in the theory of elasticity and the theory of plasticity. Scientia Sinica 49(1): 33–42Google Scholar
  16. [16]
    Feng K (1965) Difference scheme based on variational principle. Chinese Journal of Applied Mathematics and Computational Mathematics 2(4):238–262 (in Chinese)Google Scholar
  17. [17]
    Washizu K (1968, 1975, 1982) Variational Methods in Elasticity and Plasticity, 1st edn, 2nd edn, 3rd edn, Pergamon PressGoogle Scholar
  18. [18]
    Long YQ (1981) Piecewise generalized variational principles in elasticity. Shanghai Mechanics 2(2): 1–9 (in Chinese)Google Scholar
  19. [19]
    Long YQ (1986) Several patterns of functional transformation and generalized variational principles with several arbitrary parameters. International Journal of Solids and Structures 22(10): 1059–1069CrossRefMathSciNetzbMATHGoogle Scholar
  20. [20]
    Long YQ (1987) Generalized variational principles with several arbitrary parameters and the variable substitution and multiplier method. Applied Mathematics and Mechanics (English Edition) 8(7): 617–629CrossRefzbMATHGoogle Scholar
  21. [21]
    Long YQ, Xin KG (1987) Generalized conforming element. Tumu Gongcheng Xuebao/China Civil Engineering Journal 20(1): 1–14 (in Chinese)Google Scholar
  22. [22]
    Long YQ, Xin KG (1989) Generalized conforming element for bending and buckling analysis of plates. Finite Elements in Analysis and Design 5: 15–30CrossRefzbMATHGoogle Scholar
  23. [23]
    Long YQ, Long ZF, Xu Y (1997) The generalized conforming element (GCE) theory and applications. Advances in Structural Engineering 1(1):63–70Google Scholar
  24. [24]
    Shi ZC (1990) On the accuracy of the quasi-conforming and generalized conforming finite elements. Chinese Annals of Mathematics Series B 11(2): 148–155MathSciNetzbMATHGoogle Scholar
  25. [25]
    Long YQ, Bu XM, Long ZF, Xu Y (1995) Generalized conforming plate bending elements using point and line compatibility conditions. Computers & Structures 54(4): 717–723CrossRefzbMATHGoogle Scholar
  26. [26]
    Long ZF (1992) Triangular and rectangular plate elements based on generalized compatibility conditions. Computational Mechanics 10(3/4): 281–288CrossRefzbMATHGoogle Scholar
  27. [27]
    Long ZF (1993) Two generalized conforming plate elements based on SemiLoof constraints. Computers & Structures 47(2): 299–304CrossRefzbMATHGoogle Scholar
  28. [28]
    Long YQ, Xi F (1992) A universal method for including shear deformation in the thin plate elements. International Journal for Numerical Methods in Engineering 34: 171–177CrossRefzbMATHGoogle Scholar
  29. [29]
    Long YQ, Zhi BC, Kuang WQ, Shan J (1982) Sub-region mixed finite element method for the calculation of stress intensity factor. In: He GQ et al. (eds) Proceedings of International Conference on FEM. Science Press, Shanghai, pp 738–740Google Scholar
  30. [30]
    Long YQ, Fu XR (2002) Generalized conforming elements based on analytical trial functions. In: Proceedings of the Eleventh National Conference on Structural Engineering, (Vol. I), plenary lecture, China, Changsha, pp 28–39 (in Chinese)Google Scholar
  31. [31]
    Long YQ, Li JX, Long ZF, Cen S (1997) Area-coordinate theory for quadrilateral elements. Gong Cheng Li Xue/Engineering Mechanics 14(3): 1–11 (in Chinese)Google Scholar
  32. [32]
    Yuan S (1984) Spline elements in stress analysis [Doctoral Dissertation], Tsinghua University, BeijingGoogle Scholar
  33. [33]
    Fan Z (1988) Applications of spline elements and sub-region mixed elements in structural engineering [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)Google Scholar

Copyright information

© Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg 2009

Authors and Affiliations

  • Yu-Qiu Long
    • 1
  • Song Cen
    • 2
  • Zhi-Fei Long
    • 3
  1. 1.Department of Civil Engineering, School of Civil EngineeringTsinghua UniversityBeijingChina
  2. 2.Department of Engineering Mechanics, School of AerospaceTsinghua UniversityBeijingChina
  3. 3.School of Mechanics & Civil EngineeringChina University of Mining & TechnologyBeijingChina

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