Nonlinear Analysis Method Research Articles

Dynamic and uncertainty-based assessment of the progressive collapse probability of prestressed concrete frame structures with infill walls

Since progressive collapse usually has serious consequences, the problem of progressive collapse resistance has gradually become a topical issue in recent years. However, most of the existing studies have been conducted on common reinforced concrete (RC) structures. The methodologies used in the studies are also mostly static and deterministic. There is a lack of research that considers the dynamic effects and uncertainties of pre-stressed structures with infill walls. In this paper, the assessment of progressive collapse probability considering dynamic effect and uncertainties is performed for prestressed concrete frame with infill walls (IW-PC frame) structures. The finite element software OpenSEES is chosen as the analysis platform. By introducing uncertainties in material, geometry and load, five limit states and their quantitative indicators are identified. Based on the nonlinear incremental dynamic analysis (IDA) method, the vulnerability analysis of the IW-PC frame is performed under different working conditions. The vulnerability analysis indicates that the five levels of limit states can visually evaluate the degree of structural damage. Additionally, the resistance relationships of the four structural forms are as follows: IW-PC frame > reinforced concrete frame with infill walls (IW-RC frame) > prestressed concrete frame (PC frame) > RC frame. The load carrying capacity of the frames is significantly increased by the coupling effect of the infill walls and the prestressed strands. Moreover, the prestressed strands can reduce the probability of light and moderate damage, while infill walls have an excellent preventive effect on severe damage. The reliability of the four structures is evaluated using the Zhao-Ono moment method. The results indicate that IW-PC is the safest, followed by IW-RC, PC, and RC.

Data-Driven Bifurcation Analysis of Experimental Aeroelastic Systems Using Preflutter Measurements

Identification of flutter margins in modern aeroelastic systems is a challenging task due to increased nonlinearities in novel designs, which can result in instabilities occurring below the linear flutter speed. These instabilities pose a significant risk as they may involve multiple stable solutions, such as large-amplitude self-sustained oscillations. The lack of efficient nonlinear bifurcation analysis methods for experimental systems exacerbates the challenges associated with postflutter analysis. This paper presents a data-driven method for predicting flutter instabilities and bifurcation diagrams of an experimental nonlinear 2-degree-of-freedom (2-DOF) airfoil. The approach uses measurement data from the preflutter regime to forecast the postflutter dynamics, eliminating the need for computationally expensive models. This study is the first application of the recently introduced data-driven bifurcation forecasting method to experimental aeroelastic systems. The results show that the proposed method is accurate, with predictions matching the measured behavior of the system. The presented study provides valuable insights into the nonlinear stability and dynamics of experimental airfoils and demonstrates the potential for applicability of this approach in the analysis of experimental systems. The findings have significant implications for online monitoring and evaluation of the nonlinear dynamics of aeroelastic systems in the aerospace industry, where safety is of crucial importance.

A layer discrete particle based soft contact model in corroded rebar monitoring using linear and nonlinear ultrasonic guided waves

In offshore reinforced concrete (RC) structures, the phenomenon of rebar corrosion is widespread, seriously threatening the durability of the structures. However, the issue of rebar corrosion detection especially for the early corrosion situation is also challengeable. It is of great significance to use ultrasonic guided waves (UGWs) for monitoring the situation of the rebar corrosion entire process. In this paper, a mechanical model was used to establish the relationship between different rebar corrosion expansion states and layer-surface contact pressures in the layered RC components with radial cracks. Based on this model, a soft pressure-dependent contact 2D model in Abaqus was used to simulate the local corrosion layer. A linear and nonlinear signal joint analysis (LNSJA) method using PZT-based UGWs was proposed to monitor rebar corrosions, and an LNSJA-based rebar corrosion damage index (RCDI) for corroded RC components was proposed. The proposed method which can effectively detect both the micro- and macro-thickness as well as local area of rebar corrosion layer was validated by the relevant experiment and finite element analysis (FEA).

Well-Posedness for Mean Field Games with Finite State and Action Space

The main purpose of this paper is to investigate the well-posedness for mean field game with finite state and action space (FSASMFG) by using nonlinear analysis methods. First, we set up the bounded rationality model of the FSASMFG in the topological space. Next, we study some sufficient conditions of generalized strong well-posedness (GS-wp) and strong well-posedness (S-wp) for a class of FSASMFGs. Finally, we give some characterizations of GS-wp and S-wp for FSASMFGs with the help of set-valued analysis methods. These new results presented in the paper develop and improve the corresponding conclusions in the recent literature.

NLFEA of the Behavior of Polypropylene-Fiber-Reinforced Concrete Slabs with Square Opening

The bending behavior of one-war reinforced concrete (RC) slabs with polypropylene fibers (PF) was examined in this study under the effect of different opening ratios using the nonlinear finite element analysis (NLFEA) method. The investigated parameters include the effect of different square opening ratios between 0 and 24% and PF volume percentages between 0 and 1% with 0.1% increments. The objectives of this study were fulfilled using 88 NLFEA models with different combinations of the studied parameters, including 11 control slabs without openings. The slab’s behavior was studied focusing on different structural performance characteristics, such as ductility, using energy-based and deflection-based approaches, stiffness (initial and yielding), cracking, and ultimate load strength. In addition, other structural performance parameters were considered, such as the crack opening, failure modes, and strain values, which were recorded for all specimens during the loading history. Moreover, the load-carrying capacity of the slabs was compared, looking at the NLFEA method’s results and the theoretical prediction results based on the sectional analysis method. However, it was observed that the inclusion of PFs of different percentages has a superior effect on the behavior of RC slabs with small openings (less than 2% opening ratio) compared to the acceptable improvements obtained for sabs with larger opening sizes. Consequently, PF could be utilized as a replacement for conventional steel rebars for RC slabs with small openings. In addition, increasing the PF percentage increases the resulting crack-opening value at failure due to the provided stabilization effect, in addition to increasing the system’s ability to sustain loads.

Optimized Gauss–Legendre–Hermite 2-point (O-GLH-2P) method for nonlinear time-history analysis of structures

Optimized Gauss–Legendre–Hermite 2-point (O-GLH-2P) method for nonlinear time-history analysis of structures

Study on the stability and its simulation algorithm of a nonlinear impulsive ABC-fractional coupled system with a Laplacian operator via F-contractive mapping

In this paper, we study the solvability and generalized Ulam–Hyers (UH) stability of a nonlinear Atangana–Baleanu–Caputo (ABC) fractional coupled system with a Laplacian operator and impulses. First, this system becomes a nonimpulsive system by applying an appropriate transformation. Secondly, the existence and uniqueness of the solution are obtained by an F-contractive operator and a fixed-point theorem on metric space. Simultaneously, the generalized UH-stability is established based on nonlinear analysis methods. Thirdly, a novel numerical simulation algorithm is provided. Finally, an example is used to illustrate the correctness and availability of the main results. Our study is a beneficial exploration of the dynamic properties of viscoelastic turbulence problems.

Numerical investigation of elastic-plastic buckling performance of circular arched cellular steel beam using nonlinear finite element analysis method

This study presents a numerical investigation of the in-plane elastic-plastic performance, post-buckling mode, and arched web-post shear resistance of a pinned end circular arched cellular steel beam using ABAQUS nonlinear finite element analysis package. The trustworthiness of the finite element analysis results was confirmed by comparing them to the existing experimental investigation results. The main study parameters, such as the effect of a rise-to-span ratio, the radius of curvature, the impact of opening, the types of loading on elastic-plastic performance, and the buckling mode of an arched cellular steel beam, were investigated. Furthermore, the arched web-post finite element model was proposed and the shear resistance of the arched web-post was investigated. Also, the appropriateness of the currently existing different web-post shear resistance analysis approaches was reviewed and evaluated in determining the shear resistance of arched web-posts. The results showed that the web post-structural stiffness of a circular arched cellular steel beam was improved as the rise-to-span ratio increased under the mid-span concentrated load regardless of the rise-to-span ratio. However, under uniformly distributed vertical load, increasing a rise-to-span ratio beyond 0.35 or 140° subtended angles reduces the stiffness of circular arched cellular steel beams. The web post shear resistance analyzing approaches proposed by Panedpojaman et al. and SCI P-100 overestimate and yield unsafe results in determining the web-post shear resistance of arched web post cellular steel of low rise-to-span ratio.

In-plane nonlinear buckling analysis and design method of concrete-filled steel tubular catenary arches

The prevalence of concrete-filled steel tubular (CFST) catenary arches, renowned for the optimal load-bearing efficiency, has shown a marked increase over the past decades. To date, extensive research has been conducted into the nonlinear buckling behaviors and elastic-plastic strength of circular and parabolic CFST arches, grounded on the assumption that the curvature of the arch axis remains a specific constant. However, for CFST catenary arches, this assumption is not appropriate, given the substantial variation in curvature along the arch rib, and the influence of the arch axis is not adequately addressed in the existing design codes. Therefore, in this paper, a more precise strain expression is employed to conduct the nonlinear buckling analysis on CFST catenary arches. The analytic solutions for both symmetric snap-through buckling and anti-symmetric bifurcation buckling loads are obtained. In addition, a validated finite element (FE) model is adopted to investigate the influence of key parameters, including the slenderness ratio, the arch-axis coefficient, the rise-to-span ratio, and the steel ratio, on the in-plane stability bearing capacity of CFST catenary arches subjected to axial compression. Moreover, the obtained numerical results are utilized for comparison with the prediction results calculated by the existing design codes for CFST or steel arches. The comparison results indicate that the existing design codes have tended to overestimate the in-plane strength of CFST catenary arches, mainly due to the ignorance of the influence of pre-buckling deformation. Thus, based on the nonlinear buckling analysis results, a revised lower-bound design formula for predicting the in-plane stability bearing capacity of CFST catenary arches under axial compression is proposed, considering the influence of the rise-to-span ratio and the steel ratio.

Analytical method for lateral capacity of pile foundations under vertical loads considering asymmetric scour hole in sand

Offshore pile foundations are generally subjected to lateral and vertical loadings. The loss of sand around piles because of scouring reduces the soil resistance and effective depth of pile foundations. Moreover, scour holes are asymmetric both physically and in finite element simulations, which may change the effect of vertical loads on the lateral capacity of pile foundations. In this study, we propose a nonlinear analytical method to estimate the lateral capacity of pile foundations in sand considering vertical loads and asymmetric scour holes. The p–y curve, frictional resistance, shaft resistance moment, and pile-end resistance were revised considering an asymmetric scour hole. The accuracy of the analytical method was validated through comparison with experimental results. The results show that the P–Δ effect caused by vertical loads increases with increasing active scour depth, positive scour depth, active scour width, and positive scour width; and decreasing active and passive scour slopes. The most adverse lateral loading direction was 90° to the water direction with the asymmetric scour hole.

Damage Spectra of SDOF Structures Under Tsunami Actions Considering the Nonlinear Dynamic Analysis Method

This paper studies the damage spectra of single-degree-of-freedom (SDOF) systems for tsunami loading. The 2011 Tohoku tsunami wave traces are computed and obtained by adopting the Cornell Multi-grid Coupled Tsunami (COMCOT) model and are further verified by the Tohoku Tsunami Joint Survey (TTJS) data. The tsunami response analyses of SDOF systems are conducted taking into account the dynamic analysis method. The classical ductility damage is considered as the damage performance. The damage spectra are computed for five force reduction factors and 791 tsunami loadings. The effects of inundation depths, hysteretic model, post-yield stiffness ratio, [Formula: see text], viscous damping ratio, [Formula: see text], are explored and interpreted scientifically and statistically. The results demonstrate that the effect of the hysteretic model, force reduction factor, R, post-yield stiffness ratio, [Formula: see text], viscous damping ratio, [Formula: see text], on the damage of the structure is evident. Comparison with the static method and influence analysis of structural damping indicate the necessity for the application of the dynamic method. A simplified predictive formulation is developed for the evaluation of structural damage for tsunami loadings.

Nonlinear Dynamic Granger Causality Analysis Framework for Root-Cause Diagnosis of Quality-Related Faults in Manufacturing Processes

Root-cause diagnosis of quality-related faults plays a crucial role in ensuring stable product quality and high-efficient production for modern manufacturing processes. However, there exists complex nonlinear and dynamic sequential characteristics for process and quality data before and after faults, which contain important fault information. How to fully explore and use this information to locate the root-cause and identify the propagation path is a hot topic. Thus, a new nonlinear dynamic Granger causality analysis method is developed for root-cause diagnosis, which will provide timely and useful reference information to take reasonable measures for field engineers. First, an optimal variable division based on minimal redundancy maximal relevance algorithm is presented to get the quality-related variables. Then, a new attention-based random disturbance gated recurrent unit is designed for nonlinear dynamic Granger causality analysis, aiming at locating the root-cause and identifying the propagation path of quality-related faults. A typical manufacturing process, the hot strip mill process is used for verification. The results show the practicability of the proposed method, and its strong robustness to noise. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Reasonable and feasible root-cause diagnosis technology will provide timely reference information for field operators to take maintenance measures. However, the nonlinear and dynamic characteristics of time-series data before and after quality-related faults have brought great challenges to the traditional root-cause diagnosis techniques. To address this issue, a practical nonlinear dynamic Granger causality analysis method is proposed, which is purely data driven without knowing complex mechanism knowledge. It will provide feasible solutions for safety monitoring of hot strip mill process as the representative of manufacturing processes.

Features and networks of the mandible on computed tomography.

The mandible or lower jaw is the largest and hardest bone in the human facial skeleton. Fractures of the mandible are reported to be a common facial trauma in emergency medicine and gaining insights into mandibular morphology in different facial types can be helpful for trauma treatment. Furthermore, features of the mandible play an important role in forensics and anthropology for identifying gender and individuals. Thus, discovering hidden information of the mandible can benefit interdisciplinary research. Here, for the first time, a method of artificial intelligence-based nonlinear dynamics and network analysis are used for discovering dissimilar and similar radiographic features of mandibles between male and female subjects. Using a public dataset of 10 computed tomography scans of mandibles, the results suggest a difference in the distribution of spatial autocorrelation between genders, uniqueness in network topologies among individuals and shared values in recurrence quantification.

Assessment of applicability of equivalent linear and nonlinear analysis methods for site response analysis in deep soil Site

Assessment of applicability of equivalent linear and nonlinear analysis methods for site response analysis in deep soil Site

Effect of different palatal expanders with miniscrews in surgically assisted rapid palatal expansion: A non-linear finite element analysis.

Surgically assisted rapid palatal expansion (SARPE) has been the treatment of choice in subjects presenting skeletally mature sutures. The purpose of this study was to analyze stress distribution and displacement of the craniofacial and dentoalveolar structures resulting from three types of palatal expanders with surgical assistance using a non-linear finite element analysis. Three different palatal expanders were designed: Model-I (tooth-bone-borne type containing four miniscrews), Model-II (tooth-bone-borne type containing two miniscrews), and Model-III (bone-borne type containing four miniscrews). A Le Fort I osteotomy was performed, and a total of 5.0 mm palatal expansion was simulated. Nonlinear analysis (three theory) method (geometric nonlinear theory, nonlinear contact theory, and nonlinear material methods) was used to evaluate stress and displacement of several craniofacial and dentoalveolar structures. Regardless of the maxillary expander device type, surgically assisted rapid palatal expansion produces greater anterior maxillary expansion than posterior (ANS ranged from 2.675 mm to 3.444 mm, and PNS ranged from 0.522 mm to 1.721 mm); Model-I showed more parallel midpalatal suture opening pattern - PNS/ANS equal to 54%. In regards to ANS, Model-II (1.159 mm) and Model-III (1.000 mm) presented larger downward displacement than Model-I (0.343 mm). PNS displaced anteriorly more than ANS for all devices; Model-III presented the largest amount of forward displacement for PNS (1.147 mm) and ANS (1.064 mm). All three type of expanders showed similar dental displacement, and minimal craniofacial sutures separation. As expected, different maxillary expander designs produce different primary areas and levels of stresses (the bone-borne expander presented minimal stress at the teeth and the tooth-bone-borne expander with two miniscrews presented the highest). Based on this finite element method/finite element analysis, the results showed that different maxillary expander designs produce different primary areas and levels of stresses, minimal displacement of the craniofacial sutures, and different skeletal V-shape expansion.

Application of nonlinear signal analysis in millimeter-wave radar blood flow rate monitoring

Abstract Due to the advantages of millimeter-wave radar, such as its relatively simple structure, small size, high sensitivity, etc., it is used to obtain the human pulse signal and blood flow signal. Using the methods of mean cancellation, phase differencing, and smoothing, static clutter removal and heartbeat signal enhancement can be achieved, which can effectively eliminate interference information. Based on the collected information, the three-dimensional Navier-Stokes equations and boundary conditions are determined, and the theoretical knowledge related to fluid mechanics and bioengineering is used to construct the model of the multidimensional blood monitoring system, and the nonlinear signal analysis method is used to analyze the application of the constructed model. Based on the data, there is only a 0.1% difference between the waveform of the blood vessel diameter measured by the multidimensional blood monitoring system and that of the blood vessel diameter tested by commercial ultrasound equipment. The waveform trend is also consistent. In addition, the blood flow velocity at point 5 was much greater than that at point 2, when the vessel stenosis exceeded 50%. This study can accurately and efficiently monitor blood flow velocity for single and multiple individuals, which is critical for the healthcare field's development and innovation.

Analysis of models and development of a software package for assessing the impact of vibration effects of vehicles on urban infrastructure

The direction associated with the construction and research of models that can be used to predict the impact of vibration effects of vehicles on surrounding infrastructure facilities is relevant given the increasing pace of civil engineering in large cities and taking into account the expansion of transport networks. The development of models for evaluating vibration effects and for subsequent use in monitoring and diagnostic systems requires the use of modern methods of nonlinear analysis, discrete mathematics, as well as tools for the development of expert systems and artificial intelligence technologies. The purpose of the article is to obtain the results of the analysis of a complex mathematical model of spatial interactions, the development of algorithmic support and a description of the structure of a software package for assessing the impact of vibration effects of vehicles on urban infrastructure. A model of spatial interactions is proposed to assess the levels of vibration exposure with the construction of a graph of the placement of objects connected by vibration propagation channels and using the mathematical apparatus of modeling hybrid dynamic systems, expert knowledge and fuzzy rules of logical inference. Examples of constructing a model of spatial interactions taking into account three objects of vibrational observation are considered. The VibCalcAlg algorithm has been developed to calculate the states of a three-component model. The structure of the VibCalc software package is described, which includes a block of fuzzy logic, a block of model construction and a block of visualization. The results can be used in solving mathematical modeling problems related to the assessment and prediction of vibration impacts in the field of transport and civil engineering, as well as in solving environmental protection problems. The results are aimed at improving intelligent monitoring systems and decision support systems in the design, construction and operation of transport facilities.

Research on pattern dynamics of a class of predator-prey model with interval biological coefficients for capture

&lt;abstract&gt;&lt;p&gt;Due to factors such as climate change, natural disasters, and deforestation, most measurement processes and initial data may have errors. Therefore, models with imprecise parameters are more realistic. This paper constructed a new predator-prey model with an interval biological coefficient by using the interval number as the model parameter. First, the stability of the solution of the fractional order model without a diffusion term and the Hopf bifurcation of the fractional order $ \alpha $ were analyzed theoretically. Then, taking the diffusion coefficient of prey as the key parameter, the Turing stability at the equilibrium point was discussed. The amplitude equation near the threshold of the Turing instability was given by using the weak nonlinear analysis method, and different mode selections were classified by using the amplitude equation. Finally, we numerically proved that the dispersal rate of the prey population suppressed the spatiotemporal chaos of the model.&lt;/p&gt;&lt;/abstract&gt;

The Effect of Optimism on Psychological Distress in Student Victims of Body Shaming

Students who are victims of body shaming can experience psychological distress, namely symptoms of depression and anxiety. So it is important to maintain psychological well-being through an optimistic mindset. The aim of this research is to find out whether there is an influence of optimism on psychological distress in students who are victims of body shaming. Sampling used an accidental sampling technique with a total of 120 respondents who were Makassar State University students who were victims of body shaming. Hypothesis testing was carried out using non-linear regression analysis methods with exponential models. The results of this research hypothesis test show that there is a negative and very significant influence between optimism and psychological distress (r=-0.628; p=0.000). The contribution of optimism to psychological distress among Makassar State University students who are victims of body shaming is 39.5%. Other findings in this research show that the three aspects of optimism, namely permanence, pervasiveness and personalization, have a negative correlation with the two aspects of psychological distress, namely depression and anxiety. The conclusion in this research is that optimism has an influence on psychological distress in students who are victims of body shaming. The higher the optimism possessed by students who experience body shaming, the lower the level of psychological distress.

Physical fitness and motor competence performance characteristics of Chinese elite youth athletes from four track and field throwing disciplines-a cross-sectional study.

Purpose: For systematic athletic training and targeted talent development, it is essential to know the physical fitness and motor competencies of top athletes in detail. However, it can be difficult to identify differences in performance requirements and thus to provide adequate support, especially for sports that at first glance appear to have similar demands-such as track and field throwing disciplines. Therefore, the aim of the study was to examine the physical fitness and motor competence of top athletes from different throwing disciplines and to check whether the athletes' performance parameters match the specific requirements of the respective sport. Methods: The study involved 289 male youth athletes (aged 14-18years) across four distinct throwing disciplines: shot put (n = 101), hammer throw (n = 16), discus throw (n = 63), and javelin throw (n = 109). The performance evaluation comprised three anthropometric measurements and twelve motor performance prerequisites applicable to the throwing disciplines. Discriminant analysis and neural networks (Multilayer Perceptron) were implemented to determine the possibility of distinguishing among athletes from the four sports. Results: The study's findings indicate that in male throwing athletes, disparities in general physical fitness and motor proficiency assessments discern the majority of talented young athletes based on their specific sport (discriminant analysis: 68.2%; multilayer perceptron analysis: 72.2%). This remains applicable irrespective of the classification method employed. Discus throwers possessed a height advantage, while shot putters and hammer throwers exhibited superior arm strength. Javelin throwers displayed better explosive strength and sprinting speed. Except for the hammer throwers, all events demonstrated a high level of explosive power in the medicine ball forward or backward throw test, which was especially crucial for shot put and discus athletes. Conclusion: The significance of physical fitness and motor competence tests in identifying and transferring talented athletes in track and field throwing disciplines has been affirmed. Using linear and non-linear classification methods, most athletes could be assigned to their correct sport. However, this also shows that slightly different training and talent identification is required for each of these sports. Furthermore, non-linear analysis methods can provide useful support for the development processes in junior competitive sports.