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Green’s functions for problems that simulate potential fields in thin-walled structures of irregular configuration

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Abstract

Matrices of Green’s type are targeted, for the first time, for a specific class of boundary–contact value problems which arise in studying potential fields induced in thin plate and shell assemblies of irregular configuration. A specific semi-analytic approach is proposed for evaluation of such matrices. It is based on our modification of the classical Kupradze’s method of functional equations. The approach appears workable for a broad range of the indicated problem settings. Representing the key component in the approach, matrices of Green’s type are analytically constructed to a number of boundary–contact value problems stated for relevant compound regularly configurated assemblies. This is accomplished prior to the actual computer work maintaining a solid background for fast and accurate solution of targeted problems.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN, 37132, USA

    Y. A. Melnikov

  2. Department of Mechanical Engineering, Tennessee Technological University, Cookeville, TN, 38501, USA

    V. N. Borodin

Authors
  1. Y. A. Melnikov
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  2. V. N. Borodin
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Correspondence to Y. A. Melnikov.

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Melnikov, Y.A., Borodin, V.N. Green’s functions for problems that simulate potential fields in thin-walled structures of irregular configuration. J Eng Math 112, 75–93 (2018). https://doi.org/10.1007/s10665-018-9966-6

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  • DOI: https://doi.org/10.1007/s10665-018-9966-6

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