Castigliano's method

Castigliano's method, named for Carlo Alberto Castigliano, is a method for determining the displacements of a linear-elastic system based on the partial derivatives 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 structure

Castigliano'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"