Three-dimensional elasticity based on quaternion-valued potentials

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:51

Article

Weisz-Patrault, Daniel¹  Bock, Sebastian²  Guerlebeck, Klaus² 

[1] Ecole Ponts ParisTech, UR Navier, F-77455 Marne La Vallee, France

[2] Bauhaus Univ Weimar, Inst Math & Phys, Weimar, Germany

关键词: Isotropic elasticity;    Quaternions;    Monogenic potential;    Meshless;    Residual stress;    Thermal load;   

DOI  :  10.1016/j.ijsolstr.2014.06.002

来源: Elsevier

【 摘 要 】

One of the most fruitful and elegant approach (known as Kolosov Muskhelishvili formulas) for plane isotropic elastic problems is to use two complex-valued holomorphic potentials. In this paper, the algebra of real quaternions is used in order to propose in three dimensions, an extension of the classical Muskhelishvili formulas. The starting point is the classical harmonic potential representation due to Papkovich and Neuber. Alike the classical complex formulation, two monogenic functions very similar to holomorphic functions in 2D and conserving many of interesting properties, are used in this contribution. The completeness of the potential formulation is demonstrated rigorously. Moreover, body forces, residual stress and thermal strain are taken into account as a left side term. The obtained monogenic representation is compact and a straightforward calculation shows that classical complex representation for plane problems is embedded in the presented extended formulas. Finally the classical uniqueness problem of the Papkovich Neuber solutions is overcome for polynomial solutions by fixing explicitly linear dependencies. (C) 2014 Elsevier Ltd. All rights reserved.

【 授权许可】

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