Discrete Valued Optimal Design Problems

In structural synthesis problems, it frequently happens that some of the design parameters, instead of varying continuously, can only take on discrete values : standard gauge sizes, number of plies in laminated composite skins, material properties, etc ... This paper presents a method capable of solving such problems by greatly reducing the difficulties due to their combinatorial nature. Attention will be focused on problems in which both the transverse sizes of the structural members and the material properties constitute discrete variables. Starting from the simple case of a pin-joined truss, an efficient approach is developed, which proceeds by generating a sequence of explicit separable subproblems and using a dual method formulation. Then structures involving fiber reinforced resins are considered, in which the number of plies in each orthotropic layer, as well as the composite material properties, are discrete design variables. It is finally shown that the choice of the fiber orientations could be operated by defining fictitious equivalent materials. Some numerical examples will be offered to demonstrate the effectiveness and the potential practical use of the method presented.