Engineering Transactions, 11, 3, pp. 411-423, 1963

Płyta Wspornikowa Nieskończenie Długa Obciążona Siłą Skupioną

F. Dymek
Politechnika Krakowska

On the basis of the engineer's theory of thin isotropic plates the state of strain and stress of an infinitely long cantilever plate is considered. The plate, which is of constant thickness, is loaded by a concentrated force on the free end (Fig. 1).
Assuming that the deformed middle surface of the plate w(x, y) can be represented in the form of the integral (3), the Cauchy residue theorem is made use of to obtain an accurate solution of the differential Eq. (1) with the boundary conditions (2) in the form of Eq. (13). The solution of the problem in the form of Eq. (13)-(16) satisfies all the boundary conditions required (2), as well as the differential Eq. (1) and the conditions at infinity. The roots of the transcendental algebraic Eq. (11) are collated in Tab. 1 for five values of the coefficient of Poisson V.
To show the influence of the coefficient of Poisson y on the state of stress and strain of the plate, the diagrams of Fig. 3-8 have been drawn for the two extreme values of the coefficient, that is for v = 0 and y = 0.5. The first five terms of the series are used for numerical computation.

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