Form Finding Lab – Princeton University

Motivated by the need to combat coastal flooding, we re-invented pressurized thin-wall structures as an alternative to existing large-scale rigid solid seawalls. The core concept is that under extreme storm surge loading, the pressurized semi-cylindrical clamped membrane undergoes large displacements and geometrically stiffens because of the membrane’s increasing internal tension. This adaptive stiffening ensures that the structure has an adequate height to prevent water overtopping. Modeling the interaction between the pressurized membrane and the loads is complex because the loads are spatially-varying, the material (16mm thick vulcanized rubber coated nylon) behaves hyper-elastically and the membrane, lacking bending stiffness, must always be stiffened by the internal pressure.

Pressurized thin-wall structures are especially suited to resist extreme loads since they redistribute these loads over their entire three-dimensional surface. This study is challenging due to the large unprecedented scale of the pressurized membrane barrier, the extreme magnitude of the loading, the absence of engineering design codes for such application and the unknown three-dimensional interaction between the non-linear barrier and the fluid loads. The interpretation of the results of computational fluid/structure interaction models generates knowledge of the response of membranes subjected to extreme temporally and spatially varying loading conditions and further increase knowledge in this unexplored research domain in solid mechanics and lightweight structures design.

To optimize the design of the pressurized membrane, we coupled an adjoint-based method based on automatic differentiation of a finite-element model to a shape parametrization approach. At the large-scale, we were able to show that the stiffness of pressurized membranes (diameter 8m) adjusts and can be optimally designed as a function of internal pressure (20-40 kPa), under changing flood conditions found in Jamaica Bay (NY, USA), to prevent water overtopping while avoiding material rupture and resonance with the waves . The originality of this work lies in harnessing and designing the geometric stiffening effect, due to the changing tension in the membrane, as a strategy to design novel resilient structural systems with loading-dependent stiffness characteristics.