What is castigliano method?

Castigliano's method is a mathematical technique used to calculate the deflection and slope of a linear elastic structure subjected to external loads. It involves differentiating the total potential energy of the structure with respect to a specific degree of freedom and setting it equal to zero to obtain the partial derivative. This partial derivative evaluated at unit load in the direction of the degree of freedom gives the deflection or slope at that point. The Castigliano's method is widely used in the analysis of mechanical structures such as beams, trusses, and frames, and provides a useful and accurate tool for engineering design and analysis. It is named after Carlo Alberto Castigliano, an Italian engineer who developed the method in the late 1800s.