An algorithm for optimal design of structures with discrete set of specified design variables is developed. The algorithm first finds the optimum design under the assumption that the design variable can be varied continuously. Then the Phase-I search is performed to find a feasible discrete solution from a point which is near the optimum disign but is in the infeasible set. The solution is further improved in the Phase-II search, to obtain the final discrete optimal design of the problem.
The state space formulation and the adjoint variable technique are used for the design sensitivity analysis, while the gradient projection method is adopted to obtain the initial continuous value optimum design.
A computer program is written to test validity and efficiency of the algorithm with various example problems of minimum weight truss design subject to displacement, stress, and design variable constraints. As the results, it is found that the algorithm is highly stable and can be readily applicable to various structural optimization problems with discrete set of specified design variables.
