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Abstract

A modified version of the classical method of functional equations is developed for accurate evaluation of the response to a transverse point concentrated force for multiply connected Kirchhoff plates. The resolving potentials are built, in this version, with the aid of Green functions of the biharmonic equation for regions of standard shape. The importance of having readily computable representations of such Green functions is emphasized. Since the observation and the source points in the resolving potentials occupy different sets, the boundary value problems to consider reduce to some functional (integral) equations with relatively smooth kernels. It is shown that not only the deflection function, but also the stress components caused by a transverse point force, are accurately computable within this approach.

Keywords

multiply connected Kirchhoff plates Green’s function

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References

[1] Morse, P. M. and Feshbach, H. : Methods of Mathematical Physics, vols 1 and 2, McGraw-Hill, New York , 1953.

[2] Timoshenko, S. and Woinowsky-Krieger, S. : Theory of Plates and Shells, McGraw-Hill, New York , 1959.

[3] Gradstein, I. S. and Ryzhik, I. M. : Tables of Integrals, Series and Products, Academic, New York , 1980.

[4] Lebedev, N. N. , Skal’skaya, I. M. and Uflyand, Ya. S. : Problems of Mathematical Physics, Pergamon, New York , 1966.

[5] Melnikov, Yu. A. : Influence Functions and Matrices, Dekker, New York , 1998.

[6] Melnikov, Yu. A. : Some applications of the Green’s function method in mechanics . Int. J. Solids Structures, 13, 1045-1058 (1977).

[7] Melnikov, Yu. A. and Sheremet, V.D. : Some new results on bending of a circular plate subject to a transverse point force . Math. Mech. Solids, 6, 29-45 (2001).

[8] Kupradze, V.D. : Method of Potential in the Theory of Elasticity, Davey, New York , 1965.

[9] Golberg, M. D. and Chen, C. S. : Discrete Projection Methods for Integral Equations, Computational Mechanics Publications, Southampton , 1997.

Influence Functions of a Point Force for Multiply Connected Kirchhoff Plates

Abstract

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