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Acta Mechanica
Published in: Acta Mechanica 12/2023

21-09-2023 | Original Paper

Solution to boundary value problems on linear elastic confocal elliptic domain based on collocation technique

Authors: Aditya G. Konale, Tanmay K. Bhandakkar

Published in: Acta Mechanica | Issue 12/2023

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Abstract

Domains with elliptic boundaries are regularly pursued in Elasticity to elucidate the role of circular asymmetry and are associated with many classical closed form solutions. The work under consideration presents a unified semi-analytical approach to solve for stress and displacement field while being subjected to all kinds of plausible boundary conditions on any variant of elliptic geometry i.e. elliptic cylinder to confocal elliptic annulus to elliptic hole in an infinite plane. The generalized representation of Airy stress function in elliptical co-ordinates truncated to finite terms is considered and the associated coefficients are deduced to ensure boundary conditions using collocation technique. The correctness and effectiveness of the method is demonstrated through solution to a variety of problems and its validation via an independent finite element simulation.
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Metadata
Title
Solution to boundary value problems on linear elastic confocal elliptic domain based on collocation technique
Authors
Aditya G. Konale
Tanmay K. Bhandakkar
Publication date
21-09-2023
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 12/2023
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-023-03712-1

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