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- W2040070272 abstract "In problems of plane elasticity, in the absence of body forces, the stresses are derivable from a scalar function known as the Airy stress function. By expressing this relation as a tensor equation, the use of the Airy function is generalized for any plane, orthogonal coordinate system. A general expression for the compatibility equation in terms of the stress function is given. It is found that considerable simplification results if isometric coordinates are used. The geometry of the isometric, curvilinear coordinate system is determined by a conformal mapping of the rectangular, Cartesian coordinate plane upon the curvilinear coordinate plane. For a given coordinate system the components of the metric tensor are expressible in terms of the mapping function. As an application of the preceding theory the uniform flexure of a beam whose edges are bounded by logarithmic spirals is discussed. It is found that all spiral beams may be specified by two dimensionless shape parameters. Stress distributions in a typical beam are exhibited. As limiting cases of the solution for a spiral beam, the uniform flexure of a wedge acted upon by a moment at the vertex and the uniform flexure of a sector of a circular ring are obtained." @default.
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- W2040070272 date "1954-01-01" @default.
- W2040070272 modified "2023-09-27" @default.
- W2040070272 title "The airy stress function in curvilinear coordinates with application to the uniform flexure of a naturally curved spiral beam" @default.
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- W2040070272 doi "https://doi.org/10.1016/0016-0032(54)91047-9" @default.
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