- Castigliano's method
**Castigliano's method**, named forCarlo Alberto Castigliano , is a method for determining the displacements of a linear-elastic system based on thepartial derivative s of the strain energy. In the mathematics of structures, he is known for his two theorems:

***Castigliano's first theorem**– for forces in an elastic structure

***Castigliano's second theorem**– for displacements in a linearly elastic structureCastigliano's method for calculating forces is an application of his first theorem, which states::"If the strain energy of an elastic structure can be expressed as a function of generalised displacement q

_{i}; then the partial derivative of the strain energy with respect to generalised displacement gives the generalised force Q_{i}."Castigliano's method for calculating displacements is an application of his second theorem, which states::"If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q

_{i}; then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q_{i}in the direction of Q_{i}."**External links*** [

*http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Castigliano.html Carlo Alberto Castigliano*]

* [*http://en.wikibooks.org/wiki/Structural_engineering#Castagliano.27s_theorems Structural engineering*] module of Wikibooks

* [*http://www.matheplanet.com/matheplanet/nuke/html/article.php?sid=1008&mode=&order=0 Castigliano's method: some examples*] – "links to a German language page"

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