Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Equilibrium of membranes elastically supported at the edges


Author: V. G. Hart
Journal: Quart. Appl. Math. 12 (1955), 408-412
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/65370
MathSciNet review: 65370
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Abstract: The problem considered is that of finding the statical deflection of a stretched membrane, subjected to a uniform pressure on one side and elastically supported at the edges. The deflection of the membrane is supposed small and the problem reduces to solving Laplace's equation with mixed boundary conditions. Solutions are given for the cases where the bounding curve of the membrane is (i) an equilateral triangle, and (ii) a rectangle.


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DOI: https://doi.org/10.1090/qam/65370
Article copyright: © Copyright 1955 American Mathematical Society


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