Nonlinear Analysis Research Articles

Assessing the effects of trade openness and economic growth on environmental pollution in China and policy implications for sustainability: a nonlinear analysis

Assessing the effects of trade openness and economic growth on environmental pollution in China and policy implications for sustainability: a nonlinear analysis

Assessing Whether Negative Parenting Cognitions Bias Parent Report of Preschoolers' Externalizing Symptoms: A Regularized Moderated Non-Linear Factor Analysis Approach.

Parent report is frequently used to assess children's psychopathology, however, researchers have expressed concerns about the validity of parent reports. Some parental characteristics, attitudes, or beliefs may systematically bias a parent's report of their child's behaviors and functioning. Informed by social information processing models of parenting risk, parents with more difficulties reflecting on and interpreting their children's behavior may be at risk for less accurate reports. The present study conducted two regularized moderated non-linear factor analyses with LONGSCAN data to examine how parents' self-reported negative parenting cognitions were associated with structural parameters of parent-reported child aggression and attention problems. While differential item functioning (DIF) was present on the aggression and attention problems subscales as a function of negative parenting cognitions, the DIF was small in magnitude, inconsistent in directionality and did not significantly alter factor-level parameters. Negative parenting cognitions did demonstrate a small but significant negative impact on all latent externalizing factors (aggression and attention problems), such that caregivers with fewer negative parenting cognitions endorsed fewer items, and this was associated with a lower mean of each latent variable. Given that accounting for DIF did not contribute to meaningful differences in impact parameters or improve criterion validity, findings suggest that the aggression and attention subscales are functionally invariant to negative parenting cognitions, suggesting that externalizing symptoms can be reliability compared across parents of varying parenting cognitions.

On buckling of compact I-section beams subjected to biaxial bending

This paper aims at providing a new insight into the lateral-torsional buckling behavior of compact I-section steel beams subjected to biaxial bending, without axial force, a subject seldom treated in the literature. This investigation is based on both analytical and numerical results, the latter obtained using a two-node geometrically exact beam finite element developed by one of the authors (Gonçalves, 2019), which has all the required features. Several geometrically non-linear analysis (GNA) types are used to characterize the buckling behavior, namely with geometric imperfections (GNIA), with material non-linearity (GMNA) and combining material non-linearity and imperfections (GMNIA). Different boundary conditions along the two principal planes are allowed and particular attention is paid to cases which involve the same first-order bending moment diagrams but different support schemes. As a consequence, it is shown that the buckling behavior depends not only on the slenderness and the first-order moment diagrams, but also on the supports. On the basis of results obtained concerning the application of the Eurocode 3 provisions for different support conditions, it is shown that unsafe results can be obtained but may be resolved using the recommendations presented in the paper.

How do Ritz Vectors React to the Imposed Load?

All real structures behave dynamically when loaded or displaced. Additional inertial forces are equal to the force in acceleration using Newton's second law. If the forces or the change of places are applied very slowly, the inertial forces can be ignored and a static analysis can be done. Therefore, it can be said that dynamic analysis is a simple extension of static analysis. In addition, all potential real structures have unlimited degrees of freedom. Therefore, the most critical part of structural analysis is creating a model with a limited number of degrees of freedom that has several almost massless members and several nodes, which can estimate the behavior of the structure appropriately. The mass of the structure can be concentrated in the nodes. Also, for a linear elastic system, the stiffness characteristics of the members can be estimated very accurately - according to the experimental data - although the estimation of dynamic loading, energy loss, and boundary conditions can be very difficult. Therefore, the nonlinear dynamic analysis method is usually used in theoretical studies and is not used in routine designs. So, it is a worthwhile task to propose a simple and computer method for seismic estimation of structures. For this purpose, POA has been introduced. In many cases, we can get more valuable information from POA than nonlinear dynamic analysis, this method is simple and economical and has attracted more attention nowadays.

Simplified Gravity Load Collapse Dynamic Analysis of Old-Type Reinforced Concrete Frames

The results of shaking table tests from previous studies on a one-story, two-bay reinforced concrete frame—exhibiting both shear and axial failures—were compared with nonlinear dynamic analyses using simplified models intended to evaluate the collapse potential of older reinforced concrete structures. To replicate the nonlinear behavior of columns, whether shear-critical or primarily flexure-dominant, a one-component beam model was applied. This model features a linear elastic element connected in series to a rigid plastic, linearly hardening spring at each end, representing a concentrated plasticity component. To account for strength degradation through path-dependent plasticity, a negative slope model as degradation was implemented, linking points at both shear and axial failure. The shear failure points were determined through pushover analysis of shear-critical columns using Phaethon software. Although the simplified model provided a reasonable approximation of the overall frame response and lateral strength degradation, especially in terms of drift, its reduced computational demands led to some discrepancies between the calculated and measured shear forces and drifts during certain segments of the time-history response.

Vibration characteristics of rolling bearing cage under speed variation conditions

Speed variation conditions will deteriorate the stress state of the rolling bearing internal components and aggravate the vibration of the cage, thereby affecting the service life and reliability of rolling bearings. In this paper, a nonlinear dynamic analysis model of the cylindrical roller bearing is established considering the rubbing effect and hydrodynamic contact between the cage and the guiding ring, as well as the sliding between the cage and other rolling elements. The vibration characteristics of the cage is discussed under the start-stop conditions and different fluctuations of rotation rate. The results show that the vibration of the cage mainly occurs at the middle and late stages of the acceleration process, and the impact mainly occurs at the middle stage of the deceleration process under the start-stop conditions. Moreover, the fluctuation of inner ring speed will enhance the unstable motion of the cage, among which the vibration and impact of the cage are most severe under the rectangular fluctuation of speed, followed by simple harmonic and triangular fluctuations. The findings can provide a theoretical guidance for improving the performance of rolling bearings and ensuring their safe and reliable operation.

Mixed Finite Element Formulation in Nonlinear Geometrical Analysis of Space Trusses and Application to Trusses With Member Length Imperfection

Abstract Space trusses usually have a significant number of elements. As a result, it is inevitable that some elements have imperfections. In this study, the authors proposed a mixed finite element method for nonlinear geometrical analysis of space trusses. The post-buckling behavior of space trusses with length imperfections was predicted using a code list written in the programming software. The numerical results indicate that when the length imperfection approaches zero, the results converge to those obtained in studies on standard trusses. A second approach based on the displacement model is also proposed, in which the Lagrange multiplier method is used to deal with the member length imperfection. The results show that the two approaches proposed by the authors are effective, in which the mix formulation based on the finite element model is superior to that based on the displacement model. These results verify the accuracy of the method. Based on the proposed method, the effects of imperfections in the element layers on the truss were studied. The results show that the imperfections in the top two element layers have the maximum influence on the limit load value, whereas the remaining layers have a negligible influence. The combination of the imperfect lengths of these two layers of elements can produce results in which the limit load value is much larger than in the case of a perfect system. Based on the obtained results, it is possible to provide a solution for improving the overall stability of truss structures by creating reasonable imperfections.

Nonlinear association between lung needle path CT attenuation values and postprocedural immediate pneumothorax following computed tomography-guided lung biopsy: a retrospective cohort study.

Pneumothorax is a potential complication following computed tomography-guided lung biopsy (CT-LB). However, the relationship between the lung needle path CT attenuation values and risk of post-procedural immediate pneumothorax remains unclear. The study aims to investigate this relationship. The present single-center retrospective cohort study analyzed the data obtained from 453 patients who underwent CT-LB from 2019 to 2022. The relationship between the lung needle path CT attenuation values and post-procedural immediate pneumothorax was assessed using restricted cubic splines, which were adjusted for potential confounders, and validated using linear and nonlinear binomial logistic models. A total of 453 patients (mean age: 60.2 ± 12.0 years old, 217 male patients) were evaluated. The incidence of post-procedural immediate pneumothorax was 41.06% (186/453). The median needle path CT attenuation was - 831 Hounsfield units (Hu). The linear models indicated an unstable association between lung needle path CT attenuation and post-procedural immediate pneumothorax (odds ratio: 0.99, 95% confidence interval: 0.99-1.00). The nonlinear analysis identified an inflection point at a CT attenuation value of -805 Hu. A stronger negative link was identified for needle path CT attenuation values below - 805 Hu (odds ratio: 0.99, 95% confidence interval: 0.98-0.99) between the needle path CT attenuation value and pneumothorax, while no statistically significant association was identified between these when the CT attenuation value was above - 805 Hu. There is a nonlinear association between the lung needle path CT attenuation values and risk of post-procedural immediate pneumothorax. For CT attenuation values below - 805 Hu, increasing the needle path CT attenuation values might reduce the risk of pneumothorax.

A study for analysing predator–prey ecological system using Legendre polynomial

This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on Caputo operators, we present a newly developed system of differential equations for the predator–prey system using wavelet method. It is well known that a system of nonlinear singular models cannot operate smoothly since they are singular and nonlinear. Therefore, with the help of this numerical approach, we have converted the system into a nonlinear system of algebraic equations by extending it through operational matrix of Legendre wavelets. Using the wavelet collocation scheme, we have calculated these unknown coefficients. It has been demonstrated in tables and graphs that the developed approach is consistent and proficient. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyse its behaviour. In addition, a nonlinear functional analysis have used to establish uniformly boundedness for the proposed model. Also we have discussed residual error analysis and Lyapunov exponent. The applicability and efficacy of this methodology have been demonstrated through this nonlinear system. Additionally, a comparison with existing results highlights the advantages of our numerical approach. All calculations have been done using MATLAB.

Establishment of a multi-clearance coupled 3D floating nonlinear model and vibration analysis for a coaxial reverse closed differential herringbone gear transmission system

Establishment of a multi-clearance coupled 3D floating nonlinear model and vibration analysis for a coaxial reverse closed differential herringbone gear transmission system

The nonlineard association between triglyceride to HDL cholesterol ratio and long-term heart disease risk: findings from China Health and Retirement Longitudinal Study (CHARLS).

The aim of this study was to investigate the relationship between triglyceride to high-density lipoprotein cholesterol ratio (TG/HDL-C) and the risk of cardiovascular disease (CVD) in middle-aged and elderly Chinese population. CVD has high morbidity and mortality in China, with 5.09million CVD deaths in 2019 and a mortality rate of 364.5 cases per 100,000 people. Existing studies have focused on specific populations and lack studies on the general population. This study used data from the China Health and Aged Care Tracking Survey (CHARLS) to analyse the middle-aged and elderly population between 2011 and 2020. The exposure variable was TG/HDL-C ratio, the outcome variable was the occurrence of heart disease (including myocardial infarction, coronary heart disease, etc.), and the covariates included age, gender, education level, and body mass index. The final sample size was 4,551 participants. Weighted Cox regression models were used to assess the association between TG/HDL-C and CVD risk, and nonlinear associations and stratified analyses were performed. The results demonstrated a significant association between TG/HDL-C ratios and cardiac morbidity, with a risk ratio of 0.71 (95% CI: 0.71-0.71) in the adjusted model II. Nonlinear analysis revealed a threshold effect. Within the TG/HDL-C 0.15-1.5 interval (inflection point LnTG/HDL-C 0.41), each 1-unit increase in Ln (TG/HDL-C) was associated with a 17% reduction in the risk. The inflection point was associated with a 0.83-fold reduction in the risk of CVD (95% CI: 0.75, 0.92; p = 0.0003), but beyond this point, the association was no longer significant (1.00-fold reduction in risk; 95% CI: 0.95, 1.05; p = 0.9701). In contrast, stratified analyses demonstrated that the results were more applicable to women and those younger than 65 years. In summary, the study found a significant inverse relationship between the triglyceride to high-density lipoprotein cholesterol (TG/HDL-C) ratio and the risk of cardiovascular disease in the middle-aged and elderly Chinese population, with a nonlinear threshold effect observed at a TG/HDL-C ratio of around 1.5.

Nonlinear Dynamics Analysis of Handgrip Strength Using the Poincaré Plot Method Through Video Processing Techniques

Background/Objectives: The aim of this study was to analyze the nonlinear dynamics of handgrip strength (HGS) in young adults, focusing on hand dominance, by employing the Poincaré plot method to assess short- and long-term variability utilizing dynamometry and video motion capture during sustained isometric contractions. Methods: A cross-sectional exploratory study was conducted on 30 healthy subjects (mean age 21.6 ± 1.3 years, 13 males and 17 females), measuring HGS for both the dominant hand (DH) and nondominant hand (NDH) using a Saehan hydraulic dynamometer during 25-s sustained isometric contractions. A GoPro HERO11 Black camera recorded the dynamometer’s needle movements, and the video data were analyzed using Kinovea software. Angular values were converted to force using a calibration-based formula, and the Poincaré plot computed variability indices (short-term variability—SD1, long-term variability—SD2, ratio SD1/SD2, and area of the fitting ellipse) for each hand in relation to HGS and angular velocity (AV). Data analysis included descriptive and inferential statistics. Results: We demonstrated a strong correlation between mechanical and video measurements (p ≤ 0.001), confirming the reliability of the video method. The findings highlight the importance of nonlinear analysis in understanding neuromuscular function and fatigue, revealing significant correlations among HGS, AV, Poincaré indices, and fatigue levels in both hands (p ≤ 0.001). Increased maximum HGS and AV correlated with higher nonlinear variability in force production. Conclusions: This study confirms the reliability of the proposed video-based HGS assessment and demonstrates the effectiveness of Poincaré plot analysis for capturing nonlinear variability in HGS.

Effects of Velocity Pulse-Like Ground Motions on the Seismic Failure Behavior of Masonry Minarets

ABSTRACT This research is motivated by post-earthquake observations of significant structural damage to minarets during the 2023 Kahramanmaraş earthquakes. It is thought that the near-fault velocity pulse-like ground motions played a crucial role in this phenomenon. Although the seismic performance of minarets has been extensively studied, including a large body of literature on numerical and experimental analyses, no attention has been paid to the seismic damage assessment of minarets subjected to strong velocity pulse-like ground motions. The present study aims to investigate the effects of near-fault strong velocity pulse-like ground motions with different velocities on the seismic failure behavior of masonry minarets. A 33-meter-high stone masonry minaret was selected for this purpose. Nonlinear behavior of masonry unit is modeled using Concrete Damage Plasticity (CDP). For the nonlinear analysis, three near-fault strong velocity pulse-like ground motions recorded during February 6, 2023, Kahramanmaraş earthquake (M7.7) and one non-pulse-like ground motion were selected. Displacements, strains, stresses and damage patterns in masonry minarets subjected to near-fault velocity pulse-like and non-pulse-like ground motions were obtained and thoroughly evaluated across different ground velocities. The velocity, the number of pulses and the pulse duration of velocity-pulse-like ground motions have a significant influence on the structural damage behavior of minarets. The results provide a detailed understanding of how minarets respond to different velocity pulse-like ground motion scenarios, offering valuable insights for the design, rehabilitation, and retrofitting of both new and existing minarets.

The Electroencephalogram (EEG) Study for Estimating Endurance Sports Performance Base on Eigenvalues Extraction Method

Objectives. Brain–behavior connections are a new means to evaluate sports performance. This electroencephalogram (EEG) study aims to estimate endurance exercise performance by investigating eigenvalue trends and comparing their sensitivity and linearity. Methods. Twenty-three cross-country skiers completed endurance cycling tasks. Twenty-four-channel full-brain EEG signals were recorded in the motor phase and recovery phase continuously. Eighteen EEG eigenvalues calculation methods were collected, commonly used in previous research. Time-frequency, band power, and nonlinear analyses were used to calculate the EEG eigenvalues. Their regression coefficients and correlation coefficients were calculated and compared, with the linear regression method. Results. The time-frequency eigenvalues shift slightly throughout the test. The power eigenvalues changed significantly before and after motor and recovery, but the linearity was not satisfactory. The sensitivity and linearity of the nonlinear eigenvalues were stronger than the other eigenvalues. Of all eigenvalues, Shannon entropy showed completely non-overlapping distribution intervals in the regression coefficients of the two phases, which were −0.1474 ± 0.0806 s−1 in the motor phase and 0.2560 ± 0.1365 s−1 in the recovery phase. Shannon entropy amplitude decreased more in the F region of the brain than in the other regions. Additionally, the higher the level of sport, the slower the decline in Shannon entropy of the athlete. Conclusions. The Shannon entropy method provided more accurate estimations for endurance exercise performance compared to other eigenvalues.

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Exploring the relationship of sleep duration on cognitive function among the elderly: a combined NHANES 2011-2014 and mendelian randomization analysis.

As one of the key features of sleep, sleep duration (SD) has been confirmed to be associated with multiple health outcomes. However, the link between SD and cognitive function (CF) is still not well understood. We employed a combined approach utilizing data from the National Health and Nutrition Examination Survey (NHANES 2011-2014) and Mendelian Randomization (MR) methods to investigate the relationship between SD and CF. In the NHANES cross-sectional analysis, the association between these variables was primarily examined through multivariate linear regression to explore direct correlations and utilized smoothing curve fitting to assess potential nonlinear relationships. To ensure the robustness of our findings, subgroup analyses were also conducted. MR analysis was used to assess the causal relationship between SD and sleeplessness on CF. After excluding confounding factors, univariate and multivariate MR were performed using inverse variance weighting (IVW) as the main analysis method, and sensitivity analysis was performed. The results of our cross-sectional study indicate a notable negative association between SD and CF, forming an inverted U-shaped curve with the inflection point occurring at SD = 6h. This relationship remains consistent and robust across subgroup analyses differentiated by variables such as age, levels of physical activity, and frequency of alcohol intake. In MR analysis, IVW analysis showed no causal relationship between SD and sleeplessness on CF (Both P > 0.05). Cross-sectional studies suggest the existence of an inverted U-shaped correlation between SD and CF among the elderly. However, MR analysis did not reveal a causal relationship between SD and CF, which the lack of nonlinear MR analysis may limit. These findings provide evidence from a sleep perspective for optimizing cognitive strategies in older adults.

Nonlinear Isogeometric Analyses of Instabilities in Thin Elastic Shells Exhibiting Combined Bending and Stretching

Abstract Thin structures like shells are highly susceptible to mechanical instabilities. They can undergo large nonlinear elastic deformations while exhibiting combined bending and stretching modes of deformation. Here, we propose a new displacement-based finite element (FE) formulation based on the isogeometric discretization of Koiter’s nonlinear shell theory and use of the method of dynamic relaxation (DR) to solve equilibrium configurations of problems involving fine-scale and hierarchical wrinkling and buckling. No imperfection seeding is required to trigger instabilities. The use of the NURBS basis provides a rotation-free, conforming, higher-order spatial continuity such that curvatures and membrane strains can be computed directly from interpolating the position vectors of the control points using spatial finite differences. The pseudo-dissipative FE dynamical system is updated through explicit time integration and made scalable for parallel computing using a message passing interface (MPI). The proposed FE method is successfully benchmarked against several numerical and experimental results.

Nonlinear time series analysis of state-wise COVID-19 in Malaysia using wavelet and persistent homology.

The nonlinear progression of COVID-19 positive cases, their fluctuations, the correlations in amplitudes and phases across different regions, along with seasonality or periodicity, pose challenges to thoroughly examining the data for revealing similarities or detecting anomalous trajectories. To address this, we conducted a nonlinear time series analysis combining wavelet and persistent homology to detect the qualitative properties underlying COVID-19 daily infection numbers at the state level from the pandemic's onset to June 2024 in Malaysia. The first phase involved investigating the evolution of daily confirmed cases by state in the time-frequency domain using wavelets. Subsequently, a topological feature-based time series clustering is performed by reconstructing a higher-dimensional phase space through a delay embedding method. Our findings reveal a prominent 7-day periodicity in case numbers from mid-2021 to the end of 2022. The state-wise daily cases are moderately correlated in both amplitudes and phases during the Delta and Omicron waves. Biweekly averaged data significantly enhances the detection of topological loops associated with these waves. Selangor demonstrates unique case trajectories, while Pahang shows the highest similarity with other states. This methodological framework provides a more detailed understanding of epidemiological time series data, offering valuable insights for preparing for future public health crises.

Modelling reinforced masonry buildings by a mechanics‐based macroelement approach

AbstractThe seismic behaviour of unreinforced masonry (URM) buildings is frequently modelled using macroelements, in the framework of an equivalent‐frame schematisation of the walls. Although the advantages of this modelling technique, mainly related to the compromise between computational burden and accuracy of the results, appear to be valid also in the case of reinforced masonry (RM) buildings, few attempts have been made to extend its applicability to RM. This work proposes a mechanics‐based macroelement approach to simulate the in‐plane nonlinear response of RM piers, starting from a macroelement model widely adopted for URM and implemented in the TREMURI software. The strategy consists of discretising a masonry pier into sub‐macroelements, representative of masonry and horizontal reinforcement, with nonlinear beams representing vertical reinforcement. Experimental tests performed on clay blocks RM piers were simulated to test the efficiency of this model in capturing the strength and cyclic behaviour associated with different damage mechanisms. More complex structures were then studied, starting from assemblies of piers, up to entire buildings. Even in these cases, the modelling approach proved to be able to model the nonlinear cyclic behaviour. Finally, the model was used to compare the response of two buildings in their unreinforced and reinforced configurations, through nonlinear static and dynamic analyses.

Nonlinear Dynamic Analysis Using the Force Analogy Method and the Ibarra–Medina–Krawinkler Model

ABSTRACTA methodology to integrate the Ibarra–Medina–Krawinkler (IMK) hysteretic model with the force analogy method (FAM) is proposed. FAM is a powerful tool for performing nonlinear structural analysis that reduces analysis time, addressing the main limitation of nonlinear analysis. One area of opportunity for FAM lies in its access to material nonlinearity models, which enable the reproduction of inelastic behavior in structures. The IMK model, utilized in nonlinear analysis for updating the stiffness matrix, incorporates various rules of material nonlinear behavior and considers cyclic deterioration of stiffness and strength. By combining the IMK model with FAM, the capability to model material nonlinear behavior in a computationally efficient manner is enhanced. The proposed methodology is validated through four numerical examples, demonstrating its effectiveness in replicating experimental behaviors and enhancing FAM capabilities in inelastic structural analysis.