Form Finding of Compressive Gridshells Using an Elastic Force Density Framework

The force density method is an equilibrium-based form finding approach commonly used to define the geometry of funicular and anti-funicular structural networks. This study revisits form finding of compressive reticulated shells by extending the standard equilibrium equations with additional constraints that incorporate both kinematic relations and the constitutive law. The result is an enhanced formulation capable of capturing linear elastic equilibrium through constrained optimization. Using mathematical programming, a unique set of force densities is determined that governs both the structural shape and its elastic response, while naturally ensuring control over deflections. This framework enables the design of elastic no-tension configurations, which are relevant for applications such as 3D concrete printing. Numerical simulations are carried out to optimize compressive gridshells with fixed plan geometry under vertical loads. Two objectives are investigated: minimizing the maximum reaction force and minimizing structural compliance. For the first objective, results are compared with those from a traditional equilibrium-based approach, while for the second, comparisons are made with a combined force density and finite element method. The sensitivity of the resulting forms to the underlying modeling assumptions is highlighted.