Abstract
An optimum design method of truss based on dual theory, linear approximation and suboptimization of member element is presented. In the practical design problems of truss, several original design variables and constraints related to a member element are condensed into one primal variable and single artificial constraint respectively by suboptimization of member element. Then the design problem is transformed into a sequence of approximate primal problems of convex and separable form by linear approximation concepts. The convex problems are solved by dual method, in which dual function is maximized by using quasi-Newton algorithm on the dual variables and the primal variables are decided directly by explicit expressions of the dual variables. Due to the sharp nonlinear constraints imposed on member elements, move limit restrictions on the design variables are required to converge successive solutions to the optimum. Application of the envelope method based on optimality criteria and linear set of equations are also discussed to estimate appropriate initial values of the primal and dual variables respectively. The efficiency and reliability of the design method presented are demonstrated by giving numerical results for large scale trusses.
