Linking

Just as it may be desirable to restrict design variables to a certain range of values, it may also be desirable to force several design variables to take on the same value for every iteration of the optimization process. This is accomplished through linking. For example, the current formulation uses two bending elements to span a single bay. Although two elements are used, in reality this bay would be spanned by a single beam. In turn, the two separate elements should be forced to take on the same design value. Again, within the optimization algorithm it is possible to represent multiple design variables with a single variable yet still account for the change in both structural elements within the gradient calculations (Cheng et al.). Although both beam elements can be represented by a single variable, the change in cross sectional properties of each element must be accounted for as they both have an effect on the convergence to a local minimum of the objective function subject to the constraint equations.