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Applications of the reciprocal theorem to solving the equations of the deflection surface of the rectangular plates with various edge conditions

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Abstract

This paper points out that on certain condition the reciprocal theorem is equivalent to the superposition principle of displacements. On the basis of [6], applications of the reciprocal theorem are further extended; a convenient, general and new method for solving the equations of deflection surface of the rectangular plates and the straight beams with various edge conditions under various loads is presented.

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References

  1. Chien Wei-zang and Yeh Kai-yuan, Elastic Mechanics, Science Publishing House, (March, 1980). (in Chinese).

  2. Chien Wei-zang, The Variation Method and Finite Element, Vol. 1, Science Publishing House, (1980). (in Chinese)

  3. Chang Fu-fan, Elastic Thin Plates, Science Publishing House, (1963). (in Chinese)

  4. Chang Fu-fan, The Bending of Cantilever Rectangular Plates, Transactions of the National Symposium of Technical Exchange on Elastics, (June, 1980).

  5. Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shell, Second Edition, (1959).

  6. Fu Bao-lian, Energy Theorems for Solving Equations of Deflections, Applied Mathematics and Mechanics, Vol. 2, No. 6 (1981).

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Authors

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Communicated by Chien Wei-zang.

Northeast Heavy Machinery Institute

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Bao-lian, F. Applications of the reciprocal theorem to solving the equations of the deflection surface of the rectangular plates with various edge conditions. Appl Math Mech 3, 353–364 (1982). https://doi.org/10.1007/BF01897218

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  • DOI: https://doi.org/10.1007/BF01897218

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