Castigliano's method

From Wikipedia, the free encyclopedia

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.

[edit] External links

• Carlo Alberto Castigliano
• Structural engineering module of Wikibooks
• Castigliano's method: some examples – links to a German language page