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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| Published in | Applied Mechanics and Materials Vol. 5-6; pp. 541 - 550 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Zurich
Trans Tech Publications Ltd
15.10.2006
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| Subjects | |
| Online Access | Get full text |
| ISBN | 9780878494187 0878494189 |
| ISSN | 1660-9336 1662-7482 1662-7482 |
| DOI | 10.4028/www.scientific.net/AMM.5-6.541 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Barber, J.R. |
| Author_xml | – givenname: J.R. surname: Barber fullname: Barber, J.R. email: jbarber@umich.edu organization: University of Michigan : Department of Mechanical Engineering and Department of Civil and Environmental Engineering |
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| Cites_doi | 10.1088/0964-1726/14/4/019 10.1016/j.ijsolstr.2003.12.011 10.1016/0021-8928(64)90012-7 10.1080/14786435808565804 10.4171/rlm 10.1016/j.ijsolstr.2003.11.006 10.1007/978-3-642-85627-3 10.1007/978-3-642-87870-1 10.1098/rspa.1945.0015 10.1098/rspa.2005.1646 10.1002/sapm196241177 10.1093/oso/9780195074475.001.0001 10.1016/s0020-7683(00)00374-7 10.1007/BF00282340 10.1080/14786444308521444 |
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| Keywords | Papkovich-Neuber Solution Prismatic Bar General Anisotropy Three-Dimensional Elasticity Stroh Formalism |
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| Snippet | 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... 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... 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... |
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| Title | Three-Dimensional Elasticity Solutions for Isotropic and Generally Anisotropic Bodies |
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