Optimization of load-transfer and load-diffusion

The problem of optimization of a stringer, or a stiffener, attached to an elastic infinite plate is investigated. The plate is exposed to tensioning by uniformly distributed forces, and also to contact stresses due to forces as a result of enforced continuity with the reinforcing stiffener. The novelty of the optimization problem is emphasized in an elongated, needle-shaped form of the stringer. The cross-section together with its axial stiffness is variable along the axis of the stiffener. The cross-section, which is primarily unknown, represents the searchable function in the optimization problems. A flattened, plate-shaped stiffener that supports a semi-infinite prismatic body is also briefly pursued. Optimization problems of the flattened stiffener are proved to be quite similar to those of the elongated one. The governing equations of both studied cases transform into each other by means of alternation of the elastic constants. Consequently, the optimal cross-sections of both problems turn out to be identical after the appropriate choice of material parameters. The article studies two optimization problems: minimization of the ultimate stress along the stringer and minimization of the stringer mass under the constraints on the integral compliance of the reinforced body. The shape optimization is studied in the case of an isolated stiffener and in the case of a periodic array of stiffeners. The analytical expressions for the optimal cross-section profiles are found.