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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 10/2017

22-07-2017 | Original

A generalization of Castigliano’s theorems for structures with eigenstrains

Author: I. Romero

Published in: Archive of Applied Mechanics | Issue 10/2017

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Abstract

We prove two results that generalize the two classical theorems of Castigliano to structures with known (stationary) eigenstrains, including those originating from temperature changes, lack-of-fit, phase changes, etc. We show that in these situations the classical theorems of Castigliano still hold, provided that the appropriate modifications are made to the elastic energy and its conjugate. The derivation of these results follows directly from the principle of minimum potential energy and some of the properties of convex functions. Just like the classical theorems, the final results can be conveniently employed to solve simple structures by hand.
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Metadata
Title
A generalization of Castigliano’s theorems for structures with eigenstrains
Author
I. Romero
Publication date
22-07-2017
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 10/2017
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-017-1282-5

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