Nonlinear Numerical Simulations Research Articles

Modeling of nonlinear supply chain management with lead-times based on Takagi-Sugeno fuzzy control model

In this study, we present a novel fuzzy control strategy that considers the influence of lead times on nonlinear supply chain management (SCM) systems. The authors have constructed a fuzzy control model for an SCM model based on nonlinear phenomena with lead times, drawing inspiration from Takagi-Sugeno's (T-S) fuzzy control system. Additionally, the authors have designed a fuzzy H∞ control approach to mitigate the effects of lead times, switch between sub-models, and address customers' stochastic requests, all while considering the concept of maximal overlapped rules groups. The control of nonlinear supply chain management is implemented in a manner that ensures asymptotic stability and facilitates smooth transitions from one subsystem to another. The introduction of the membership function into the fuzzy system results in reduced fluctuations in the system's variables. The key contributions of the research include the design of a fuzzyH∞ control approach, leveraging maximal overlapping-rules group (MRRG) to ensure stability through localized definite positive matrices identification. This strategy achieves two primary objectives: asymptotic stability of the supply chain system and smooth switching between nonlinear SCM elements. The authors demonstrate the effectiveness of their proposed method through comprehensive comparisons with the fuzzyH∞ control technique. The study provides a valuable insight into managing lead times in SCM through dynamic and stable control methodologies. Finally, a comprehensive comparison is provided between the suggested H∞ management approach and the fuzzyH∞ control strategy. This comparison is demonstrated through two-stage nonlinear numerical simulations, keeping SCM lead times in mind. Movement results are presented to illustrate the effectiveness of our suggested algorithm.

Development and implementation of shear wall finite element in OpenSees

Shear walls are widely used as lateral load-resisting systems in high-rise building structures. The design and nonlinear analysis of shear walls under seismic loads for recoverability are complicated and challenging, which demands nonlinear computer modeling procedures. This paper presents a novel finite element named Double Vertical Beam-column with Shell Element (DVBSE) for the nonlinear analysis of complex reinforced concrete shear walls with columns. The DVBSE is implemented in the open-source finite element program OpenSees. The theoretical formulations of DVBSE are described in detail. The accuracy of the developed DVBSE is established by comparing the finite element analysis results with existing experimental data on recoverable steel-GFRP composite bar reinforced concrete shear walls. The comparative study demonstrates that the proposed DVBSE is superior to the commonly used finite element model in simulating the responses of recoverable complex shear walls under seismic loads. These research findings contribute to further advancements in the development of new shear wall elements and lay a solid foundation for the nonlinear numerical simulation of innovative shear walls.

An Improved Adaptive Iterative Extended Kalman Filter Based on Variational Bayesian

The presence of unknown heavy-tailed noise can lead to inaccuracies in measurements and processes, resulting in instability in nonlinear systems. Various estimation methods for heavy-tailed noise exist. However, these methods often trade estimation accuracy for algorithm complexity and parameter sensitivity. To tackle this challenge, we introduced an improved variational Bayesian (VB)-based adaptive iterative extended Kalman filter. In this VB framework, the inverse Wishart distributionis used as the prior for the state prediction covariance matrix. The system state and noise parameter posterior distributions are then iteratively updated for adaptive estimation. Furthermore, we make adaptive adjustments to the IEKF filter parameters to enhance sensitivity and filtering accuracy, thus ensuring robust prediction estimation. A two-dimensional target tracking and nonlinear numerical UNGM simulation validated our algorithm. Compared to existing algorithms RKF-ML and GA-VB, our method showed significant improvements in RMSEpos and RMSEvel, with increases of 21.81% and 22.11% respectively, and a 49.04% faster convergence speed. These results highlight the method’s reliability and adaptability.

Reinforced concrete wall buildings with force‐limiting connections: Modeling effects and uncertainty propagation

AbstractThis paper assesses the effects of (1) the gravity load‐resisting system (GLRS) modeling approach, (2) the seismic force‐resisting system (SFRS) modeling approach, and (3) the uncertainty of the model parameters of the constitutive law of the longitudinal reinforcing steel of the SFRS on the seismic responses of a 12‐story reinforced concrete wall building with force‐limiting connections. This is achieved by conducting nonlinear numerical earthquake simulations. The seismic responses of the building models with force‐limiting connections using two GLRS modeling approaches, (1) a moment frame system and (2) a pin‐base lean‐on‐column system, are compared. The seismic responses of the building models with conventional connections and force‐limiting connections, respectively, using two SFRS modeling approaches, (1) a distributed‐plasticity modeling approach and (2) a lumped‐plasticity modeling approach, are compared. A joint probability density function for the ASTM‐A615 Grade 60 steel available in the literature is used to conduct an uncertainty propagation analysis through Monte Carlo simulation. The uncertainty in the steel model parameters is propagated to the seismic responses of the building models with conventional connections and force‐limiting connections, respectively. The distributions of the mean values of the peak structural responses of the building models are studied. The effects of the GLRS modeling approach on the seismic responses are not significant in the context of seismic performance‐based design and assessment of buildings with force‐limiting connections. The effects of the SFRS modeling approach and the uncertainty in the steel model parameters on the floor total acceleration and force responses are reduced by including force‐limiting connections.

Instabilities in Models of Supergiants MWC 137 and MWC 314

In several B-type supergiants, photometric and spectroscopic variabilities together with episodes of enhanced mass-loss have been observed. Here we present the preliminary results of a linear stability analysis followed by nonlinear numerical simulations in two B-type supergiants MWC 137 and MWC 314. All the considered models of MWC 137 having mass in the range of 30M⊙ to 70M⊙ are unstable while for the case of MWC 314 models with mass below 31M⊙ are unstable. The instabilities have been followed into the nonlinear regime for selected models of these two supergiants. During the nonlinear numerical simulations, instabilities lead to a finite pulsation amplitude with a well defined saturation level in the considered models of MWC 137 with mass greater than 42M⊙. The model of MWC 314 with mass of 40M⊙ - the suggested mass for the primary star - does not show any instabilities both in linear stability analysis and nonlinear numerical simulations. The velocity amplitude reaches to 107 cm s−1 in the nonlinear regime for the model of MWC 314 with mass of 30M⊙. Further extensive numerical simulations and observations are required to understand the origin of the observed variabilities in these stars.

Review and analysis of RC bridge half-joints strengthening techniques

In the past, the extensive use of the Gerber scheme in the construction of existing bridges has been justified by the advantages in terms of reduced stresses of the statically determined scheme and rapid execution. On the other hand, the presence of junction elements at the ends of the beams has over time led to a series of issues, especially related to their durability. In fact, the half-joints’ geometric configuration leads to the accumulation of degradation due to platform water seepage, resulting in the initiation of reinforcement corrosion, especially in the presence of chlorides derived from de-icing salts used in the winter season. Furthermore, these elements have been designed for lower loads than those specified in current regulations, and therefore, they may be in critical conditions where the strength reduction, due to existing degradation, can lead to failure. For these reasons, local repairs and/or strengthening interventions are necessary to ensure adequate levels of safety. Within this study, the topic of reinforcing half-joints is addressed, first by describing the currently available intervention techniques in the literature, and then by deepening an intervention technique based on the use of external post-tensioned bars, applied to a case study bridge through nonlinear numerical simulations. These analyses allow quantifying the performance improvements of this technique under both service conditions and ultimate loads, considering various parameters, including the pre-stress value applied to the external tendons and different scenarios of chloride-induced corrosion.

Non-linear orthotropic numerical simulation for monitoring wood embedment tests according to BS EN 383 (2007) Standard European

RESUMO A maioria dos estudos realizados no Brasil sobre o comportamento de conexões em estruturas de madeira é de natureza experimental, com poucos utilizando análises numéricas baseadas no Método dos Elementos Finitos (FEM). Em testes de embutimento, além de determinar os valores experimentais de resistência, é crucial entender os pontos de concentração de estresse para identificar os principais modos de falha. Este estudo teve como objetivo apresentar uma estratégia de modelagem numérica para monitorar o comportamento dos espécimes em testes de embutimento de acordo com a norma BS EN 383: 2007 [1]. Para a simulação numérica, utilizou-se o software ANSYS [2], considerando vários critérios de resistência para os materiais envolvidos. Os modelos incorporaram propriedades elásticas e plásticas dos materiais, obtidas por caracterização experimental em laboratório. Foram realizados testes experimentais de embutimento em espécimes nas direções paralela e perpendicular às fibras, usando pinos metálicos de 6.72 mm de diâmetro para calibração dos resultados numéricos. A estratégia de modelagem numérica proposta permitiu a análise global dos espécimes de teste de embutimento, bem como a investigação de aspectos localizados de interesse, como concentrações de estresse, um fator difícil de quantificar em análises experimentais.

Bifurcation analysis of double cavity flows

The first few bifurcations in a two-dimensional incompressible double cavity flow are investigated using the linear stability analysis, the Floquet analysis, and the nonlinear direct numerical simulations (DNS). The prediction of the critical Reynolds number and the type of bifurcation (Hopf, pitchfork, inverse pitchfork, and Neimark–Sacker), which depend on cavity configuration, by the linear stability analysis and the Floquet analysis is consistent with nonlinear DNS. The nonlinear DNS results show that the state of the system passes through multiple intermediate (unstable) states before it reaches the stable attractor (heteroclinic chain), and the type of intermediate states depends on initial conditions. The intermediate states are reported as the asymptotic state in the literature for some flow conditions because it is not known a priori how long it will take to reach the asymptotic state in nonlinear simulations. The present study reports the actual asymptotic state for those flow conditions.

Comment on “Numerical simulation of magnetohydrodynamic buoyancy-induced flow in a non-isothermally heated square enclosure” [Communications in nonlinear science and numerical simulation, 14(2009) 770-778

This article aims to correct incorrect formulations and clarify inaccurate notations in the above mentioned publication. All results are recreated and compared using the numerical simulation of the corrected model.

Nonlinear numerical simulation of insertion loss for structures having a compressed softened porous layer sandwiched by double walls under acoustic excitation

We perform nonlinear numerical simulation of insertion loss for structures having compressed porous layers sandwiched by double walls under acoustic excitation. The double walls are consisted of a steel base plate and a plastic cover plate. We compare the insertion loss including Urethane foam with felt. These porous layers are compressed by a heavy frame around the cover plate. As increasing weight of the frame, Urethane foam has soft-hardening characteristics in its restoring force. If we set appropriate weight of the frame to get 33% compression, lower rigidity is obtained for Urethane foam. This leads to softer porous layer for the double walls. And vibration and sound decrease from the base plate to the cover plate. For felt, the hardening characteristics appear. This leads to the higher rigidity and the more transmission. In the numerical calculation using LS-Dyna as a nonlinear FEM code, geometric nonlinearity is considered. For compressed porous materials, Storaker model is adopted in consideration of material nonlinearity with hysteresis. Further, under compression, we also investigate the reason of the softening mechanism for the Urethane foam using another model of microscopic structures. We reveal that the softening mechanism is due to geometric nonlinearity by using multiple Kelvin cells.

Tailored Dispersion and Nonlinear Effects in Flint Glass Honeycomb PCF for Optical Communication

This paper describes a highly nonlinear flint glass-based honeycomb photonic crystal fiber (FGH-PCF) with a wavelength of 1550 nm. The PCF’s distinctive honeycomb lattice structure, combined with the nonlinear capabilities of flint glass, enables a wide range of nonlinear optical applications. To adjust the PCF's dispersion and nonlinear effects, numerical simulations and optimization approaches were used. To achieve maximum performance, fabrication procedures were carefully regulated. Dispersion values of −436.6 ps/(nm.km) for x polarization and −448.1 ps/(nm.km) for y polarization were verified by experimental characterization. The PCF displayed low confinement losses of 2.289 dB/cm (x polarization) and 4.935 dB/cm (y polarization), as well as birefringence of 2.202×10-3. The PCF measured 558.8 and 547.9 W-1 km-1 for x and y polarization, respectively, indicating a high nonlinear coefficient. The highly nonlinear FGH-PCF shows promising potential for nonlinear optical applications such as four-wave mixing, supercontinuum generation, frequency conversion, and parametric amplification. This research paves the way for compact and efficient nonlinear devices in modern optical communication systems and other cutting-edge technologies.

Analytical resistance of the laterally offset rectangular hollow sections connections under concentrated force

The study aims to address the lack of design techniques for welded rectangular hollow sections connections made with offset, i.e., where the members of the branch adjacent to the connection are laterally shifted away from the chord centreline towards the chord web. To estimate the plastic resistance of the laterally offset truss-type RHS T-connection, a theoretical investigation was conducted. As a result, an analytical model has been developed and verified against the outcomes of a series of non-linear numerical simulations. During the construction of the model, specific attention was paid to the most general case of the branch location relative to the chord web, namely, the scheme of connection where adjacent vertical faces of the branch and chord members are in different planes is considered as prevailing. The proposed analytical model is an extension of a plastic mechanism model for traditional stepped rectangular hollow sections (RHS) T-connections. The model predicts the yield load and the post-yield response of the connections under concentrated load. The model presented in this paper is compared with other recently proposed methods of analytically determining limit loads of offset connections, and it provides reliable results in yield load computation. Moreover, the model yields sufficient accuracy in predicting the ultimate load for the offset connections with matched faces of the chord web and brace lateral surface.

Ultimate in-plane shear behaviour of clay brick masonry elements strengthened with TRM overlays

This paper studies the response of unreinforced masonry (URM) members made of hydraulic lime mortar and fired clay bricks, commonly found in heritage structures, strengthened with textile reinforced mortar (TRM) overlays. The investigation includes URM and TRM-strengthened diagonal compression tests on square panels, and relatively large-scale wall specimens subjected to combined gravity and lateral cyclic loads. Complementary compression, tension, and interface material tests are also carried out. The diagonal panel tests show that the TRM effectiveness depends in a non-proportional manner on the overlays, render thickness, and substrate strength. The enhancement in stiffness, strength, and ultimate shear strain, using one to four mesh layers on each side, is shown to vary in the range of 49–132%, 102–536%, and 300–556% respectively. It is shown that strut crushing typically governs the response of such low-strength URM masonry elements confined by TRM overlays. The cyclic tests on the comparatively larger walls show that the TRM is effective, shifting the response from URM diagonal tension to rocking, and enhancing the stiffness, strength, and ultimate drift capacity by more than 160%, 30%, and 130%, respectively. It is shown that analytical assessment methods for predicting the response of TRM-strengthened and URM members in terms of stiffness, strength and load-deformation can be reliably adapted. The cumulative contribution of the URM and TRM components, in conjunction with a suitable fibre textile strain, is also found to offer an improved prediction of the shear strength compared to codified procedures. The findings enable the evaluation and improvement of analytical models for determining the main inelastic response parameters of TRM-strengthened masonry and provide information for validating future detailed nonlinear numerical simulations.

Artificial intelligence (AI)-assisted simulation-driven earthquake-resistant design framework: Taking a strong back system as an example

Traditional earthquake-resistant structural design considers only a limited number of factors, mainly elastic structural properties, to determine key design parameters. However, these parameters are often not optimal because they do not take into account the extensive plasticity expected in building structures during earthquakes. To address this issue, an artificial intelligence (AI)-assisted simulation-driven framework has been developed in this study. This framework can automatically output optimal design parameters while considering nonlinear structural response under strong earthquakes and a large number of input factors. The primary innovation of the proposed framework lies in the fusion and integration of nonlinear numerical simulation and AI tools for earthquake-resistant design of building structures, marking a promising trend in this field. The framework consists of two steps. In the first step, a database that consists of optimal design parameters and covers a wide range of design inputs will be created through numerical nonlinear response history analyses (NRHAs). In the second step, AI models will be created and trained based on the database to automatically output the optimal design parameters. To illustrate the basic components underlying the proposed framework, the determination of the height-wise distribution (denoted by Ψ) of the total design lateral force for a strong back system is taken as an example. A database of 1200 samples was created through NRHAs, and an artificial neural network (ANN) model was created, optimised, and trained. The developed ANN model yielded optimal Ψ with the majority of absolute errors within 1%, demonstrating the feasibility of the proposed AI-assisted simulation-driven earthquake-resistant design framework.

PDEM-based seismic performance evaluation of circular tunnels under stochastic earthquake excitation

ABSTRACT Tunnels are a vital component of urban infrastructure that must be robust against seismic hazards. Given the randomness of earthquake occurrence, the seismic response of tunnel structures mut be studied by stochastic analysis methods. To this end, this study proposes a probability density evolution method (PDEM)-based framework to investigate the seismic performance of a circular tunnel under stochastic earthquake excitation. First, a suite of nonstationary earthquake motions compatible with the seismic design code was derived using a stochastic earthquake model. Then, a series of nonlinear dynamic numerical simulations were conducted for a typical circular tunnel that considers the soil-structure interaction. Finally, using the tunnel inclination angle as the performance index, the probability density function of the structural response of the tunnel was solved using the PDEM to obtain the corresponding exceedance probabilities of the tunnel under various damage states. The results show that the PDEM-based framework can be applied to evaluate the seismic performance of circular tunnels and could serve as a reference on the seismic fragility of tunnels and underground structures.

Quantitative stability analysis of complex nonlinear hydraulic turbine regulation system based on accurate calculation

The current stability studies of the hydraulic turbine regulation system (HTRS) mostly adopt the linear hydro-turbine model ignoring its strong nonlinearity, leading to insufficient disclosure of the true characteristics of the HTRS and also causing great inconvenience to the controller parameter tuning. To address this issue, based on the Hopf bifurcation theory, bisection method, and stability criterion, this paper proposes an algorithm (HBBSC) for determining the controller parameter constraint considering the nonlinearity of the hydro-turbine. Firstly, the nonlinear model of the hydro-turbine is constructed based on the model reconstruction strategy (NNGW) combining the backpropagation neural network (BPNN) with the improved grey wolf optimization algorithm (IGWO) to obtain an accurate nonlinear HTRS numerical simulation platform under the power control mode (PCM) and frequency control mode (FCM). Then, the HBBSC-based quantitative calculation procedure of stability region constraint is introduced in detail. Further, in a case study of stability region calculation of HTRS, the HBBSC is applied to calculate the stability region constraint, and the HBBSC-based stability region is verified through a simulation platform. Finally, the stability region of complex HTRS under all operating conditions is calculated based on HBBSC. The results indicate that the HBBSC can replace the traditional methods for stability region calculation during stability analysis of HTRS, outperforming the latter in accuracy and reliability.

Numerical study on steel plate girders ‐ Intermediate transverse stiffeners axial force

AbstractTransverse stiffeners are used in steel plate girders with slender webs to provide lateral support to the web along the span and thus increase the plate girder shear resistance. Furthermore, transverse stiffeners anchor the tension field, resulting in axial compression in the stiffener. Despite this, it is widely assumed that the design axial force provided by the FprEN 1993‐1‐5 [1] for the transverse stiffeners is significantly greater than that observed in experimental testing and numerical simulations.The results of 550 nonlinear numerical simulations of plate girders loaded in shear up to failure are presented. Shear resistance and axial stiffener forces are evaluated while the effects of a wide parameter range as web aspect ratio and thickness, flange‐to‐web area ratio, and steel grade are investigated. The numerical results are compared to the European standard design values. Finally, a statistical analysis of the set of results is presented.The numerical analyses show that the axial forces installed in the intermediate transverse stiffeners are significantly lower than those specified by FprEN 1993‐1‐5 [1].

Towards Tolerance Specifications for the Elastic Buckling Design of Axially Loaded Cylinders

Abstract The quest for safe lower bounds to the elastic buckling of axially loaded circular cylindrical shells has exercised researchers for the past 100 years. Recent work bringing together the capabilities of nonlinear numerical simulation, interpreted within the context of extended linear classical theory, has come close to achieving this goal of defining safe lower bounds. This paper briefly summarizes some of the important predictions emerging from previous work and presents new simulation results that confirm these earlier predictions. In particular, we show that for a specified maximum amplitude of the most sensitive, eigenmode-based geometric imperfections, normalized with respect to the shell thickness, lower bounds to the buckling loads remain constant beyond a well-defined value of the Batdorf parameter. Furthermore, we demonstrate how this convenient means of presenting the imperfection-sensitive buckling loads can be reinterpreted to develop practical design curves which provide safe, but not overly conservative, design loads for monocoque cylinders with a given maximum permitted tolerance of geometric imperfection. Hence, once the allowable manufacturing tolerance is specified during design or is measured post-manufacturing, the greatest expected knockdown factor for a shell of any geometry is defined. With the recent research interest in localized imperfections, we also attempt to reconcile their relation to the more classical, periodic, and eigenmode-based imperfections. Overall, this paper provides analytical and computational arguments that motivate a shift in focus in defect-tolerant design of thin-walled cylinders—away from the knockdown experienced for a specific geometric imperfection and towards the worst possible knockdown expected for a specified manufacturing tolerance.

Robust gain-scheduled missile autopilot design based on multifrequency extended state observers

This paper describes the design and implementation of a three-axis acceleration control autopilot for an asymmetric tail-controlled, skid-to-turn tactical missile. In an earlier flight test, degraded autopilot performance was attributed to multiple disturbances and uncertainties and the presence of hidden coupling terms, giving rise to a miss distance of greater than 20 m. To address these issues, the missile dynamics are decomposed into the angular rate dynamics as fast and the acceleration dynamics as slow subsystem using the singular perturbation theory to analyze a multi-time-scale property. Multifrequency extended state observers are then incorporated into the gain scheduling technique to attenuate disturbances, thus enhancing the control performance significantly. In the proposed engineering/practical design framework for missile autopilot, simple, conventional, and explicit tuning rules are provided. And the proposed control scheme can achieve input-to-state stability across the entire flight envelope under unknown but bounded disturbances. The advantages of the method over existing benchmark approaches are shown through nonlinear numerical simulations. This is supported by evidence from a new flight test result with a miss distance of only 2 m.

A chemotaxis reaction–diffusion model for Multiple Sclerosis with Allee effect

In this paper, we study a modification of the mathematical model describing inflammation and demyelination patterns in the brain caused by Multiple Sclerosis proposed in Lombardo et al. (J Math Biol 75:373–417, 2017). In particular, we hypothesize a minimal amount of macrophages to be able to start and sustain the inflammatory response. Thus, the model function for macrophage activation includes an Allee effect. We investigate the emergence of Turing patterns by combining linearised and weakly nonlinear analysis, bifurcation diagrams and numerical simulations, focusing on the comparison with the previous model.