Corrected Reciprocal Theorem of Works for Bending Thin Plates and Its Application

FU Bao-lian

doi:10.3879/j.issn.1000-0887.2014.11.003

Volume 35 Issue 11

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FU Bao-lian. Corrected Reciprocal Theorem of Works for Bending Thin Plates and Its Application[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1197-1209. doi: 10.3879/j.issn.1000-0887.2014.11.003

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Corrected Reciprocal Theorem of Works for Bending Thin Plates and Its Application

doi: 10.3879/j.issn.1000-0887.2014.11.003

FU Bao-lian

College of Architectural Engineering and Mechanics, Yanshan University,Qinhuangdao, Hebei 066004, P.R.China

Received Date: 2014-03-07
Rev Recd Date: 2014-07-07
Publish Date: 2014-11-18

Abstract

Abstract

It was discovered that the 2 main premises in the proposition of Betti’s reciprocal theorem of works for bending thin plates, ‘1 bending thin plate’ and ‘action of 2 sets of forces’, were contradictory to each other because any one of the 2 sets of forces might change ‘1 bending thin plate’ to a different one. The contradiction results in the fact that Betti’s reciprocal theorem of works for bending thin plates is one with error in logic. Based on the analysis of the contradiction, a corrected reciprocal theorem was proposed, in which the correct proposition of the reciprocal theorem for bending thin plates was given. The corrected reciprocal theorem provides a theoretical foundation for the reciprocal method of work, which makes a novel and powerful way to the analysis of bending plates.
- Betti’s reciprocal theorem of works,
- corrected reciprocal theorem of works,
- 1 bending thin plate,
- action of 2 sets of forces

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References(26)

References

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