27.7 : 卡斯提利亚诺定理

Castigliano's theorem is useful for determining displacements and rotations in structures undergoing elastic deformations.

It states that the partial derivative of the elastic strain energy concerning a given load is equivalent to the displacement at the point of application of the particular load.

Similarly, suppose the structure is subjected to couples. In this case, the angle of rotation of the structure at the point of application of a couple is calculated by partially differentiating the strain energy with respect to the applied couple.

For structures undergoing twisting due to slowly applied torques, the angle of twist for a section of the shaft can be calculated by taking the partial derivative of the strain energy with respect to the applied torque.

If a beam with non-uniform cross-sections undergoes deformation due to loading, the strain energy is expressed in terms of an integral. Here, the deflection at the point of application of the load is calculated by differentiating the strain energy with respect to the load before the integration.