An explicit exact formula is derived for the objective function of the dual problem of a class of separable convex programming problems.It makes more mature and efficient methods can be chose to solve the dual model.Therefore,the advantage of applying the duality theory of nonlinear programming to efficiently solve structural topology optimization problems is fully exploited.The research work is rooted in that the gap of a nonlinear convex programming with its dual programming is zero.Solving original programming can be equivalently transformed into solving its dual programming.