Search Results (49)

We present a novel method to estimate blood cortisol concentration from sweat cortisol measurements, incorporating a kinetic model to simulate cortisol transport dynamics. Cortisol dysregulation is observed in conditions like Cushing’s syndrome, characterized by excessive cortisol production, and stress-related disorders, which can lead to metabolic disturbances, anxiety, and impaired overall health. Sweat-sensing technology offers a non-invasive and continuous alternative to blood sampling. However, the limited research exploring the sweat–blood cortisol relationship in patients shows a moderate correlation ($R<0.6$), hindering its clinical application for long-term monitoring. In this paper, we propose a novel kinetic model describing cortisol transport from blood to sweat. The model was validated using data from 44 patients before and after cardiac surgery. A high Pearson correlation coefficient of 0.95 (95% CI: 0.92–0.97) was observed between our model’s estimated and experimental blood cortisol concentrations. Moreover, the method enables personalized estimation of physiological parameters, accurately reflecting patients’ status under varying clinical conditions. The method paves the way for the clinical application of long-term, non-invasive monitoring of cortisol using sweat-sensing technology. Enabling the personalized estimation of physiological parameters could potentially support clinical decision-making, helping doctors diagnose and monitor patients with health conditions involving cortisol dysregulation. Full article

Suyukou Gully, located on the eastern slope of the Helan Mountains in northwest China, is a typical debris-flow-prone catchment characterized by a steep terrain, fractured bedrock, and abundant loose colluvial material. The area is subject to intense short-duration convective rainfall events, which often trigger destructive debris flows that threaten the Suyukou Scenic Area. To investigate the dynamics and risks associated with such events, this study employed the FLO-2D two-dimensional numerical model to simulate debris flow propagation, deposition, and hazard distribution under four rainfall return periods (10-, 20-, 50-, and 100-year scenarios). The modeling framework integrated high-resolution digital elevation data (original 5 m DEM resampled to 20 m grid), land-use classification, rainfall design intensities derived from regional storm atlases, and detailed field-based sediment characterization. Rheological and hydraulic parameters, including Manning’s roughness coefficient, yield stress, dynamic viscosity, and volume concentration, were calibrated using post-event geomorphic surveys and empirical formulations. The model was validated against field-observed deposition limits and flow depths, achieving a spatial accuracy within 350 m. Results show that the debris flow mobility and hazard intensity increased significantly with rainfall magnitude. Under the 100-year scenario, the peak discharge reached 1195.88 m³/s, with a maximum flow depth of 20.15 m and velocities exceeding 8.85 m·s⁻¹, while the runout distance surpassed 5.1 km. Hazard zoning based on the depth–velocity (H × V) product indicated that over 76% of the affected area falls within the high-hazard zone. A vulnerability assessment incorporated exposure factors such as tourism infrastructure and population density, and a matrix-based risk classification revealed that 2.4% of the area is classified as high-risk, while 74.3% lies within the moderate-risk category. This study also proposed mitigation strategies, including structural measures (e.g., check dams and channel straightening) and non-structural approaches (e.g., early warning systems and land-use regulation). Overall, the research demonstrates the effectiveness of physically based modeling combined with field observations and a GIS analysis in understanding debris flow hazards and supports informed risk management and disaster preparedness in mountainous tourist regions. Full article

Plants dynamically regulate ions in the tree to defend against abiotic stresses such as drought and saline-alkali, However, it is not clear how ‘Junzao’ jujube regulates ions to maintain a normal life cycle under saline-alkali stress. Therefore, in this study, the roots of 10-year old steer jujube trees were watered using a saline and alkaline gradient solution simulating the main salt (NaCl) and alkali (NaHCO₃) of Aral with NaCl:NaHCO₃ = 3:1 gradient of 0, 60, 180, and 300 mM, and three jujube trees with uniform growth were taken as samples in each treatment plot, and the ion contents of potassium (K), sodium (Na), calcium (Ca), magnesium (Mg), iron (Fe), manganese (Mn), zinc (Zn) and carbon (C) in each organ of the fruit at the dot red period (S1) and full-red period (S2) were determined, in order to elucidate the relationship between physiological adaptation mechanisms of saline-alkali tolerance and the characteristics of mineral nutrient uptake and utilisation in jujube fruit. The results showed that under saline-alkali stress, Na was stored in large quantities in the roots, Ca and Mg in the perennial branches at S1, Na and Fe in the leaves at S2, and K, Mg and Mn in the perennial branches. There was no significant difference in the distribution of C content in various organs of ‘Junzao’. Compared with CK (0 mM), under salinity stress, the K content in the leaves was significantly reduced at S1 and S2, and the K/Na ratios remained > 1.0. At S2, under medium and high concentrations of saline-alkali stress (180–300 mM), the K/Na is less than 1, and the ionic homeostasis was disrupted, and the leaves die and fall off, and the Na is excreted from the body. The selective transport coefficients SK/Na, SCa/Na and SMg/Na from root to leaf showed a downward trend at S1, but still maintained positive transport capacity. At S2, this stage is close to leaf fall, the nutrient transport coefficient is less than 1, and a large amount of nutrients are returned to the perennial branches and roots occurred. These results indicated that the mechanism of nutrient regulation and salt tolerance in jujube trees was different at different growth stages. Full article

The majority of extant studies concentrate on the reactivation of dormant Anammox biomass or the recovery of activity under specific storage conditions. Research on rehabilitation strategies for anaerobic ammonium oxidation (Anammox) systems is limited, with the exception of research on inhibitory factors. The recovery characteristics of biofilm systems after collapse induced by varying degrees of ammonia-nitrogen and small-molecular organic compound composite shocks have not been thoroughly elucidated. This study addresses the collapse of Anammox biofilm systems caused by sodium acetate inhibition through multi-phase rehabilitation strategies, stoichiometric analysis, and microbial community succession dynamics. Two regression algorithms—Support Vector Regression (SVR) and eXtreme Gradient Boosting (XGBoost)—were employed to construct predictive models for Total Nitrogen Removal Efficiency (TNRE) and Total Nitrogen Removal Rate (TNRR) in the CANON system, with model performance evaluated via coefficient of determination (R²) and root mean square error (RMSE). Results demonstrated that after terminating moderate-to-high sodium acetate dosing (300 mg/L and 500 mg/L), reactors R300 and R500 achieved TNRE recovery to 57.98% and 58.86%, respectively, and TNRR of 0.281 and 0.275 kgN/m³·d within 60–100 days, indicating the reversibility of high-concentration sodium acetate inhibition but a positive correlation between recovery duration and inhibition intensity. Microbial community analysis revealed that Planctomycetota (including Candidatus_Kuenenia) rebounded to 46–49% relative abundance in R100, synchronized with TNRE improvement. In contrast, R300 and R500 exhibited ecological niche replacement of denitrifiers (Denitratisoma) and partial TNRE restoration despite enhanced performance. Model comparisons showed SVR outperformed XGBoost in TNRE prediction, whereas XGBoost demonstrated superior TNRR prediction accuracy with R² approaching 1 and RMSE nearing 0, significantly surpassing SVR. This work provides critical insights into recovery mechanisms under organic inhibition stress and establishes a robust predictive framework for optimizing nitrogen removal performance in CANON systems. Full article

This paper investigates the significance of various physical factors affecting the wave generated by submerged jet and the synchronization relationship between the wave surface process and different fluid dynamic parameters, based on three-dimensional numerical simulations using a large eddy simulation (LES) model. An orthogonal experimental design was employed, and range analysis and variance analysis revealed that the orifice contraction ratio has the most significant effect on wave height, followed by upstream water depth and orifice elevation. Through wavelet coherence and spectral correlation analysis, the wave surface process was examined in relation to fluid kinetic energy, Reynolds stress, and vortex structure parameters along the jet axis. The results indicate that regions of strong wavelet coherence are concentrated between 0.01 and 1.0 Hz. In the low-frequency range (0.01~1.0 Hz), there are narrow yet continuous coherence bands, while in the slightly higher frequency range (1.0~5.0 Hz), intermittent coherence relationships with wider bands are observed. Additionally, there is a certain degree of correlation between the power spectral density of the wave surface process and these physical quantities, with a maximum spectral correlation coefficient reaching 0.91. This study contributes to a deeper understanding of the factors affecting waves generated by submerged jets, enabling better prediction and control of their effects. Full article

The rheological properties of mortar are of vital importance to ensure the quality and durability of engineering structures, improving construction efficiency and adapting to different construction environments. This research focused on examining the rheological properties of geopolymer mortar (GM) with the incorporation of metakaolin (MK), nano-SiO₂ (NS) and polyvinyl alcohol (PVA) fibers. The research focused on varying concentrations of PVA fiber ranging from 0 to 1.2% (interval of 0.2%) and NS ranging from 0 to 2.5% (interval of 0.5%). As the mix proportion optimization of GM is normally carried out experimentally, a significant amount of labor and material resources was consumed. Based on large amounts of authentic operation data, a prediction model of rheological properties for NS- and PVA-fiber-reinforced GM was developed using a back propagation (BP) neural network. Subsequently, the parameters were refined using a genetic algorithm (GA) to predict the rheological properties of GM reinforced with different dosages of NS and PVA fiber. Three rheological parameters, including static yield stress, plastic viscosity and dynamic yield stress, were used to evaluate the rheological properties of GM. Moreover, parameters of Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE) were applied to assess the capability of the algorithms. When the GA–BP neural network was used, compared with the BP neural network, the coefficient of determination (R²) of the static yield stress, plastic viscosity, and dynamic yield stress increased by 4.40%, 2.11% and 15.28%, respectively, and the GA–BP neural network provided a superior fitting effect, higher prediction accuracy and faster convergence. Based on the outputs of the developed model, the GA–BP neural network can be adopted as a precise method to forecast the rheological properties of GM reinforced with NS and PVA fibers. Full article

Using the two-dimensional Particle Flow Code (PFC2D), a model of red sandstone containing fractures with different inclination angles under impact load was established to study the influence of fracture inclination angles on the dynamic compressive strength, stress wave attenuation, and crack evolution laws of the model. The results indicate that, under the same impact load, the dynamic compressive strength of the cracked specimens exhibits a “V”-shaped variation, with the specimen at a 45° inclination angle showing the lowest strength. The influence of inclination angles on strength is most significant in the 30° to 45° inclined specimens. As the inclination angle increases, the reflection coefficient rises, the transmission coefficient decreases, stress wave attenuation intensifies, and the time for specimen penetration shortens, making the specimen more prone to failure. The location of crack initiation shifts toward the middle of the fracture as the inclination angle increases, and the cracks tend to develop parallel to the impact load. When the inclination angle is ≥45°, stress concentration at fracture tips prolongs the shear-dominated phase during failure progression. However, the tensile ratio k consistently exceeds 0.7 at ultimate failure, indicating tensile mechanisms remain the dominant failure mode. Both absorbed energy and total crack number generally decrease with increasing inclination angle, while no clear correlation exists between absorbed energy and fragment number. Large fragments are distributed on both sides of the fracture during the fragmentation process. In contrast, small fragments concentrate near the through cracks. Specimens with 45° and 60° inclination angles exhibit a higher number of fragments and more significant fragmentation. In the initial loading stage, the specimen with a 90° inclination angle shows the weakest resistance to failure, while the 0° inclination angle specimen exhibits the strongest resistance. The research findings contribute to elucidating the dynamic failure mechanisms of fractured red sandstone, analyzing slope stability, and optimizing blasting designs. Full article

As mining depths increase, the highly metamorphosed anthracite in Southwest China progressively develops into a complex dynamic disaster influenced by both in situ stress and gas pressure. By utilizing characteristic indicators of mining-induced stress and gas dynamic emissions, a grading evaluation method for coal and gas dynamic disasters (CGDDs) based on fuzzy mathematics l theory is proposed and validated at the No. 1 Well of the Yuwang Coal Mine. The results indicate that the acceleration of microseismic wave velocity and the increase in the wave velocity anomaly coefficient are indicative of a more pronounced stress concentration. The working face exhibits distinct gradations of stress concentrations, categorized as weak, moderate, and strong. Moreover, the increase in microseismic wave velocity and the anomaly coefficient further confirm the intensity of the stress concentrations. Gas dynamic emissions show a clear correlation with the drill cuttings gas desorption indicator ($K_1$ value) and drill cuttings volume ($S$ value). Characteristic indicators A, B, and D are suitable for assessing the risk of CGDDs in the working face. For the application of individual indicators for classifying the CGDD risk at different distances from the crosscut (128 m, 247.5 m, 299.4 m, and 435 m) in the 1010201-working face, contradictory classification results were observed. However, the classification results derived from the fuzzy mathematics method were consistent with the findings of field investigations. As the working face advanced through the pre-concentrated stress zone, significant changes were observed in both the source wave velocity and wave velocity anomaly coefficient. Concurrently, gas emissions displayed a distinct pattern of fluctuation characterized by increases and decreases. The consistency between the periodic weighting of the working face, the gas emission, the drill cuttings gas desorption indicator, and the stress field inversion result further validates the classification outcomes. These research results can provide theoretical support for the monitoring of CGDDs. Full article

This paper presents a targeted study on the dynamic stress concentration (DSC) in piezoelectric materials induced by SH waves, focusing on the impact of elliptical openings. By using the elliptic cylindrical coordinate system and Mathieu functions, the wave fields are decomposed into functional series. Through the establishment of a set of infinite equations with mode coefficients based on the boundary conditions, the distribution of the dynamic stress concentration coefficient is visualized via numerical simulation. Furthermore, the impact of incident wave frequency, incident angle, and elliptic eccentricity on the stress concentration coefficient is analyzed. The results demonstrate a strong correlation between these parameters and the dynamic stress concentration coefficient. These findings hold significant implications for enhancing the strength and fatigue life of piezo-electric materials, as well as for selecting appropriate nondestructive testing methods. Full article

The multi-parameter and nonlinear characteristics of the Smith Watson Topper (SWT) equation present considerable challenges for predicting the fatigue life of 2024-T3 clad Al alloy. To overcome these challenges, a novel model integrating traditional fatigue analysis methods with machine learning algorithms is introduced. An improved SWT fatigue life prediction equation is developed by incorporating key factors such as the mean stress effect, stress concentration factor, and surface roughness coefficient. Extreme gradient boosting, Random Forest, and their derived models are used to construct the fatigue life prediction model. The L-BFGS algorithm was then integrated with the established machine learning model to solve for the multi-parameter of the improved SWT equation. Thus, an accurate modified SWT prediction equation for 2024-T3 clad Al alloy was obtained. To further optimize the solution, the deep deterministic policy gradient and deep reinforcement learning algorithms are introduced to dynamically optimize the nonlinear equation, achieving a more efficient and accurate solution. The improved SWT fatigue life prediction equation and its solution method proposed in this study provide new insights for fatigue life prediction of clad metallic materials. Full article

The PsnWRKY70 transcription factor (TF) was reported to play an important role in the salt stress response mechanism of Populus simonii × Populus nigra in our previous research, and we also produced several PsnWRKY70 overexpression (OEXs) and RNAi suppression (REXs) P. simonii × P. nigra lines. In order to further compare the photosynthetic and physiological characteristics of NT (non-transgenic line) and transgenic lines under salt stress, the dynamic phenotypic change, Na⁺ and K⁺ content in leaf and root tissues, superoxide dismutase (SOD) and peroxidase (POD) activity, malondialdehyde (MDA) content, chlorophyll content (Chl), photosynthesis parameters (net photosynthetic rate, P_n; stomatal conductance, Gs; intercellular CO₂ concentration, C_i; transpiration rate, T_r), chlorophyll fluorescence parameters (electron transport rate, ETR; maximum photochemical efficiency of photosystem II (PSII), F_v/F_m; actual efficiency of PSII, Φ_PSII; photochemical quenching coefficient, q_P; non-photochemical quenching, NPQ; the photosynthetic light-response curves of Φ_PSII and ETR) and RNA-seq of NT, OEX and REX lines were detected and analyzed. The phenotypic observation, MDA content and Chl detection results indicate that the stress damage of REXs was less severe than that of NT and OEX lines under salt stress. Photosynthesis parameter (P_n, Gs, T_r and C_i) and chlorophyll fluorescence parameter (ETR, F_v/F_m, Φ_PSII q_P and NPQ) detection results indicate that the REX lines exhibited much better photosynthetic adaptability than NT and OEX lines during salt stress. The photosynthetic light-response curves of Φ_PSII and ETR of NT, OEX and REX lines indicate that REXs exhibited better ability to activate the photosynthetic protection mechanism and adapt to a certain degree of strong light than NT and OEX lines under salt stress. RNA-seq analysis indicates that the DEGs between OEX1 vs. NT and REX1 vs. NT in different tissues (apical bud and fifth functional leaf) were all different in category and change trend. The expression of PsnWRKY70 was significantly up-regulated in both the apical bud and fifth functional leaf of OEX1, and showed no significant change (namely maintained low expression level) in both the apical bud and fifth functional leaf of REX1, thus indicating the negative regulation role of PsnWRKY70 in P. simonii × P. nigra under salt stress. Additionally, there were a lot of stress response-related TF genes (such as bHLH, WRKY, MYB, NAM and AP2/EREBP) and photosynthesis-related genes among all the DEGs. In REX1, the expression of three Photosystem I P700 chlorophyll a apoprotein A1 genes (Potri.003G065200, Potri.013G141800 and Potri.019G028100) and a Photosystem II protein D1 gene (Potri.013G138300) were significantly up-regulated after 6 days of salt stress. In OEX1, the Heterodimeric geranylgeranyl pyrophosphate synthase small subunit gene (Potri.015G043400) and Phospho-2-dehydro-3-deoxyheptonate aldolase 1 gene (Potri.007G095700) were significantly down-regulated after 6 days of salt stress. These photosynthesis-related genes are probably regulated by PsnWRKY70 TF in response to salt stress. In conclusion, the REX lines suffered less severe salt damage and exhibited better photosynthetic adaptability than NT and OEXs under salt stress. The differences among the DEGs between OEX1 vs. NT and REX1 vs. NT in apical bud and fifth functional leaf, and the significantly differentially expressed photosynthesis-related genes are probably the key clues for discovering the photosynthesis adaptability mechanism of PsnWRKY70 transgenic P. simonii × P. nigra under salt stress. Full article

The transport of pollutants with flowing waters is one of the most common processes in the natural environment. In general, this process is described by a system of differential equations, including the continuity equation, dynamic equations, pollutant transport equations and equations of state. For the analyzed problem of pollutant migration in wide rivers and the coastal zone, a two-dimensional model is particularly useful because the velocity and mass concentration profile is vertically averaged. In this model, taking into account the dispersion flux leads to appropriate equations, and the dispersion process is described by the dispersion tensor. Due to the transverse isotropy of the dispersion process, the coordinates of this tensor are expressed in terms of local dispersion coefficients along the direction of the velocity and in the direction perpendicular to it. Commonly used methods for determining mass dispersion coefficients refer to a gradient velocity profile, typical for rivers. However, in the coastal zone, the velocity profile changes from gradient to drift when shear stresses on the surface caused by the wind begin to dominate. The drift profile also occurs in estuaries, where there is a difference in the density of fresh and salt water. This paper analyzes the numerical solution of the two-dimensional dispersion equations in the coastal zone for the dispersion coefficients adopted for the gradient and drift velocity profiles and then assesses how this affects the final result. Four typical scenarios of pollutant migration in the coastal zone of the Bay of Puck are presented. The calculated dispersion coefficients differ significantly depending on the adopted velocity profile: for the gradient, D_LG = 0.17 [m²/s], and for the drift, D_LD = 89.94 [m²/s]. Full article

This paper presents a comprehensive analysis of a multi-door check valve using computational fluid dynamics (CFD) and finite element analysis (FEA) to evaluate flow performance under pressure test conditions, with an emphasis on its ability to prevent backflow. Check valves are essential components in various industries, ensuring fluid flow in one direction only while preventing reverse flow. The non-return multi-door reflux valve is increasingly preferred due to its superior backflow prevention, fluid control, and effective flow regulation. Rigorous testing under varying pressure conditions is essential to ensure that these valves perform optimally. This study uses CFD and FEA simulations to evaluate the structural integrity and flow characteristics of the valve, including pressure drop, flow velocity, backflow prevention effectiveness, and flow coefficient. A high-fidelity 3D model was created to simulate the valve’s behavior under various conditions, analyzing the effects of parameters such as the number of doors, their orientation, geometry, and operating conditions. The CFD results demonstrated a significant reduction in backflow and pressure drop across the valve. However, localized turbulence and flow separation near the valve doors, particularly under partially open conditions, have raised concerns about potential wear. The velocity profiles indicated a uniform distribution at full opening with laminar velocity profiles and minimal resistance to flow. The results of the FEA showed that the stresses induced by the fluid forces were below critical levels, with the highest stress concentrations observed around the hinge points of the valve doors. Although the valve structure remained intact under normal operating conditions, some areas may have required reinforcement to ensure long-term durability. Combined CFD and FEA analyses demonstrated that the valve effectively preserves system integrity, prevents backflow, and maintains consistent performance under various pressure and flow conditions. These findings provide valuable insights into design improvements, performance optimization, and enhancing the efficiency and reliability of reflux valve systems in industrial applications. Full article

This study investigates the tribological properties of graphite foils (GF) with densities of 1.0, 1.3, and 1.6 g/cm³, produced from purified natural graphite of different particle sizes (40–80 μm, 160–200 μm, >500 μm). Surface roughness was measured after cold rolling and friction testing at static (0.001 mm/s) and dynamic conditions (0.1 Hz and 1 Hz). Results showed that static friction tests yielded similar roughness values (S_a ≈ 0.5–0.7 μm, S_q ≈ 0.5–1.0 μm) across all densities and particle sizes. Dynamic friction tests revealed increased roughness (S_a from 0.7 to 3.5 μm, S_q from 1.0 to 6.0–7.0 μm). Friction coefficients (µ) decreased with higher sliding speeds, ranging from 0.22 to 0.13. GF with 40–80 μm particles had the lowest friction coefficient (µ = 0.13–0.15), while 160–200 μm particles had the highest (µ = 0.15–0.22). Density changes had minimal impact on friction for the 40–80 μm fraction but reduced friction for the 160–200 μm fraction. Young’s modulus increased with density and decreased with particle size, showing values from 127–274 MPa for 40–80 μm, 104–212 MPa for 160–200 μm, and 82–184 MPa for >500 μm. The stress–strain state in the graphite foil samples was simulated under normal and tangential loads. This makes it possible to investigate the effect of the anisotropy of the material on the stress concentration inside the sample, as well as to estimate the elasticity modulus under normal compression. Structural analyses indicated greater plastic deformation in GF with 40–80 μm particles, reducing coherent-scattering region size from 28 nm to 24 nm. GF samples from 160–200 μm and >500 μm fractions showed similar changes, expanding with density increase from 18 nm to 22 nm. Misorientation angles of GF nanocrystallites decreased from 30° to 27° along the rolling direction (RD). The coherent scattering regions of GF with 40–80 μm particles increased, but no significant changes in the coherent scattering regions were observed for the 160–200 μm and >500 μm fractions during dynamic friction tests. Microstrains and residual macrostresses in GF increased with density for all fractions, expanding under higher friction-induced loads. Higher values of both stresses indicate a higher level of accumulated deformation, which appears to be an additional factor affecting the samples during friction testing. This is reflected in the correlation of the results with the roughness and friction coefficient data of the tested samples. Full article

The structural elements of buildings have recently required the development of efficient design solutions due to increased dynamic and thermal loads. The main solution for improving the efficiency of such elements involves creating lightweight non-uniform beam and arch structures from alloyed steel, which has better mechanical characteristics. The most promising approach is the use of welded beams and arches with perforated partitions and composite beams, which are often used together, for instance, as structural elements of cylindrical shells. The development of an effective cross-sectional shape for perforated beams and crane girders is considered, taking into account the strength, local stability, resistance to flat bending, and fatigue deformation. It has been shown that the effective form for perforated beams is a box-shaped structure made of perforated shvellers. Calculations for selecting a rational design from the assortment of hot-rolled shveller profiles have demonstrated that a significant reduction in the weight of the structure can be achieved by using the proposed cross-sectional shape. An evaluation of the fatigue strength of composite metal crane girders operating in harsh conditions has shown the effectiveness of using hot-rolled I-beams as their upper flange, as well as the necessity of using hot-rolled I-beams to ensure strength in their lower part. When choosing the rational parameters of an arch design, multiple recalculations of its bending with respect to technological cutouts in the thickness are necessary; hence, simplified calculation schemes are commonly used. Some authors simplify this process by replacing an arch with a cutout with a solid arch reduced in height by the cutout radius. We have shown that this model does not accurately describe the actual distribution of forces and displacements, leading to inadequate results. We have developed a simplified methodology for the preliminary calculation of a circular arch with a cutout, which includes correction coefficients calculated by us. A calculation of the flat stress–strain state of an elastic circular metal arch with a central semicircular cutout under various ratios of design parameters and uniform external pressure was conducted. A dependence of the stress concentration coefficient at the cutout’s apex on the ratio of the cutout radius and arch thickness was obtained. These results can be generalized for reinforced non-uniform shells and for the fuzzy application of external influences. Full article