Wooden structures in the form of a hypar: modeling, analysis, and comparison of three structural variants
DOI:
https://doi.org/10.36910/6775-2410-6208-2025-14(24)-24Keywords:
deformability, stresses, compression, bending element, hypar, wooden shell, ribbed frame, combined system.Abstract
The article investigates the spatial behavior of wooden structural systems shaped as a hypar, using the roof of the Summer Theater in Kyiv as a case study. The geometric model of the roof was constructed by approximating the real form with a hyperbolic paraboloid surface, which made it possible to accurately represent the curvature and ensure the adequacy of subsequent numerical analysis. The calculations were performed using the finite element method in the LIRA-SAPR software, taking into account geometric nonlinearity, the specific spatial behavior of wood, and the influence of the curved form on the stress–strain state.
Three structural configurations were analyzed: a solid wooden shell, a ribbed frame composed of intersecting curved elements, and a combined system of the “shell + ribs” type. For each configuration, stress fields, displacements, and buckling modes were obtained, and the deformation behavior under identical boundary conditions was evaluated. A comparison of the stress state in the directions of the principal curvatures, an analysis of out-of-plane deformation behavior, and an assessment of the influence of rib elements on the redistribution of internal forces were performed.
The results show that the combined wooden system provides the smallest deflections (10–12 mm), the highest buckling coefficient (λcr = 3.4–3.8), and a uniform stress distribution across the surface. The solid shell exhibits stable membrane behavior and moderate displacements but is sensitive to local buckling phenomena. The ribbed frame demonstrates the largest deflections, reduced stiffness, and a non-uniform distribution of internal forces, which limits its independent application without additional reinforcement. It is shown that combining a thin wooden shell with spatial stiffening ribs is the most effective solution for lightweight roofs of complex geometry, ensuring an optimal balance of stiffness, stability, and material efficiency.
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