Summary
A complex potential solution for the problem of an infinite beam subjected to simple bending and axial traction along its longitudinal axis was established by using simple complex stress functions for the plain beam case, to which stress functions expressed in the form of integral equations were superimposed which satisfy the boundary conditions at the rim of the central perforation of the beam. Evaluation of the first stress invariant along the rim the hole allows the definition of the caustics and its initial curves formed around the hole which define the state of stress at its neighborhood. The characteristic properties of the caustics were studied which were three-lobe epicycloids and the relationships of their dimensions with the surrounding elastic stress field.
The domain of influence of these perforations was defined which allowed their use as stress rosettes for evaluating the stress field at different points of the beam without any mutual influence and with the longitudinal boundaries of the beam. The method may be used as a hybrid measuring device in applications.
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Theocaris, P.S. A simple solution for a perforated beam in bending and traction. Acta Mechanica 71, 21–38 (1988). https://doi.org/10.1007/BF01173935
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DOI: https://doi.org/10.1007/BF01173935