Optimum Elastic Design of Redundant Trusses

The problem studied is that of designing planar redundant trusses having fixed geometry and whose force distribution under applied loading may be adequately described by a linear analysis. The flexibility approach is used and it is assumed that all internal forces are caused purely by the application of the external forces, the latter being independent of the design. The problem is to minimize an objective function equal to the product of a vector of group areas and a vector of the products of group cost coefficients and the total length of members contained within the group. For all cost coefficients equal to unity the objective function is the total volume of structural material required and it may be converted into a weight or cost function by a choice of suitable coefficients. The optimization is subject to no member stress or cross-sectional area exceeding its upper or lower bound, but no deflection constraints are considered.