Optimization of folded plate roofs

Abstract

Increased usage of prefabricated structural components and the advantages offered by folded plate roofs necessitates the optimization of their configurations. In order to reduce the material expenditure, transportation and erection costs the dead-weight of the roof systems need to be minimized. The reported study defines a technique for the optimization of the structural weight of the folded plate roof without intermediate stiffeners and subjected to one loading system. The developed method enabled the generation of the different, and consequently the optimum, geometries by starting with an arbitrary initial geometry. The azimuthal angles, the width and the thickness of the individual panels were permitted to vary. The optimization employed a variational approach and flexibility formulation. The total weight of the roof was taken as the target function, subject to minimization. The equilibrium equations for the panels were taken as the constraint equations for the optimization process. The pseudo-weight function was established through the use of the Lagrangian multipliers. The standard Lagrangian formulation was then applied to the pseudo-weight function, and a set of optimization equations were generated. These equations, along with the original equilibrium equations, formed a system of simultaneous nonlinear transcendental equations. This set was solved using an iterative approach. The overall formulation was kept general enough to permit the inclusion of any given loading condition to permit the application of the given methodology to any folded plate roof system.