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**Edge effect in the bending of a thin three-dimensional plate.**
*(English.
Russian original)*
Zbl 0722.73037

J. Appl. Math. Mech. 53, No. 4, 500-507 (1989); translation from Prikl. Mat. Mekh. 53, No. 4, 642-650 (1989).

Summary: The boundary layer near the rigidly clamped edge of a thin three- dimensional plate subjected to bending loads is investigated. It is shown that taking account of the next term in the deflection asymptotic form results in the appearance of inhomogeneities in the boundary conditions on the plate edge. It is proved that far from the edge the difference in the solution of the problem in an invariant formulation and the three- dimensional solution is inversely proportional to the plate thickness (the error for the Kirchhoff solution is inversely proportional to the square of the thickness; near the edge the accuracies of both solutions are identical). A correction term is found in a representation of the eigenfrequencies of the bending vibrations and a comparison is made with the Reissner theory.

### MSC:

74K20 | Plates |

35J55 | Systems of elliptic equations, boundary value problems (MSC2000) |

35B40 | Asymptotic behavior of solutions to PDEs |

### Keywords:

boundary layer; rigidly clamped edge; deflection asymptotic form; inhomogeneities in the boundary conditions; correction term; representation of the eigenfrequencies
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\textit{I. S. Zorin} and \textit{S. A. Nazarov}, J. Appl. Math. Mech. 53, No. 4, 500--507 (1989; Zbl 0722.73037); translation from Prikl. Mat. Mekh. 53, No. 4, 642--650 (1989)

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### References:

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