Based on Melan's theorem, the symmetric Galerkin boundary element method (SGBEM) is used to discretize two dimensional structures and a computational formulation of structural limit analysis is established. The self equilibrium stress field is constructed by linear combination of several basic vectors, which are the stress differences between different iteration steps at the same increment using the traditional elastoplastic incremental method. Then the complex method is used to solve the nonlinear programming directly, so that the lower bound load multiplier of two dimensional structures is obtained. The validation of the present method has been confirmed by some numerical examples.