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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(2):160-168; doi:10.1093/qjmam/10.2.160
© 1957 by Oxford University Press
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STRESS SOLUTIONS FOR RECTANGULAR PLATES BY CONFORMAL TRANSFORMATION

A. M. WINSLOW

( University of Washington Seattle )

Rectangular plates with distributed forces on the boundaries, x = ±a, y = ±b, are considered. The x, y-components of the coplanar tractions are expressed as monomials or polynomials in positive integral powers of x; or y. For these conditions, two-dimensional stress analysis given by Muskhelishvili is supplemented by additional developments. A function of the tractions, in terms of the complex variable z and its conjugate , is separated into two parts. In this manner an exact polynomial solution is combined with a solution derived by a conformal transformation. The transformation, without rotation of coordinate axes, maps z-points of the rectangular area as {zeta}points in a circular area of unit radius. In this transformed solution where finite summations are taken as approximate values of infinite series, bounds of the approximations can be determined. Typical procedures are shown in examples with square and rectangular plates.


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