Abstract
In the previous chapter, we exploited the idea that the strain energy U stored in an elastic structure must be equal to the work done by the external loads, if these are applied sufficiently slowly for inertia effects to be negligible. Equation (33.1) is based on the premise that the loads are all increased at the same time and in proportion, but the final state of stress cannot depend on the exact history of loading and hence the work done W must also be historyindependent. This conclusion enables us to establish an important result for elastic systems known as the reciprocal theorem.
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Barber, J.R. (2010). The Reciprocal Theorem. In: Elasticity. Solid Mechanics and Its Applications, vol 172. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3809-8_34
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DOI: https://doi.org/10.1007/978-90-481-3809-8_34
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Publisher Name: Springer, Dordrecht
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