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

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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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Acknowledgements

TKB gratefully acknowledges the financial assistance extended by Science and Engineering Research Board (SERB) through the MATRICS Grant MTR/2020/000217.

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  1. Aditya G. Konale

    Present address: Brown University, Providence, RI, USA

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

    Aditya G. Konale & Tanmay K. Bhandakkar

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  1. Aditya G. Konale
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Correspondence to Tanmay K. Bhandakkar.

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Konale, A.G., Bhandakkar, T.K. Solution to boundary value problems on linear elastic confocal elliptic domain based on collocation technique. Acta Mech 234, 6359–6376 (2023). https://doi.org/10.1007/s00707-023-03712-1

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