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On Monogenic Series Expansions with Applications to Linear Elasticity

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Abstract

In this paper recently studied orthogonal Appell bases of solid spherical monogenics in \({\mathbb{R}^3}\) are used to construct a polynomial basis of solutions to the Lamé equation from linear elasticity. To this end, a compact closed form representation of the Appell basis elements in terms of classical spherical harmonics is proved and a recently developed spatial generalization of the Kolosov-Muskhelishvili formulae in terms of a monogenic and an anti-monogenic function is applied.

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Authors and Affiliations

  1. Junior professorship “Simulation and Experiment”, Bauhaus-University Weimar, Marienstraße 7A, 99423, Weimar, Germany

    Sebastian Bock

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  1. Sebastian Bock
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Correspondence to Sebastian Bock.

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Dedicated to Klaus Gürlebeck on the occasion of his 60th birthday

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Bock, S. On Monogenic Series Expansions with Applications to Linear Elasticity. Adv. Appl. Clifford Algebras 24, 931–943 (2014). https://doi.org/10.1007/s00006-014-0490-0

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