Abstract
A problem is two-dimensional if the field quantities such as stress and displacement depend on only two coördinates (x, y) and the boundary conditions are imposed on a line f(x, y)=0 in the xy-plane.
In this sense, there are strictly no two-dimensional problems in elasticity. There are circumstances in which the stresses are independent of the z-coördinate, but all real bodies must have some bounding surfaces which are not represented by a line in the xy-plane. The two-dimensionality of the resulting fields depends upon the boundary conditions on such surfaces being of an appropriate form.
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© 2010 Springer Science+Business Media B.V.
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Barber, J.R. (2010). Plane Strain and Plane Stress. In: Elasticity. Solid Mechanics and Its Applications, vol 172. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3809-8_3
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DOI: https://doi.org/10.1007/978-90-481-3809-8_3
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