Abstract: In this paper, the solution of elliptic equation (sum from k-0 to n) a_kΔ^kφ=0 is discussedin detail by the method of separation of variables in complex field. The general solution which can be used in the approximation to the boundary conditions of the practical problems is presented. Two practical examples in mechanics are given.

Key words: discrete variables, structure optimization, topological optimization, dynamic stress constraint, dynamic displacement constraint