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The random variational principle in finite deformation of elasticity and finite element method

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Abstract

In the present paper, we have introduced the random materials, toads, geometrical shapes, force and displacement boundary condition directly into the functional variational formula, by use of a small parameter perturbation method, a unified random variational principle in finite deformation of elasticity and nonlinear random finite element method are established, and used for reliability analysis of structures. Numberical examples showed that the methods have the advantages of simple and conveninet program implementation and are effective for the probabilistic problems in mechanics.

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References

  1. Zienkiewicz, O. C. and T. L. Taylor,The Finite Element Method, 4th Edition, McGraw-Hill, New York (1989).

    Google Scholar 

  2. Liu, W. K., T. Belytschko and A. Mani, Radom field finite elements,Int. J. Numer. Meth. Eng.,23, 10 (1986), 1831–1845.

    Article  MATH  MathSciNet  Google Scholar 

  3. Vanmarcke, E. H. et al., Random fields and stochastic finite elements.Structural Safety,3 (1986), 143–166.

    Article  Google Scholar 

  4. Nakagiri, S. and F. Hisada,Stochastic Finite Element Method. An Introduction, Baifu-Kan (1985), (in Japanese)

  5. Zhang Ru-qing and Gao Hang-shan, The random variational principle and finite element method,Appl. Math. and Mech. (English Ed.),13, 5 (1992), 401–406.

    MathSciNet  Google Scholar 

  6. Zhang Ru-qing,The Variational Principle and Its Applications in Solid Mechanics, Chongqing University Press, Chongqing (1991). (in Chinese)

    Google Scholar 

  7. Rackwitz, R. and B. Fiessler, Structural reliability under combined random load sequences,Comput. Struct.,9, 5 (1978), 489–494.

    Article  MATH  Google Scholar 

  8. Rosenblatt, M., Remarks on a multivariate transformation,Annals of Math. Statistics,23, 3 (1952), 470–472.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Northwesten Polytechnical University, Xi’an

    Gao Hang-shan

  2. Chongqing University, Chongqing

    Zhang Ru-qing

Authors
  1. Gao Hang-shan
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  2. Zhang Ru-qing
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Hang-shan, G., Ru-qing, Z. The random variational principle in finite deformation of elasticity and finite element method. Appl Math Mech 15, 903–911 (1994). https://doi.org/10.1007/BF02451033

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  • DOI: https://doi.org/10.1007/BF02451033

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