Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application

FU Bao-lian

doi:10.3879/j.issn.1000-0887.2015.05.008

Volume 36 Issue 5

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FU Bao-lian. Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application[J]. Applied Mathematics and Mechanics, 2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008

Citation:

FU Bao-lian. Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application[J]. Applied Mathematics and Mechanics, 2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008

Citation:

FU Bao-lian. Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application[J]. Applied Mathematics and Mechanics, 2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008

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Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application

doi: 10.3879/j.issn.1000-0887.2015.05.008

FU Bao-lian

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

Received Date: 2014-11-17
Rev Recd Date: 2015-02-07
Publish Date: 2015-05-15

Abstract

Abstract

It was discovered that the 2 main premises in the proposition of Betti’s reciprocal theorem for 3D linear elasticity, i.e. “1 elastic body” and “action of 2 sets of forces”, were contradictory to each other because either of the 2 sets of forces may change the given elastic body to another one. This contradiction leads to the result that Betti’s reciprocal theorem is one with error in logic. On the basis of the analysis of contradiction, the corrected reciprocal theorem was proposed, in which the correct proposition of the reciprocal theorem was given. In addition, the corrected reciprocal theorem provides a theoretical basis for the reciprocal method of works, which makes a novel and powerful way to the analysis of elastic bodies and structures.
- 1 elastic body,
- action of 2 sets of forces,
- reciprocal work,
- Betti’s reciprocal theorem,
- corrected reciprocal theorem,
- reciprocal method of works

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References(16)

References

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