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Point loads on a straight slot with rounded ends for a plane elasticity problem

David J. Unger
Vol. 19 (2024), No. 5, 907–918
DOI: 10.2140/jomms.2024.19.907
Abstract

A plane stress linear elastic problem is proposed for two opposed point loads applied at the center of a linear slot with rounded ends in an infinite plate. A Kolosov–Mushelishvili solution technique is applied to this problem. A conformal mapping function is found that transforms the slot geometry in the plane onto the surface of a circular cylinder. As the mapping function contains branch points, a series expansion of the coordinates is necessary in order to obtain an approximate solution to the original problem. A simple expression for an equivalent slot is given for an elliptical hole.

Keywords
point load, slot, plate, elasticity
Milestones
Received: 14 November 2024
Accepted: 7 December 2024
Published: 25 December 2024
Authors
David J. Unger
Mechanical and Civil Engineering
University of Evansville
Evansville, IN 47722
United States
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