Optimization of layout and shape of stiffeners in 2D structures

The problem of layout and shape optimization of stiffeners in plates loaded in plane and in bending Kirchhoff’s plates is considered in the paper. Two types of reinforcement are analyzed here, namely introduction of elements made of stiffer material like fibers or beams and introduction of ribs. The problem of minimization (maximization) of arbitrary objective functional of displacements, strains, stresses or reactions with constraint imposed on the structure cost is considered. Using adjoint method, expressions for sensitivities with respect to introduction of stiffeners are derived and on this basis conditions of modification are formulated. In order to find optimal reinforcement, heuristic algorithm is proposed in the paper. At first, using information from sensitivity analysis, initial localization of a new fiber or rib is determined. Next, in order to correct their positions and to determine other parameters characterizing stiffened structure standard optimization is performed. Usually, optimal position of the stiffener only a little differs from the initial position. Numerical examples illustrate applicability of the method.