Three-Dimensional Elasticity Solutions for Isotropic and Generally Anisotropic Bodies

Classical methods of two-dimensional elasticity can be extended to give an exact solution of the three-dimensional problem for the beam — i.e. a general solution for the pris- matic bar loaded on its lateral surfaces, subject only to the restriction that the tractions can be expanded as power series...

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Bibliographic Details
Published inApplied Mechanics and Materials Vol. 5-6; pp. 541 - 550
Main Author Barber, J.R.
Format Journal Article
LanguageEnglish
Published Zurich Trans Tech Publications Ltd 15.10.2006
Subjects
Papkovich-Neuber Solution
Prismatic Bar
General Anisotropy
Three-Dimensional Elasticity
Stroh Formalism
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ISBN9780878494187
0878494189
ISSN1660-9336
1662-7482
1662-7482
DOI10.4028/www.scientific.net/AMM.5-6.541

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Summary:Classical methods of two-dimensional elasticity can be extended to give an exact solution of the three-dimensional problem for the beam — i.e. a general solution for the pris- matic bar loaded on its lateral surfaces, subject only to the restriction that the tractions can be expanded as power series in the axial coordinate z. A series of sub-problems Pj is defined by successive partial differentiations with respect to z. For isotropic materials, a recursive al- gorithm can be used for generating the solution to Pj+1 from that for Pj in the context of the Papkovich-Neuber solution. For the generally anisotropic material, a similar strategy is proposed, based on partial integrations of Stroh’s formulation of the two-dimensional problem.
Bibliography:Proceedings of the 6th International Conference on Modern Practice in Stress and Vibration Analysis, University of Bath, UK, 5-7 September 2006
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ISBN:9780878494187
0878494189
ISSN:1660-9336
1662-7482
1662-7482
DOI:10.4028/www.scientific.net/AMM.5-6.541