The effects of membrane thickness and asymmetry in the topology optimization of stiffeners for thin-shell structures

Thin-walled shell structures are extensively used in architecture and engineering owing to their light weight and ease of shaping. But they suffer from poor overall stiffness, something addressed by the strategic addition of stiffeners. The optimization of stiffeners is divided between those that include shell membrane in the optimization and those that do not. However, no studies were found that indicate when it is necessary or valid to use either approach. In most cases it was also found that symmetry was forced in the optimization of stiffening layers. These two effects were investigated, and the following conclusions were reached. Membranes with thicknesses less than 20% of the structure do not affect the final topology, whereas membrane thicknesses greater than 20% must be included in the optimization as they have a considerable effect. When bending and membrane loadings are present, symmetry should not be forced, otherwise suboptimal designs are generated.