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One variant of the finite-element method in elasicity theory

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Abstract

The problem of analyzing the stress-strain state (SSS) of structures is most frequently solved using finite elements in displacements. Combined elements do not always possess sufficient accuracy, however, as applies to shell structures. Equilibrium elements based on the principle of a minimum of additional energy and approximations of the stress fields exhibit good accuracy, and, as Gallagher [1] has indicated, are extremely promising. These same methods of combined and equilibrium elements has not, however, found broad development and application due to difficulties in its implementation. A limited number of studies [1–6] are focused, as a rule, on plates under an external load. The purpose of this paper is to refine the equilibrium-element method and develop it for other types of effects. The efficiency of the method is illustrated by calculations of bendable plate.

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References

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    R. Gallagher, Finite-Element Method. Fundamentals [Russian translation], Mir, Moscow (1984).

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    S. A. Kalanta, "Method of equilibrium finite elements in the mechanics of elastic deformable systems. System of solving equations," Mat. Modeli Algorit. Zadach Prikl. Mekh., No. 19, 42–54 (1978).

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Additional information

Vilnius Technical Institute (Lithuania). Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 77–83, February, 1984.

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Kalanta, S.A. One variant of the finite-element method in elasicity theory. Int Appl Mech 30, 148–152 (1994). https://doi.org/10.1007/BF00848514

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Keywords

  • Stress Field
  • Good Accuracy
  • External Load
  • Additional Energy
  • Sufficient Accuracy