Geometric modeling of a moment-free shell of a given shape

In modern construction and architectural design, approaches aimed at optimizing structures to reduce material consumption without compromising strength, aesthetics, and functionality are becoming increasingly relevant. One such approach is the static-geometric modeling method, which enables the design of moment-free shells that are characterized by the absence of bending moments under their own weight. The main goal of this study was to develop an efficient methodology for designing shell structures with minimal material usage while ensuring their stability. The work presents an approach that utilizes discrete models approximated by planes. Additionally, an algorithm for calculating specific parameters of moment-free shells is introduced, including the coordinates of the discrete grid nodes, surface area, and nodal forces. Special attention is given to determining the optimal thickness of shell elements, ensuring their equilibrium and resistance to external influences. To verify the method’s effectiveness, modeling was conducted for spherical and rotational paraboloid shells. The developed methodology allowed for the consideration of geometric features and the interaction of structural elements.