Optimal layout of long-span truss-grids. I (Q1064850)

After reviewing briefly Prager's optimal layout theory, the optimization of isolated trusses is considered, and then optimality criteria are derived for the minimum-weight layout of truss-grids. The theory is applied to simply supported circular truss-grids, whose radius does not exceed a certain limiting value. It will be shown that layout optimization for long-span systems results in most substantial savings. In all problems considered, the optimal solution is derived analytically and confirmed by three independent methods: namely, primal (variational) formulation, dual formulation and direct minimization of the cost with respect to some geometrical parameters of the layout. Although the problems discussed in this paper are formulated in the context of optimal plastic design, the solutions obtained are statically determinate and hence they are also valid in optimal elastic design for given permissible stresses.