Flowers are the reproductive, seed-producing structures of angiosperms. Typically, flowers consist of sepals, petals, stamens, and carpels. Sepals and petals are the vegetative flower organs. Stamens and carpels are the reproductive organs.

Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.