Assessment of Equilibrium Path Sensitivity in Truss Domes Vulnerable to Node Snap-Through with Respect to Load Distribution

The objective of the article is the assessment of the sensitivity of the equilibrium path of structures susceptible to loss of stability due to node snap-through. Increasingly, architectural designs feature organic forms and structures with complex geometry, which makes it possible to create very large, column-free spaces. These developments lead to the design of structures with ever smaller rise while simultaneously increasing their span. Due to the parameters of structures of this type, it is justified to analyze such systems with consideration of nonlinear effects. The Newton–Raphson algorithm was used to determine the limit points on the equilibrium path, employing both load control and displacement control. To accurately determine the position of the limit point on the equilibrium path, the step length was defined adaptively. Four dome space trusses were analyzed. Individual load sets were differentiated in terms of load location. The developed algorithm was implemented in a proprietary finite element method program created in the Matlab R2025b software. The analysis showed that, despite significant differences in the critical force (Pult), the global response of the structure at the moment of snap-through remains similar. The displacement of the apex node at the moment of snap-through remains similar across most of the proposed load sets. In the case of low-rise structures, a significant increase in the sensitivity of the load location to the critical load value and in the displacement of the apex node at the moment of snap-through was observed.