Least weight design of truss structures with discrete variables

Least weigt design of truss structures with discrete variables is in fact a combinatorial problem, where the members of a geometrically defined truss, are selected from a given profile set. In order to reduce the number of combinations, two phased optimization approach is used in this work. In the first phase of the two phased optimization approach, the truss optimization problem, with continuous variables, which is a nonlinear optimization problem, is solved by sequential linear programming method, where the additional profile constraints are also considered. In the second phase of the optimization approach, in the near vicinity of the continuous optimum solution, where the additional profile constraints are also considered, a limited design space is defined in which the optimum of the discrete truss optimization problem is searched for.By introducing the additional profile constraints to the truss optimization problem with continuous variables, an original optimization problem is obtained. In the near vicinity of this continuous optimum solution, a limited design space is defined in which the optimum of the discrete truss design problem is searched for by an originally developed computer program by employing the multiple combination method. If the solution by the multiple combination method is time consuming then the approximation methods for solving discrete problems, which are originally developed in this work, are used such as double combination method or rounding the seniour area method, in order to obtain an approximate discrete solution.In this work, twelve truss optimization problems with discrete variables, which are taken from the publications, are satisfactorily solved by the above mentioned two phased optimization approach. In five of these problems even lighter discrete truss optimum designs are obtained. In this work, an additional thirty one truss optimization problems with discrete variables, which do not appear in the publications, are also satisfactorily solved by the above mentioned two phased optimization approach.