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Equilibrium of elastic rectangle: Mathieu-Inglis-Pickett solution revisited

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Abstract

This paper addresses a general analytical method for investigating the two-dimensional distributions of stresses set up in a rectangular plate by a load applied along its sides in any arbitrary manner. Proposed independently by Mathieu (1890), Inglis (1921) and Pickett (1944), and later named the ‘superposition method’, it has been applied with success to the study of distribution of stresses inside a rectangle. The object of this paper is to prove the advantages of that approach when studying a stress field near the boundaries, including specific cases of discontinuous and concentrated normal and shear loadings. The method is illustrated by several numerical examples, the rapidity of convergence and the accuracy of results are investigated. The distribution of stresses along some typical lines in the plate are computed and shown graphically.

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Author notes

  1. V. V. Meleshko

    Present address: Institute of Hydromechanics, National Academy of Sciences, Kiev, Ukraine

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  1. Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

    V. V. Meleshko

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Meleshko, V.V. Equilibrium of elastic rectangle: Mathieu-Inglis-Pickett solution revisited. J Elasticity 40, 207–238 (1995). https://doi.org/10.1007/BF00043957

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