FEM Validation of Form-Found Shell Roofs Designed in Seismic Areas

Shell structures offer high structural efficiency when their shapes allow loads to be carried mainly through compression, making them particularly suitable for materials with limited tensile strength, such as masonry, unreinforced concrete, and unreinforced 3D-printed concrete. The purpose of this work is to evaluate the structural quality and practical reliability of shells obtained through a physics-informed neural network-based optimized constrained form-finding (PINN-OCFF) methodology. This form-finding approach explicitly accounts for both vertical and horizontal loading conditions at the design stage by identifying an isoresistant volume capable of withstanding these actions through pure compression. Unlike traditional form-finding methods that focus primarily on gravity loading, the PINN-OCFF strategy generates shell shapes intended to remain in compression under combined loading conditions relevant to real design situations. The study focuses on a shell designed through this PINN-OCFF framework and assesses its performance through finite-element method (FEM) analyses carried out in Abaqus, following modeling assumptions commonly adopted in engineering practice and required by design codes such as the Eurocodes, ACI, or the Italian NTC. The FEM results are compared with the membrane equilibrium predicted by the form-finding process in terms of the stress distribution, development of tensile zones, and overall structural response. To investigate the influence of boundary conditions, three different constraint configurations are considered: fully fixed edges, fully hinged edges, and hinges located only at the base supports. For comparison, a shell of uniform thickness is considered and analyzed under the same vertical and horizontal loads used during form finding. The analyses show that the shell designed through the PINN-OCFF form-finding process better preserves compression-dominated behavior under realistic modeling assumptions, even when horizontal loading conditions and nonideal boundary conditions are introduced. Compared to shells designed considering vertical loads alone or employing a uniform thickness, the optimized shell exhibits reduced bending effects and limited tensile stresses. These findings demonstrate that incorporating horizontal actions directly into the form-finding stage leads to more robust and practically reliable shell designs, supporting the use of the PINN-OCFF methodology as an effective preliminary design tool for compression-dominated shell structures.