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The application of generalized variational principle in finite element-semianalytical method

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Abstract

The method developed in this paper is inspired by the viewpoint in ref. [1] that sufficient attention has not been paid to the value of the generalized variational principle in dealing with the boundary conditions in the finite element method. This method applies the generalized variational principle and chooses the series constituted by spline function multiplied by sinusoidal function and added by polynomial as the approximate deflection of plates and shells. By taking the deflection problem of thin plate, it shows that this method can solve the coupling problem in the finite element-semianalytical method. Compared with the finite element method and finite stripe method, this method has much fewer unknown variables and higher precision. Hence, it proposes an effective way to solve this kind of engineering problems by minicomputer.

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References

  1. Chien Wei-zang, Studies on the generalized variational principle in elasticity and its application in finite element calculations,Mechanics and Practice, 2 (1979). (in Chinese)

  2. Chien Wei-zang,Variational Method and Finite Element, Science Press (1980).

  3. Qin Rong, spline finite point method,Proc. of The first national conference of computational Mechanics (1980).

  4. Shi Zhong-ci, Spline finite element,Computational mathematics, 1 (1981).

  5. Wang Lei, Finite stripe method with sinusoidal functions and polynomials,Acta Mechanica Solida Sinica, 2 (1981).

  6. Tang Bang-ben, A common on finite stripe method with sinusoidal functions and polynomials. (Submitted for publication)

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Authors and Affiliations

  1. Human University, Changsha

    Tan Bang-ben

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  1. Tan Bang-ben
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Communicated by Chien Wei-zang

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Bang-ben, T. The application of generalized variational principle in finite element-semianalytical method. Appl Math Mech 9, 693–700 (1988). https://doi.org/10.1007/BF02465698

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  • DOI: https://doi.org/10.1007/BF02465698

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