Geodesic
The generalization of Stevenson's theory of plates
Theoretical and applied mechanics, Tome 9 (1983) no. 1, p. 59 .

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The problem of exact solving of three equilibrim equations, six compatibility equations of Beltrami-Michell and six equations of Hook’s law is based in the Stevenson’s theory [3] on the assumption that the transverse load q (x,jy) is a harmonic function. This assumption which namely leads to a more realistic theory than Kirchhoff’s, introduces some restrictions on applicability of Stevenson’s theory. In this, article we treat the bending of elastic, homogeneous and isotropic plates by the assumption that the transverse load is a biharmonic function. Based on this, and the assumption that the weight is the only body force, exact solution of the above mentioned equations is obtained. The generalized theory is therefore exactly applicable to the extended set of transverse loads. In this article we do no represent the complete results, but only the differences between the generalized theory and Stevenson’s theory. Complete results of the Stevenson’s theory may be found in [1]. 
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     author = {Vitodrag Kumper\v{s}\v{c}ak},
     title = {The generalization of {Stevenson's} theory of plates},
     journal = {Theoretical and applied mechanics},
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Vitodrag Kumperščak. The generalization of Stevenson's theory of plates. Theoretical and applied mechanics, Tome 9 (1983) no. 1, p. 59 . http://geodesic.mathdoc.fr/item/TAM_1983_9_1_a5/