Variational Principles with Several Adjustable Parameters

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


This chapter also focuses on the development of the variational principles. Firstly, it introduces three patterns of functional transformation, i.e., pattern I, pattern II and pattern III. Then, on the basis of pattern III, some variational principles with several adjustable parameters are formulated. Finally, a variable-substitution-multiplier method is also proposed based on pattern I and pattern II[1,2].


variational principle functional transformation adjustable parmeters variable-substitution-multiplier method 


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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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