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**Exact mixed-classical solutions for the bending analysis of shear deformable rectangular plates.**
*(English)*
Zbl 1097.74562

Summary: The thin plate model leads to a differential equation of fourth-order, while the mixed first-order shear deformation plate is modeled by a system of differential equations of second-order. The first model does not provide a very good analysis of shear deformity in plates in which the thickness-to-length ratio is relatively large. Nevertheless, the latter is more difficult and much more accurate. In this paper, the relationships between the findings of the two models allowing shear deformation results to be obtained from the results of classical thin theories are displayed without using any shear correction factors. The exact solutions are presented for bending of six types of rectangular plates having two opposite edges simply supported, and the other two edges may be quite general. The accuracy of the present model is demonstrated via problems for which the exact solutions and numerical results are available, and solutions are also presented as benchmark solutions for researchers to use in checking their numerical thick plate solutions.

### MSC:

74K20 | Plates |

### Keywords:

Classical thin plate theory; Mixed thick plate theory; Lévy-type approach; Bending relationships
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\textit{A. M. Zenkour}, Appl. Math. Modelling 27, No. 7, 515--534 (2003; Zbl 1097.74562)

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### References:

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