Applied Mechanics

The current paper addresses the lack of explicit analytical solutions for stress evaluations in variable-thickness flywheels by proposing an approximate formulation for conical profiles, where thickness varies linearly along the radius. The main objective was to develop a compact and practical expression to estimate radial and tangential stresses without relying on finite element analysis. Starting from a stress function, the model was simplified under the assumption of a small-thickness gradient, allowing the derivation of a closed-form solution. The resulting expression explicitly relates stresses to geometric and material parameters. To validate the approximation, stress distributions were computed for various outer-to-inner thickness ratios and compared with results obtained through FEA. The comparison, evaluated using the coefficient of determination, mean absolute percentage error, root mean squared error, normalized root mean squared error, and stress ratios, demonstrated strong agreement, especially for moderate-thickness ratios ($1\leqq t_o/t_i\leqq 4.5$). The method was more accurate for radial stress than tangential stress, particularly at higher gradients. The results confirmed that the proposed analytical approach provides a reliable and efficient alternative to numerical methods in the design and optimization of conical flywheels, offering practical value for early-stage engineering analysis and reducing reliance on time-intensive simulations. Full article

The paper analyzes the process of indentation of polymeric materials with a spherical indenter. The loading diagrams P(h) obtained experimentally and by means of finite element method (FEM) are analyzed. The material under study was high-density polyethylene (HDPE) of PE100 grade, taken from a pipeline for gas distribution systems. The aim of the work was to determine the parameters of the computer model, taking into account hardening and creep processes when verifying P(h) diagrams with experimental studies. The influence of variation of the parameters of the calculation formulas on the reliability of the simulation results was analyzed. The results of the calculation of mechanical properties of material on the basis of P(h) diagrams by the Oliver–Pharr method for model and experimental diagrams were compared. The possibility of using computer modeling for the analysis of instrumented indentation processes is demonstrated, since the results revealed the convergence of the elastic modulus of 1078 GPa for FEM and 1083 GPa for the experiment. The conformity of the Oliver–Pharr method for determining the contact depth is also shown, which differed from the model geometry by only 2.3%. Simulation of the indentation process using the Norton model via FEM, as well as determining the parameters of the material deformation function while taking creep into account, makes it possible to describe the process of contact interaction and shows good agreement with experimental data. Full article

In recent years, a series of studies have examined the effects of blast loads on structures and proposed new materials to enhance or retrofit the resistance of conventional materials, such as steel or concrete. Polymeric materials, including foams and elastomers, play a significant role in this field due to their low density and favorable mechanical properties under dynamic loads. This study investigates the use of polyurethane elastomer to improve the mechanical properties of 2 mm A36 steel sheets. The efficiency of this material in steel structures has not yet been studied in the scientific literature through blast tests. A total of 18 near-field blast tests were conducted at standoff distances of 300 mm and 500 mm. The explosive charges consisted of 334 g of bare Composition B in a spherical shape. The steel sheets were fixed to rigid supports and exposed to the blast either bare or covered with different layers of commercial Shore A 60 or 90 polyurethane elastomer, with thicknesses varying from 2 to 6 mm. The maximum displacement of the steel sheets was measured using a high-speed camera and the results were compared. The elastomer retrofitted sheets exhibited a reduction in maximum displacement ranging from 5% to 20% when compared to the sheet without the elastomer. Full article

Ultra-high-performance concrete (UHPC) has attracted considerable attention from both the construction industry and researchers due to its outstanding durability and exceptional mechanical properties, particularly its high compressive strength. Several factors influence the shear capacity of UHPC deep beams, including compressive strength, the shear span-to-depth ratio (λ), fiber content (FC), vertical web reinforcement (ρ_sv), horizontal web reinforcement (ρ_sh), and longitudinal web reinforcement (ρ_s). Considering these factors, this research proposes a novel hybrid algorithm that combines an adaptive neuro-fuzzy inference system (ANFIS) with an artificial neural network (ANN) to predict the shear capacity of UHPC deep beams. To achieve this, ANN and ANFIS algorithms were initially employed individually to predict the shear capacity of UHPC deep beams using available experimental data for training. Subsequently, a novel hybrid algorithm, integrating an ANN and ANFIS, was developed to enhance prediction accuracy by utilizing numerical data as input for training. To evaluate the accuracy of the algorithms, the performance metrics R² and RMSE were selected. The research findings indicate that the accuracy of the ANN, ANFIS, and the hybrid ANN-ANFIS algorithm was observed as R² = 0.95, R² = 0.99, and R² = 0.90, respectively. This suggests that despite not using experimental data as input for training, the ANN-ANFIS algorithm accurately predicted the shear capacity of UHPC deep beams, achieving an accuracy of up to 90.90% and 94.74% relative to the ANFIS and ANN algorithms trained on experimental results. Finally, the shear capacity of UHPC deep beams predicted using the ANN, ANFIS, and the hybrid ANN-ANFIS algorithm was compared with the values calculated based on ACI 318-19. Subsequently, a novel reliability factor was proposed, enabling the prediction of the shear capacity of UHPC deep beams reinforced with fibers with a 0.66 safety margin compared to the experimental results. This indicates that the proposed model can be effectively employed in real-world design applications. Full article

This paper describes a simulation study on the hard turning of AISI 52100 alloy steel with coated carbide tools under minimal cutting fluid conditions using the commercial software AdvantEdge. A finite element analysis coupled with adaptive meshing was carried out to accurately capture temperature gradients. To minimise the number of experiments while optimising the cutting parameters along with fluid application parameters, a cutting speed (v) of 80 m/min, feed rate (f) of 0.05 mm/rev, depth of cut (d) of 0.15 mm, nozzle stand-off distance (NSD) of 20 mm, jet angle (JA) of 30°, and jet velocity (JV) of 50 m/s were observed to be the optimal process parameters based on the combined response’s signal-to-noise ratios. The effects of each parameter on machined surface temperature, cutting force, cutting temperature, and tool–chip contact length were determined using ANOVA. The depth of cut affected cutting force, while cutting speed and jet velocity affected cutting temperature and tool–chip contact length. Cutting speed influenced machined surface temperature significantly, whereas other parameters showed minimal effect. Nozzle stand-off distance exhibited less significant effect. Taguchi optimisation determined the optimal combination of process parameters for minimising thermal effects during hard turning. Cutting temperature and cutting force simulation results were found to be highly consistent with experimental results. On the other hand, the simulated results for the tool–chip contact length and machined surface temperature were very close to the values found in the literature. The result validated the finite element model’s ability to accurately simulate thermal behaviour during hard-turning operations. Full article

Additive Manufacturing, or 3D Printing, is based on manufacturing physical objects by sequential deposition of layers of material. Although the usage of AM is growing, no straightforward methodology exists to produce parts with specific, or optimized, mechanical properties. In this work, an approach for optimizing the mechanical properties of AM specimens under bending stress is presented, using DOE. For the experimental procedure, Fused Deposition Modeling (FDM) technology was used along with Polylactic acid (PLA) as the in-process material. Nozzle temperature, printing speed, infill pattern and printing orientation were selected as manufacturing factors to be optimized to achieve so maximum load and deflection to be acquired. Both optimized sets of values were increased by 53% and 28%, respectively, and were experimentally checked to validate the accuracy of the approach. Full article

Liquid-storage tanks are critical components in industrial plants, especially during seismic events. Tank failures can cause significant economic losses, operational disruptions, and environmental damage. Therefore, accurate design and performance evaluation are essential to minimize these risks. However, past earthquakes have highlighted the need for a better understanding of tanks’ seismic behavior. This requires selecting the appropriate seismic input and ground motion records to properly simulate tank responses. This study examines the seismic behavior of various tank types using different earthquake record sets, including both far-field and near-field events. The tanks were modelled with varying geometries, such as diameter–height ratios, wall thickness, liquid height, and radius. Time-history analyses were conducted to generate fragility curves and evaluate the seismic performance of the tanks based on specific limit states. The findings show that the choice between far- and near-field records significantly influences seismic response, particularly in terms of fragility curve variation. The fragility curves derived from this analysis can serve as valuable tools for risk assessments by governments and stakeholders, helping to improve the safety and resilience of industrial plants. Full article

A testing method is developed to evaluate the acceleration- and strain-based fatigue life of a thermal interface layer in the high-cycle fatigue regime. The methodology adopts vibration-based fatigue testing, where adhesively bonded beams are excited at their resonant frequency under variable amplitude loading using an electrodynamic shaker. Fatigue failure is monitored through shifts in modal frequency and modal damping. Key findings include the identification of a 4% frequency shift as the failure criterion, corresponding to macro-delamination. The thickness of the thermal interface material influences acceleration-based fatigue life, decreasing by a factor of 0.2 when reduced from 0.3 mm to 0.15 mm and increasing by 5.5 when increased to 0.5 mm. Surface quality has a significant impact on both acceleration-based and strain-based fatigue curves. Beams from chemically etched aluminum–magnesium alloy specimens exhibit a sevenfold increase in fatigue life compared to beams from untreated printed circuit boards. Strain-based fatigue life increases with temperature, with a 0.2 reduction at $-40$ °C and an eightfold increase at $100$ °C relative to $23$ °C. The first principal strain ${\epsilon }_{1,\mathrm{rms}}$ is validated as a reliable local damage parameter, effectively characterizing fatigue behavior across varying TIM thicknesses. Full article

In the seismic design of steel moment-resisting frames (MRFs), the panel zone region can significantly affect overall ductility and energy-dissipation capacity. This study investigates the influence of panel zone flexibility on the seismic response of steel MRFs by comparing two modeling approaches: one with a detailed panel zone representation and the other considering fixed beam-column connections. A total of 30 2D steel MRFs (15 frames incorporating panel zone modeling and 15 frames without panel zone modeling) are subjected to nonlinear time–history analyses using four suites of ground motions compatible with Eurocode 8 (EC8) soil types (A, B, C, and D). Structural performance is evaluated at three distinct performance levels, namely, damage limitation (DL), life safety (LS), and collapse prevention (CP), to capture a wide range of potential damage scenarios. Based on these analyses, the study provides information about the seismic response of these frames. Also, lower-bound, upper-bound, and mean values of behavior factor (q) for each soil type and performance level are displayed, offering insight into how panel zone flexibility can alter a frame’s inelastic response under seismic loading. The results indicate that neglecting panel zone action leads to an artificial increase in frame stiffness, resulting in higher base shear estimates and an overestimation of the seismic behavior factor. This unrealistically increased behavior factor can compromise the accuracy of the seismic design, even though it appears conservative. In contrast, including panel zone flexibility provides a more realistic depiction of how forces and deformations develop across the structure. Consequently, proper modeling of the panel zone supports both safety and cost-effectiveness under strong earthquake events. Full article

Masked Stereolithography (mSLA) is an additive manufacturing technique that has been recently explored. Currently, studies in the literature addressing the investigation of stress concentrators in photosensitive resin parts printed on mSLA devices using the Whitney–Nuismer analytical method combined with Finite Element Analysis (FEA) and Digital Image Correlation (DIC) are rare. This work utilizes the combination of these techniques to analyze stress concentrators in specimens subjected to axial and eccentric loads, considering the effects imposed by the clamp restraint and a complementary study considering the free loading condition. For axial loading, the results are consistent, with variations in the stress concentration factor ranging from 0.42% to 5.25%. For the eccentric loading studies, the results indicate that the most suitable method for the test was the analysis considering the restraint imposed by the clamp, as the deformation results show a maximum error of 6.9% compared to 24.7% when the restraints were disregarded. The consistency of the results reinforces the quality of the employed technique, demonstrating that this study not only achieved its objectives but also provided a foundation for future investigations in the field. Full article

Burst pressure is one of the critical strength parameters used in the design and operation of pressure vessels because it represents the maximum pressure that a vessel can withstand before failing. Historically, the Barlow formula was used as a design base for estimating burst pressure. However, it does not consider the plastic flow response for ductile steels and is applicable only to thin-walled cylinders (i.e., the diameter to thickness ratio D/t ≥ 20). A new multiaxial plastic yield theory was developed to consider the plastic flow response, and the associated theoretical (i.e., Zhu–Leis) solution of burst pressure was obtained and has gained extensive applications in the pipeline industry because it was validated by different full-scale burst test datasets for large-diameter, thin-walled pipelines in a variety of steel grades from Grade B to X120. The Zhu–Leis flow theory of plasticity was recently extended to thick-walled pressure vessels, and the associated exact flow solution of burst pressure was obtained and is applicable to both thin and thick-walled cylindrical shells. Many full-scale burst tests are available for thin-walled line pipes in the pipeline industry, but limited pressure burst tests exist for thick-walled vessels. To validate the newly developed exact solutions of burst pressure for thick-walled cylinders, this paper conducts a series of burst pressure tests on small-diameter, thick-walled pipes. In particular, six burst tests are carried out for three thick-walled pipes in Grade B carbon steel. These pipes have a nominal diameter of 2.375 inches (60.33 mm) and three nominal wall thicknesses of 0.154, 0.218, and 0.344 inches (3.91, 5.54, and 8.74 mm), leading to D/t = 15.4, 10.9, and 6.9, respectively. With the burst test data, comparisons show that the Zhu–Leis flow solution of burst pressure matches well the burst test data for thick-walled pipes. Thus, these burst tests validate the accuracy of the Zhu–Leis flow solution of burst pressure for thick-walled cylindrical vessels. Full article

This study investigates the effect of a polyurethane (PUR) foam layer on impact force, impact duration, and deformation with regard to radiosondes during drop tests. Numerical (Finite Element Method) and experimental approaches were used to model collisions with and without protective PUR layers. The numerical results demonstrated that adding a soft PUR foam layer reduced peak impact force by 10% while it increased impact duration up to 71%. Experimental drop tests confirmed the numerical outcomes as peak impact force difference was 7% between simulations and experiments, while impact duration differed only by 11%. Besides force and duration, impact deformation was also investigated by an FEM model and high-speed camera footage on radiosondes with a PUR foam layer. The FEM model was able to approximate well the deformation magnitude since the numerical deformation was only 2% lower compared to the experimental data. In summary, a reliable and validated FEM model was created. On the one hand, this model allows the analysis of different protective layers around a radiosonde. On the other hand, it can adequately predict the impact behavior of radiosondes by incorporating multiple important factors. In addition, it has been confirmed that incorporating a soft PUR foam layer significantly improves safety by reducing impact force and extending impact duration. Full article

One of the challenging aspects of designing body-in-white stiffness test rigs is measuring test accuracy. This paper proposes a method of integrating the body-in-white stiffness test rig and the body-in-white into an overall model for the optimization design. It establishes an optimization mathematical model based on the overall structure of the stiffness test rig, taking into account the factors affecting the accuracy of the test results of the body-in-white stiffness test rig. The stiffness test rig’s testing accuracy can be significantly increased by designating the degrees of freedom at each connection position as discrete variables. The Hybrid and Adaptive Metamodeling Method (HAM) is used to optimize the mathematical model. This approach uses and integrates three distinct metamodels with various attributes. The body-in-white torsional stiffness test result error is only 1.1%, and the body-in-white bending stiffness test result error is only 3.4%, owing to the optimization result that was used to design and manufacture a set of body-in-white stiffness test rigs and use them for a body-in-white stiffness test verification. Full article

This study investigates the influence of various printing parameters on the tensile, compressive, and bending stiffness of fused deposition modeling (FDM)-printed polylactic acid (PLA) parts through a comprehensive full factorial design of experiment. Key factors, including infill percentage, infill pattern, number of outer shells, and part orientation, were systematically varied to quantify their impact on mechanical performance. A total of 36 parameter combinations, selected based on a literature review and experimental feasibility, were tested using standardized specimens: beams for bending, cylinders for compression, and dogbones for tensile testing. Mechanical tests were performed according to ISO 5893:2019, employing a 1 kN load cell to determine stiffness and elastic modulus. The results indicate that the number of outer shells and infill density are the most influential parameters, whereas infill pattern and part orientation have a minor effect, depending on the loading condition. This study provides a novel and robust evaluation of the interactions between key printing parameters, offering new insights into optimizing the mechanical properties of FDM-printed parts. These findings establish a foundation for further optimization and material selection in future additive manufacturing research. Full article

The aim of this work is to perform a detailed dilatometric analysis of the decomposition of austenite during the cooling process using experimentally derived continuous cooling transformation (CCT) diagrams for two specific tool steels, X153CrMoV12 Bohdan Bolzano, Bratislava, Slovakia and 100MnCrW4. The dilatometric curves were compared with metallographic evaluations using scanning electron microscopy (SEM). In addition, hardness measurements were performed to obtain additional information about the mechanical properties of the materials. All experimental work was performed using a DIL 805A. The accuracy of the resulting CCT diagrams was verified by comparing them with those calculated with the JMatPro software v12.4. The cooling rates ranged from 20 °C/s to 0.01 °C/s, depending on the specific type of steel tested. The novelty of this research is the combination of experimental and simulation methods to analyze the influence of alloying elements on the kinetics of phase transformations in tool steels. It was found that one of the most significant factors affecting the CCT diagrams is the weight percentage of alloying elements in the steels. These results clearly show that increasing the weight percentage of the content of alloying elements has a significant impact on the accuracy of the simulation results derived from the JMatPro software. Full article

Chatter is a complex dynamic instability in machining processes and presents nonlinear and nonstationary behavior. Detection of this phenomenon before a catastrophic failure occurs has great importance in the industry today. This behavior demands online monitoring signal-processing techniques suitable for facing these kinds of dynamics such as approximate entropy (AE) and wavelet transform. Moreover, AE is useful for dealing with noisy signals and requires a relatively small amount of observations. In this study, we propose an improved AE methodology, the multiscale maximum approximate entropy (MMAE), to detect chatter in milling processes. The maximum AE is achieved by the calculation of the parameter r proposed by Sheng and Chon. In the past, the calculation of this parameter was a drawback of the AE technique. The results show the effectiveness of this proposed technique in detecting clearly different gradual and drastic changes in chatter conditions. Moreover, a more known technique is presented: the time–frequency maps provided by continuous wavelet transform (CWT). The results also show the efficacy of this technique in detecting different levels of chatter. The results are corroborated by the machining piece observation of the chatter phenomenon. MMAE is also compared with sample entropy (SE) and the Hurst exponent obtained by the R/S analysis. At the end, a comparison analysis of the mentioned techniques is carried out, showing that they all have advantages and disadvantages. However, the disadvantages of MMAE and CWT can be solved, as mentioned in the comparison section. Thus, the conclusion is that MMAE and CWT techniques are optimal for the online monitoring of chatter in machining processes. Full article

In model calibration, the identification of the unknown parameter values themselves, but also the uncertainty of these model parameters, due to uncertain measurements or model outputs might be required. The analysis of parameter uncertainty helps us understand the calibration problem better. Investigations on the parameter sensitivity and the uniqueness of the identified parameters could be addressed within uncertainty quantification. In this paper, we investigate different probabilistic approaches for this purpose, which identify the unknown parameters as multivariate distribution functions. However, these approaches require accurate knowledge of the model output covariance, which is often not available. In addition, we investigate interval optimization methods for the identification of parameter bounds. The correlation or interaction of the input parameters can be modeled with a convex feasible domain that belongs to a feasible solution of the model output within given bounds. We introduce a novel radial line-search procedure that can identify the boundary of such a parameter domain for arbitrary nonlinear dependencies between model input and output. Full article

Transfer-path analysis (TPA) is a reliable and effective diagnostic tool for determining the dominant vibration transfer paths from the actively vibrating components to the connected passive substructures in complex assemblies. Conventional and component-based TPA approaches achieve this by estimating a set of forces that replicate the operational responses on the passive side of the assembly, requiring separate measurements of the transfer-path admittance and the operational responses, followed by an indirect estimation of the interface forces. This demands significant measurement effort, especially when only the dominant transfer paths are desired. Operational transfer-path analysis (OTPA) overcomes this by identifying transfer-path contributions solely from operational response measurements. However, OTPA is susceptible to measurement errors as minor inaccuracies can result in discrepancies regarding transfer-path characterization. This is especially evident when poor placement of the sensors results in similar response measurements from multiple channels, introducing redundancy and amplifying measurement noise. This is typically resolved using regularization techniques (e.g., singular-value truncation and Tikhonov regularization) that promote vibration transfer related to dominant singular vectors. As an alternative, this paper explores the benefits of using established reduction-based approaches from dynamic substructuring within OTPA. Measured responses are projected onto different dynamic sub-spaces that include the dominant dynamic behavior of the interface between the active and passive sides (i.e., dominant interface modes). In this way, only the vibration transfer related to the interface modes included in the reduction step is evaluated, leaving stiff modes obscured by noise unobserved. This paper proposes using interface-deformation modes and physical modes, demonstrating their feasibility via various experimental setups and comparing them to standard OTPA. Full article

In this work, an analytical solution for the natural frequencies of elastically supported stepped beams with rigid segments is presented. The elastic end boundary conditions are modeled with a translational stiffness element, a rotational stiffness element, and an end-concentrated mass. This model is of great significance in machine construction studies. Under the assumption of Euler–Bernoulli beam theory, the non-dimensional equations of the motion and main equations that can give all of the boundary conditions were obtained by using Hamilton’s principle. After deriving the transverse displacement functions by means of using the separation-of-variables technique, the frequency equation was found by setting the determinant of the coefficient matrix to zero. The natural frequencies of the transverse vibrations were found according to physical and geometric parameters. The method was validated by using FEM results and findings from the literature. This study indicates that the physical and geometric parameters of the elastic supports and rigid segments affect the natural frequencies of the beam. The revealed analytical method can be used to calculate the natural frequencies and mode shapes of all beam types, such as elastically supported uniform beams and single-step beams with or without concentrated mass and/or rigid segments. Full article