Definitions

# 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 qi; then the partial derivative of the strain energy with respect to generalised displacement gives the generalised force Qi.

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 Qi; then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement qi in the direction of Qi.