Abstract
Many physical problems are reducible to two dimensions which facilitate their eventual solution. If there is no traction on one plane passing through the body, this state is known as plane stress since all nonzero stresses are confined to planes parallel to the traction-free plane. This is an obvious possibility for bodies with one dimension much smaller than the other two, such as a thin sheet or diaphragm loaded in the plane perpendicular to the small dimension. Another possibility is a body in which one dimension is much greater than the other two, such as a long pipe or a dam between massive end walls. This is known as plane strain.
The development is primarily confined to the realm of isotropic elasticity with some extensions to more complex material laws.
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Notes
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This prompted a favorite saying among graduate students and professors in an earlier era, that “All you really need is Love.”
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Gould, P.L., Feng, Y. (2018). Two-Dimensional Elasticity. In: Introduction to Linear Elasticity. Springer, Cham. https://doi.org/10.1007/978-3-319-73885-7_7
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DOI: https://doi.org/10.1007/978-3-319-73885-7_7
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