Nonlinear Analysis Research Articles

Development and characterization of kaolin-based PVA/alginate polymer composite (KPA) for removal of uranium and strontium from aqueous solutions

The present study used low-cost, abundant, and nontoxic kaolin and kaolin-based PVA/alginate composite (KPA) as adsorbents to remove U(VI) and Sr(II) ions from aqueous solutions. The characterization of the adsorbents was performed by several techniques. The results showed that PVA/alginate enhanced the functional groups and changed the surface morphology. Adsorption isotherm parameters were determined through both linear and non-linear regression analyses, from which it was inferred that the Langmuir model provides a better fit than other ones. The uranium removal capacity of KPA significantly improved as compared to that of kaolin, reaching 104.17 mg/g under the conditions of 30 min, pH 4.0, 298 K, and a solid-to-liquid ratio of 1.2 g/L. The strontium removal capacity of kaolin was significantly high as compared to that of KPA, reaching 68.96 mg/g under the optimum conditions. Removal of the radionuclides on both adsorbents was better described by the pseudo-second-order kinetic model, showing the ions to be immobilized on the adsorbents through chemical adsorption. Kaolin was not affected by interfering metals for U(VI) and Sr(II) adsorption, but KPA composite was influenced by the other metals. The adsorbents display potential as candidates to remove uranium and strontium from wastewater.

Nonlinear Finite Element analysis of concrete corbels with hybrid reinforcements

This study utilizes nonlinear finite element analysis to simulate the structural response of Reinforced Concrete (RC) corbels with hybrid reinforcements under monotonic loading. The models implemented in ABAQUS examine RC corbels with combined Carbon Fiber Reinforced Polymer (CFRP) and steel reinforcing bars to study the interaction between the concrete and hybrid reinforcement system. Specifically Ultimate load capacity, energy absorption and failure mode. Compressive strength, shear span/depth ratio, and the ratio of CFRP/steel reinforcement were the main parameters that considered in this paper. Results demonstrated a significant improvement in the ultimate load capacity of concrete corbels by up to 53% when both conventional steel and CFRP bars were integrated within the concrete corbel. The numerical test outcomes revealed that an increased hybrid reinforcement ratio effectively managed crack distribution, resulting in reduced concrete crack widths.

Study on buckling characteristics of PC/PET spherical-cylindrical combined pressure cabin

The buckling characteristics of PC/PET spherical–cylindrical combined pressure cabins under uniform external pressure were studied via experimental and numerical methods. The material properties of the PC/PET plastic alloy were tested. Six spherical–cylindrical combined pressure cabins with different structures were designed and fabricated, and the thickness and geometry of each model were measured. The hydrostatic pressure experiment was carried out on all the pressure cabins, and the ultimate load of the pressure cabin was recorded. Linear buckling analysis and nonlinear buckling analysis of PC/PET spherical–cylindrical combined pressure cabins were carried out, and the numerical and experimental results were found to be consistent. Moreover, the effects of the spherical shell radius and the thicknesses of different combinations on the buckling load were studied.

Traumatic and Adverse Childhood Experiences and Developmental Differences in Psychiatric Risk

While adverse childhood experiences (ACEs) are known to impart significant risk for negative mental health and cognitive outcomes in youth, translation of ACE scores into clinical intervention is limited by poor specificity in predicting negative outcomes. This work expands on the ACE framework using a data-driven approach to identify 8 different forms of traumatic and adverse childhood experiences (TRACEs) and reveal their differential associations with psychiatric risk and cognition across development. Building upon the traditional ACEs model, this study aimed to characterize unique components of commonly co-occurring TRACEs and to examine moderation of longitudinal change in mental health and cognitive development during adolescence. This work draws from youth and their caregivers who completed up to 4 annual behavioral assessments from 2016 to 2021 as part of the ongoing Adolescent Brain Cognitive Development (ABCD) study. Data collection was performed at 21 regionally-distributed sites across the United States. Analyses for this work were conducted January 2023 through November 2023. Youth participants in the ABCD study's exposure to 268 different TRACEs, which were distilled into adversity components using nonlinear principal components analysis. Mixed-effects and latent change score models considered TRACEs components as moderators of longitudinal change in internalizing and externalizing mental health problems, as well as longitudinal change in cognitive ability. Data were distilled from 11 876 youth participants, who were grouped into dyads with a caregiver. ABCD study youth participants were 9 to 10 years old at baseline assessment (year 0) and 12 to 13 years old at ABCD year 3. A total of 5679 participants (47.8%) were female. Analyses revealed that TRACEs organized into 8 thematic adversity components (e.g., family conflict, interpersonal violence). At baseline assessment (year 0), exposure to nearly every adversity component was associated with poorer mental health and diminished cognitive ability. Yet across time, it was observed that different forms of adversity were variably linked to both increases and decreases in internalizing and externalizing problems. For example, while peer aggression (t = 5.31) and family conflict (t = 5.67) were associated with increases in both internalizing and externalizing problems over early adolescence, community threat (t = 2.82) and poverty (t = 2.07) were linked to decreased problems, potentially representing adaptive suppression of symptoms. Finally, adversity types related to resource deprivation (eg, poverty, caregiver maladjustment) were associated with declines in cognitive ability over early adolescence. In this cohort study, distinct forms of TRACEs differentially moderated developmental changes in psychiatric risk and cognitive ability in different ways, offering the possibility for precision-based prediction of risk for youth. Such findings could be used in targeted early prevention and intervention strategies for at-risk youth.

Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames

In eccentrically braced frames (EBFs), inelastic behavior is only permitted in the links. All members, except for the links, are designed according to the capacity design concept by using the link overstrength factor, Ω, so that they remain elastic even when the links develop their ultimate strength (including the strain-hardening effect). AISC 341 specifies that the Ω factor of link members must be 1.25 for beam and brace design and 1.1 for column design. In this study, the relevance of the current Ω factor was investigated. A total of 471 K-braced EBF systems with various conditions were designed using a multi-objective optimization technique, and nonlinear dynamic analyses were performed to evaluate the Ω factor. The results indicate that it is reasonable to use the current Ω factor for the design of beam outside link and brace; however, it leads to an overestimation of axial force in columns, especially in the lower stories of tall buildings. From the analysis results, a new Ω factor equation for column design was proposed. It was demonstrated that the structural quantities of 15-story frames designed using the proposed equation decreased by an average of 19% compared to those designed using the current Ω factor.

The Influence of the Convergence of Digital and Green Technologies on Regional Total Factor Productivity: Evidence from 30 Provinces in China

This paper explores the development of digital and green collaboration, empirically examining both the linear and nonlinear impacts of the convergence of digital and green technologies on regional total factor productivity (TFP). Using data from 30 provinces and cities in China from 2010 to 2022, the study constructs a panel threshold model with business environment and intellectual property protection as threshold variables to investigate their roles in mediating the effects of digital–green technology convergence on regional TFP. The key findings are as follows: (1) The linear analysis reveals that the convergence of digital and green technologies significantly enhances regional TFP. (2) The nonlinear analysis demonstrates a nonlinear relationship between the convergence of these technologies and regional TFP. (3) The threshold effect test identifies a single-threshold effect for the business environment, showing that once the threshold is surpassed, the positive influence of the convergence of digital and green technologies on TFP increases. Additionally, a double-threshold effect is found with intellectual property protection; as intellectual property protection surpasses the first and second thresholds, the positive impact initially strengthens but then weakens. (4) A heterogeneity analysis shows that the convergence of digital and green technologies significantly contributes to TFP in the eastern regions, while the effects in central and western regions are not significant.

Existence of Solutions for a Perturbed N-Laplacian Boundary Value Problem with Critical Growth

In this paper, we investigate a perturbed elliptic boundary value problem that exhibits critical growth characterized by a Trudinger–Moser-type inequality. Our primary focus is to establish the existence of two nontrivial solutions. This is achieved by employing a combination of the Trudinger–Moser-type inequality and a linking theorem based on the Z2-cohomological index. The main feature and novelty of this paper lies in extending the equation to N-Laplacian boundary value problems utilizing the aforementioned methods. This extension not only broadens the applicability of these techniques but also enriches the research outcomes in the field of nonlinear analysis.

Target‐drift seismic‐force‐based design of one‐story reinforced concrete precast buildings considering the requirements of the second generation of the Eurocode 8 standard

AbstractResults are presented concerning the force‐based design of a wide range of reinforced concrete, single‐story precast buildings, considering the requirements of the new Eurocode 8 standard. The relevant criterion defining the cross‐sectional dimensions of the columns was the 2% drift limitation. Buildings were designed considering a behavior factor of 3 and a 50% reduction in stiffness corresponding to the gross cross‐section. The design evaluation, using a nonlinear pushover analysis, revealed that all the buildings could expect approximately twice the drift considered in the design with significant second‐order effects, particularly in very tall columns. The main reasons for large discrepancies between the elastic and nonlinear analyses were the arbitrarily selected behavior factor and the arbitrarily selected reduction in stiffness corresponding to the gross cross‐section (the stiffness considered in the design was approximately double what the nonlinear analysis revealed). The analysis revealed that these two quantities are closely correlated. Once the dimensions of the columns had been selected, the force and initial stiffness reduction could not be chosen arbitrarily. Correlations were determined between the column dimensions, theoretical stiffness reduction, seismic force reduction (behavior factor) and second‐order effects. From these correlations, a new target‐drift force‐based design methodology was proposed. All considered buildings were redesigned using the proposed method. The results of the new design and the nonlinear‐pushover‐based analysis correlated well.

Special Issue: Nonlinear Analysis and Its Applications in Symmetry II

Nonlinear analysis has been a rapidly growing area of research [...]

Nonlinear finite analysis on the behavior of mono and hybrid fiber out-of-plane beams reinforced with GFRP bars

Nonlinear finite analysis on the behavior of mono and hybrid fiber out-of-plane beams reinforced with GFRP bars

Transverse compressive behavior of plain and polypropylene fiber-reinforced concrete infilled steel tubes as hybrid steel-concrete nodes for discrete reticulated shell structures

This study investigates using concrete infilled steel tubes as hybrid nodes for discrete reticulated shell structures under compressive loading transverse to the tube axis. Three configurations were tested: empty, plain concrete infilled and polypropylene fiber-reinforced concrete infilled steel tubes. Displacement-controlled loading was applied through welded steel plates. Simplified beam theory models and nonlinear finite element analysis were used to evaluate the structural behavior. The concrete infilled steel tube specimens had higher stiffness and load-bearing capacity than the empty ones. The structural behavior of the concrete infilled specimens could be split into pre- and post-split-tensile cracking phases. No significant difference was found between the plain and fiber-reinforced concrete specimens under loads up to 1500 kN, which was the load limit of the testing machine. An additional fiber-reinforced concrete specimen, tested on a higher capacity machine, had a load-bearing capacity of 2400 kN and exhibited ductile failure.

A novel optimization‐based modal pushover analysis procedure for estimating the response of structures

AbstractIn recent years, studies have focused on the seismic behavior of various structural systems, including single‐ and double‐layered spatial structures. While nonlinear dynamic analyses are common for these studies, they are time‐consuming and complex. To address this, many pushover procedures have been developed, but their effectiveness in spatial structures remains underexplored. This study introduces an optimized lateral loading profile for evaluating the seismic response of walled bilayer spatial structures. By combining dominant inertial forces and optimizing their corresponding coefficients with the particle swarm optimization (PSO) algorithm, an optimal loading profile is derived. The method's accuracy was tested on models with varying arch height‐to‐span ratios and a constant wall height‐to‐span ratio, as well as a 15‐story frame structure. The results obtained showed that the proposed method closely matches incremental dynamic analyses (IDAs) in predicting base shear, initial stiffness, and displacements, especially for higher arch height‐to‐span ratios. Additionally, the method accurately estimates drift profiles and nodal displacements on roofs and walls, and performs better than similar mode‐based methods for frame structures.

Influence of masonry infills on seismic performance of BRB‐retrofitted low‐ductile RC frames

AbstractReinforced concrete (RC) frames with masonry infills represent a prevalent construction typology across the globe, including moderate to high seismic regions. Such structures are often characterized by high seismic vulnerability, and consequently, there is an urgent need for retrofit solutions to effectively improve their seismic performance. Buckling‐restrained braces (BRBs) represent one such solution. They are a type of dissipative device that can be included within the frames of an existing structure to increase its strength, stiffness, and energy dissipation capacity. Although a substantial amount of research has already been performed to understand the effectiveness of BRBs as a retrofit strategy, these studies have often neglected the contribution of masonry infills and the interactions between the infills and the BRBs. While masonry infills are usually overlooked in the analysis and design stage (owing to their brittle nature), past studies indicated that their strength and stiffness may significantly alter the structure's seismic performance, leading to undesirable and unexpected results. This study presents a detailed investigation of the impact of masonry infills on the seismic response and fragility of BRB‐retrofitted RC frames. A three‐story, three‐bay, low‐ductile RC frame has been selected for case study purposes. High‐fidelity finite element models are developed in OpenSees for combinations of infilled and non‐infilled structures—with and without BRBs. Nonlinear static and dynamic analyses are performed to evaluate the seismic response of the different configurations at local and global levels. Successively, cloud analyses are conducted by considering a set of 150 ground motion records to account for the record‐to‐record variability and develop seismic fragility curves. The present study sheds some light on the mutual interaction between the infill panels and BRBs retrofit intervention and highlights the critical aspects that must be considered in the design.

Seismic design of steel moment‐resisting knee‐braced frame system by failure mode control

AbstractThis paper presents the seismic design of a steel moment‐resisting knee‐braced frame (MKF) using the theory of plastic mechanism control (TPMC) within the capacity‐based design framework. The MKF is an alternative system to MRFs, wherein knee elements are utilized to provide rigid connections and enhance lateral stiffness. Capacity‐based design, the predominant approach in current seismic provisions, relies on two key principles: (1) selecting specific structural components as fuses with sufficient ductility to dissipate seismic energy, and (2) ensuring non‐fuse elements can resist the maximum probable reactions from these fuses. The ultimate goal is to achieve a global mechanism where yielding occurs in all structural fuses and at the base of first‐story columns. However, existing seismic design provisions often struggle to fully satisfy the second principle due to the lack of a method for controlling failure modes. TPMC addresses this challenge by ensuring compliance with the second principle, grounding its approach in the kinematic method and the mechanism equilibrium curve within the rigid‐plastic analysis framework. By considering all potential story‐based undesirable mechanisms and calculating the required plastic moment of columns up to a target design displacement, TPMC ensures adherence to the second principle of the capacity‐based design approach, leading to the achievement of a global collapse mechanism. In this paper, an iterative method is proposed for designing beams and knee elements by considering plastic hinges at both ends of the beams, followed by a TPMC‐based methodology for designing columns to ensure a global mechanism. A parametric analysis of a single‐story single‐span MKF explores the effects of knee element geometry ( and ) on component demands. The results indicate that optimal parameter ranges of and can minimize the demands for MKF components. Practical design examples are illustrated using three steel MKFs, each consisting of four, seven, and ten stories with five spans. Pushover analysis and nonlinear dynamic analyses were performed to demonstrate the effectiveness of the proposed design procedure in ensuring the attainment of a global mechanism and excellent seismic performance under real ground motions.

Nonlinear Frequency Response Analysis of Distributed Parameter Systems with One Spatial Coordinate

AbstractThe objective of this paper is to investigate possible strategies for applying nonlinear frequency response (NFR) analysis based on the concept of higher‐order frequency response functions to distributed parameter systems. Three approaches are presented and compared: one based on applying the existing procedure directly to the partial differential model, and two based on approximation of the distributed parameter system with a series of lumped parameter segments. One of them treats the complete series of segments integrally, while the other treats it segment by segment, so it uses only the model of a single segment. A simple example, an isothermal plug‐flow reactor with a simple reaction mechanism, is used as a case study. Pros and cons for all three approaches are given.

A novel high-Q Lamé mode bulk acoustic resonator

This study introduces a novel high-Q Lamé mode MEMS resonator, optimized through support beam structures and etching hole distributions to minimize anchor losses and thermal elastic dissipation (TED). Fabricated using a Silicon-On-Insulator (SOI) process, the resonators achieved Q values of 129,200 and 102,100 in different designs, demonstrating significant improvements in vacuum conditions and highlighting air damping as a key loss mechanism. Nonlinear analysis revealed material nonlinearity dominance. These findings offer valuable guidelines for developing high-end MEMS devices, such as low phase noise oscillators and high-resolution sensors, by showcasing substantial reductions in energy dissipation and enhanced Q factors through structural optimizations.

Enhanced Multi‐Objective Optimization Model for Bridge Performance Assessment and Prediction, Based on Improved PCA, K‐Means Clustering, and Kaplan–Meier Survival Algorithm

ABSTRACTThe research proposes a hybrid algorithm model that combines model‐driven and data‐driven approaches for the direct application of bridge health monitoring technology in bridge management. This comprehensive study encompasses a series of analytical techniques and methodologies to build a multi‐objective optimization model for bridge performance assessment and prediction. It focuses on the processing of multi‐source heterogeneous data, selection of key sub‐parameters using Principal Component Analysis (PCA), enhanced K‐means clustering analysis, determination of structural component target thresholds, time‐dependent survival probability analysis, regression fitting, and timing prediction of the bridge system for both the components of double‐layer truss arch bridge and the bridge system. The initial phase of the study concentrates on the diversification and decentralization of monitored data from various sources, integrating and cleaning data obtained from different sources to ensure data quality and consistency. PCA technique is applied to identify key sub‐parameters that have significant impacts on the performance of structural components. Enhanced K‐means clustering analysis is carried out to effectively group and classify the identified key sub‐parameters. Numerical simulations, including structural nonlinear analysis, are conducted to determine the target thresholds of bridge structure, providing important benchmarks for performance evaluation. Finally, a multi‐parameter regression model is used to evaluate and update the performance of the bridge structure, taking into account survival probability (using the Kaplan–Meier method), maintenance history, and material deterioration to estimate the most critical time for the bridge system. A case study is conducted to validate the suggested comprehensive algorithms for a double‐layer truss arch combination bridge, which contributes to enhancing performance evaluation and predicting the most critical time for structural components and bridge system in the bridge management and maintenance practices. It should not be ignored that, the accuracy and reasonability of bridge structure system performance evaluation and prediction depend largely on the selection of target thresholds.

Rapid Urban-Scale Building Collapse Assessment Based on Nonlinear Dynamic Analysis and Earthquake Observations

Rapid damage assessment after an earthquake is crucial for allocating and prioritizing emergency actions. Building damage due to an earthquake depends on the seismic hazard and the building’s strength. While it is now possible to promptly access acceleration data as seismic input through online strong motion networks in urban areas, good models are necessary to evaluate the damage in different zones of the affected area. This study aims to present a rapid method for such an urban-scale building collapse evaluation by conducting a nonlinear dynamic analysis of modeled buildings. Based on the Nagato and Kawase model, this study estimates the yield shear strength of 3-story steel buildings, 3-story reinforced concrete buildings, and 1-story masonry buildings in Sarpol-e-Zahab City after the 2017 Mw7.3 earthquake. The damage ratio is calculated through nonlinear dynamic analyses using estimated records from the main earthquake shock in different city zones. The research found that the seismic yield shear strength of steel and reinforced concrete buildings might be weaker than that of the Iranian seismic code’s standard value. Conversely, masonry-building resistance is stronger than the guidelines assumed. The constructed numerical models can be used for the rapid building damage assessment immediately after a damaging earthquake.

Association of initial serum sodium change and clinical outcome in patients with diabetes receiving sodium-glucose cotransporter-2 inhibitor therapy: A multicentre database analysis in Taiwan.

The study aimed to assess the impact of varying degrees of initial serum sodium change among patients with type 2 diabetes (T2D) starting sodium-glucose cotransporter-2 inhibitor (SGLT2i) therapy and their subsequent clinical outcome. We used medical data from a multicentre health care provider in Taiwan and recruited 4400 patients with T2D with baseline normal serum sodium (135-145 mmol/L) and follow-up serum sodium measures available after 3 months of SGLT2i treatment from 1 June 2016 to 31 December 2021. After a median of 2.9 (2.4, 3.4) months of SGLT2i treatment, overall, there was a minimal change in serum sodium levels (from 139.6 ± 2.4 to 139.5 ± 3.7 mmol/L). Most patients (87.8%) maintained normal sodium levels, while 8.6% (n = 378) experienced hyponatraemia (<135 mmol/L) and 3.6% (n = 158) hypernatraemia (>145 mmol/L). Factors independently associated with hyponatraemia included cancer history, chronic lung disease, insulin use, higher glycated haemoglobin, impaired liver function, lower baseline sodium and greater initial decline in kidney function. Conversely, factors linked to hypernatraemia included older age, absence of cancer history, loop diuretic and non-steroidal anti-inflammatory drug use, higher baseline sodium and a lesser initial decline in kidney function. Over a median of 26.0 months of follow-up, hyponatraemia shortly after starting SGLT2i therapy was associated with significantly increased risks of major adverse cardiovascular events [hazard ratio (HR): 2.52; 95% confidence interval (CI): 1.83-3.48], heart failure for hospitalization (HR: 1.66; 95% CI: 1.16-2.37), major adverse renal events (HR: 2.27; 95% CI: 1.73-2.96) and all-cause death (HR: 2.98; 95% CI: 2.17-4.11) after adjusting for clinically relevant factors. Non-linear analysis indicated that a more pronounced initial decline in serum sodium levels correlated steeply with higher risks of these adverse events. While most patients with T2D maintain stable serum sodium homeostasis on SGLT2i therapy, a subset may experience dysnatraemic events with potential worse clinical consequences. Physicians should be vigilant about monitoring sodium levels and considering the associated risks when initiating SGLT2i therapy in patients with risk.

Optimizing pectin lyase production using the one-factor-at-a-time method and response surface methodology.

Pectinases are commonly industrially synthesized by molds. This study aimed to optimize pectin lyase synthesis by a bacterium, Pseudomonas fluorescens, using both the one-factor-at-a-time (OFAT) method and response surface methodology. First, on optimization of pectin lyase fermentation by the OFAT method, the effects of pectin, peptone, yeast extract, (NH4)2SO4, pH, and salts were investigated. The highest pectin lyase activity was determined to be 28.63U/mL at pH 8, 30°C, with 1% (w/v) pectin and 0.14% (w/v) (NH4)2SO4 concentration at the 90th hour. The effect of substrate inhibition on the microbial growth was also investigated, and the results showed that the process can be described by noncompetitive inhibition model. The values of kinetic constants were determined as µm=0.175h-1, KS=6.931g/L, and, KI=6.932g/L by nonlinear regression analysis. It was reported that pectin lyase enzymes exhibited peak activity at 50°C and pH 8. Finally, response surface methodology (RSM) was utilized to optimize pH, concentrations of ammonium sulfate, and pectin, which were chosen as independent variables. The interactions between these variables were also examined. According to RSM, the optimum values of the parameters to achieve a maximum pectin lyase activity of 35.62U/mL were determined to be pH 7.97, 1.25% (w/v) pectin concentration, and 0.25% (w/v) (NH4)2SO4 concentration.