Example: If a plate, m = 1 , n = 2 , is loaded with a single force, i = 0 , the inequality is not valid, 1 − − 0 ≯ ≯ 2 / 2 , also not in 3 − − D , m = 1 , n = 3 , 1 − − 0 ≯ ≯ 3 / 2 . Nor does it apply to a membrane (Laplace), m = 1 , n = 2 , i = 0 , or a Reissner-Mindlin plate, m = 1 , n = 2 , i = 0 . In general Castigliano's theorems do not apply to 2 − − D and 3 − − D problems. The exception is the Kirchhoff plate, m = 2 , n = 2 , i = 0 , since 2 − − 0 > 2 / 2 . But a moment, i = 1 , causes the energy of a Kirchhoff plate to overflow, 2 − − 1 ≯ ≯ 2 / 2 . In 1 − − D problems the strain energy is finite if m − − i > 1 / 2 .