Betti's theorem
Betti's theorem, also known as Maxwell-Betti reciprocal work theorem, discovered by Enrico Betti in 1872, states that for a linear elastic structure subject to two sets of forces {Pi} i=1,...,m and {Qj}, j=1,2,...,n, the work done by the set P through the displacements produced by the set Q is equal to the work done by the set Q through the displacements produced by the set P. This theorem has applications in structural engineering where it is used to define influence lines and derive the boundary element method.