MATHEMATICAL MODELING OF THE STRESS-STRAIN STATE OF FRAMELESS ARCH STRUCTURES MADE OF TRANSVERSELY CORRUGATED PROFILES USING THE FINITE ELEMENT METHOD

Methodological recommendations are proposed for constructing mathematical models to analyze the stress-strain state (SSS) of arch-type frameless structures made of cold-formed steel transversely corrugated profiles using the finite element method (FEM). Despite the widespread use of such structures in modern construction due to their high load-bearing capacity with low self-weight, the lack of a unified regulatory framework creates significant challenges in design. The main issue lies in the need to account for the specific behavior of thin-walled corrugated elements, where the local stability of profile webs and flanges becomes critically important. Research shows that modeling should avoid excessive simplifications: either scientifically justified reduction methods with correct stiffness characteristics should be applied, or detailed finite element models that accurately account for corrugation geometry should be used. Special attention is given to selecting the optimal finite element mesh density. A comparative analysis of different discretization approaches was conducted, establishing a rational element size that ensures sufficient accuracy with acceptable computational costs. Experiments demonstrated that a finite element size of 0.25 times the corrugation wavelength (considering its shape) provides reliable results. For method verification, a fragment of a real structure was analyzed using three approaches: linear analysis of a beam model, linear buckling analysis of plate elements, and nonlinear analysis considering geometric and material nonlinearity. The linear beam model may significantly overestimate load-bearing capacity, unlike plate-based models, potentially leading to structural failure in real-world applications. The linear plate model does not accurately reflect stress distribution but can be used for preliminary stability-based capacity assessment. The most precise results were obtained from nonlinear SSS analysis, which accounts for structural flexibility (iterative calculations based on the "deformed configuration") and correctly captures stress redistribution in stress concentration zones-areas of transverse and longitudinal bends. The results indicate that the employed modeling approaches generate distinct stress and strain distribution patterns within the structure. This underscores the necessity of rigorously validating computational model parameters to ensure faithful representation of the object’s actual mechanical behavior.