Nonlinear Behavior Research Articles

Weakly nonlinear analysis of rotating magnetoconvection with anisotropic thermal diffusivity effect

The influence of anisotropic thermal diffusive coefficient on the stability of the horizontal fluid planar layer rotating about its vertical axis and permeated by the horizontal homogeneous magnetic field is studied. The linear stability analysis is carried out using the normal mode method. The stationary cross/oblique and parallel modes are calculated for different ranges of control parameters arising in the system. The SA (Stratification Anisotropy) parameter, α (the ratio of horizontal and vertical thermal diffusivities), plays a key role in deciding the boundaries between these modes and their instability regions when there is a combination of high and low rotation with weak and strong magnetic fields. The obtained isotropic results coincide with those obtained by pioneers in the literature. The weakly nonlinear behavior of the stationary convective motion in the vicinity of primary instability threshold is studied using the two-dimensional Landau–Ginzburg (LG) equation with cubic nonlinearity. This equation derived using the multiple scale analysis is similar to the one obtained in the literature having different relaxation time, nonlinear coefficient, and coherence lengths. These coefficients are used to study the heat transfer rate. In the case of high rotation, Nusselt number gets decreased from atmospheric (α < 1) to oceanic (α > 1) SA types. The domain for secondary instability of Eckhaus is obtained using the spatiotemporal LG equation and it is observed that the Eckhaus instability region decreases with increasing α.

Geometrically nonlinear analysis of plates and shells by a cell-based smoothed CS-MITC18+ flat shell element with drilling degrees of freedom

A development of a 3-node triangular flat shell element to analyze geometric nonlinearity of plate and shell structures is presented in this study. The proposed flat shell element has 6 degrees of freedom per node, including the drilling rotational ones, by using the Allman-type approximations for the in-plane displacements and the bending displacement approximations enriched by a cubic shape function at the bubble node located at the element's centroid. The geometrically nonlinear behaviors are described by the von Karman's large deflection assumption. The membrane and bending strains of the presented flat shell elements are averaged over sub-triangular elements based on the cell-based smoothed (CS) technique. To attenuate the shear locking phenomenon, the transverse shear strains are re-interpolated following the mixed interpolation of tensorial components (MITC) technique designed for the 3-node triangular degenerated shell elements enriched by a cubic bubble function (MITC3+). Combined with the Newton-Raphson iterations and load increments predicted by the arc-length method, the suggested 3-node triangular flat shell elements, namely the CS-MITC18+ element, can analyze moderately geometrical nonlinearity, including the snap-thought and snap-back behaviors, of various plates and shells with the different shapes, thickness, and boundaries. The numerical investigations show that the load-displacement curves provided by the CS-MITC18+ flat shell elements well agree with other references.

Optimal intensity measure for seismic performance assessment of shield tunnels in liquefiable and non-liquefiable soils

Relating the ground motion intensity measure (IM) and the structural engineering demand parameter is a crucial step in the performance-based earthquake engineering framework. This study investigates the selection of IM for development of probabilistic seismic demand model of urban shield tunnels subjected to earthquake ground motions in liquefiable and non-liquefiable soils. Nonlinear dynamic effective stress analyses are conducted to develop a database of the intensity measures and structural seismic responses exposed to ground shaking and soil liquefaction. Two advanced soil constitutive models (i.e., Pressure DependMultiYield03 and PressureIndependMultiYield for liquefiable and non-liquefiable soils, respectively) are employed to capture the nonlinear behavior. A suite of 23ground motion intensity measures is selected and assessed based on the evaluation criteria of correlation, efficiency, practicality and proficiency. Eventually, the multi-level fuzzy comprehensive evaluation method is employed to comprehensively consider the four evaluation criteria and establish the optimal ground motion IM suitable for probabilistic seismic demand analysis of shield tunnel structures. The obtained results show that the sustained maximum acceleration is the optimal IM for evaluating the structural seismic response, followed by the peak ground acceleration in both liquefiable and non-liquefiable soils. Peak pseudo velocity spectrum, displacement square integral and Housner spectral intensity are found to be not suitable for the probabilistic seismic demand analysis of shield tunnel structures.

Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems.

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.

Multiscale modeling of friction hysteresis at bolted joint interfaces

Friction at connection interfaces plays an important role in understanding the nonlinear vibration response of jointed structures. A reliable friction contact model capable of reproducing nonlinear behaviors at the friction interface is critical in the design and optimization of jointed structures. In this paper, a multiscale friction model is proposed. This approach provides a novel perspective for improving prediction accuracy by combining the predictability offered by a physics-based model and the convenience of a phenomenological model. Specifically, this method considers the actual topography of joint interfaces by measuring the three-dimensional (3D) topography data with high-resolution instruments. The surface topography data is then processed to obtain the geometry data at different scales, and the finite element method is used to determine the physics-based multiscale contact pressure distribution of surfaces. The twofold Weibull mixture model is used to represent the contact pressure distribution and further determine the Iwan density function. The effectiveness of the proposed approach is validated by comparing the model predictions with the experiment results of a new as-built structure. Moreover, the effects of the surface roughness and waviness on the friction behavior are discussed.

Numerical Simulation of the Behaviour of RC T-Beams Strengthened by EB-CFRP Composites Under Bending and Shear Effects

This article presents the results of numerical simulations performed using ABAQUS/CAE version 2019. The study aims to evaluate the structural integrity of reinforced concrete (RC) T-beams strengthened with externally bonded carbon fiber reinforcements polymer composite materials (EB) (CFRP), especially their response to bending and shear forces. The numerical model was validated by comparing the numerical and experimental results of eight RC T-beams. The numerical analysis was then extended to include various factors, including the impact of the tilt angle of the U-CFRP shell on the shear strength. The goal of this numerical extension is to implement a numerical model capable of simulating the nonlinear behavior of these beams accurately. A comparative analysis is also performed on the experimental and computational models, focusing on the damage modes and their load-induced deformation characteristics. The results showed a satisfactory level of agreement between the two sides. The average ratio of ultimate load to deflection in the numerical model simulation and experimental beam test is 1.004 and 1.046, respectively. The main finding is that inclined U-CFRP deformed at a 45° angle exhibits greater shear stiffness than beams embedded with vertical CFRP panels at a 90° angle, maintaining a constant CFRP panel spacing.

Thermal vibration analysis of bi-directionally stepped porous functionally graded plates with segment-specific material property variation supported by Kerr foundation

This paper presents a comprehensive analysis of the nonlinear dynamic response of stepped rectangular plates made of functionally graded porous material (FGPM), supported by the Kerr foundation, in a thermal environment. A novel analytical framework is developed to explore geometric and material variations. The study investigates structural variations in plate thickness with abrupt changes in uni- or bi-directional orientations, examining both single and double stepped thickness profiles. Material properties vary with thickness, featuring distinct horizontal discontinuities across plate segments. Porosity distributions, both even and uneven, are addressed using modified mixture rules. Nonlinear kinematic relationships are established using Reddy’s third-order shear deformation plate theory and von Kármán’s nonlinear geometric assumptions, with equations of motion solved via Galerkin’s technique. This improved model effectively addresses non-continuous thickness variation through integral calculus, enhancing computational efficiency. Validation is achieved by comparing outcomes with published literature and Finite Element Analysis (FEA). The study investigates the influence of material properties, elastic foundation, boundary conditions, and geometric parameters on the free vibration and nonlinear behaviors of the plates. Some of the key findings include: increasing the thickness of the stepped segment significantly heightens the fundamental frequency while reducing vibrational amplitudes; optimizing the location of the stepped segment directly impacts the plate’s fundamental frequency and vibrational amplitudes; and as the load factor increases, the difference between linear and nonlinear deflection becomes evident. Therefore, accurate FGPM stepped plate design requires incorporating nonlinear terms in the strain–displacement relationships. Suggestions for future model modifications are also discussed, contributing to advancements in structural design and analysis.

Harvesting vibration energy by quad-stable piezoelectric cantilever beam: Modeling, fabrication and testing

The combination of beams with piezoelectric patches has become a prevalent energy harvesting tool due to its ease of use. Typical energy harvesting systems are usually linear, and their efficiency is not satisfying due to low-frequency bandwidth. In this paper, a quad-stable piezoelectric vibration energy harvester is analyzed both numerically and experimentally. The primary purpose of this investigation is to analyze the static and dynamic characteristics of a proposed quad-stable system to consider its potential for application in broadband energy harvesting comprehensively. The harvester system consists of a slotted cantilever beam, a piezoelectric patch, a pair of tip-mass blocks, and a double-sided clip. The cantilever beam is subjected to pre-displacement constraints made by a mutual self-constraint at the free end of it. The nonlinear behaviors of the harvester system, including snap-through and softening phenomena, are analyzed using the assumed modes and finite element method (FEM). The harvester’s vibration equation is solved numerically and through an FE model which is made by an in-house finite element software. A prototype is designed and fabricated to validate the mathematical model and FE simulation. The experimental force-displacement diagram of the harvester displays distinct discontinuities, reflecting abrupt transitions occurring while switching its stable states. The prototype dynamics are analyzed by harmonic base excitation with different amplitude levels in two conditions, including the presence and absence of the piezoelectric patch. The results obtained from the mathematical and FEM model demonstrate a satisfactory correlation with the experimental data. Furthermore, the experimental data reveal the occurrence of the snap-through phenomenon, accompanied by a significant widening of the frequency bandwidth at relatively high amplitude levels. The system has the ability to provide an average output electrical power of 0.288 mW for an electrical resistance of 3.262 kΩ at the excitation frequency of 12.695 Hz and base acceleration amplitude of 3g.

Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems.

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.

Nonlinear dynamics of planetary roller screw mechanism.

The synchronous meshing of the gear pair and the screw pair is a typical feature of the planetary roller screw mechanism. In order to fully derive and analyze the nonlinear dynamic characteristics of the system, this paper creatively incorporates the time-varying meshing stiffness of gear pair and the comprehensive transmission error into the research content. Combined with the thread contact force and friction force between the roller and the screw and between the roller and the nut, the nonlinear dynamic model of the planetary roller screw mechanism considering the meshing excitation of the gear pair is established. According to the time domain diagram, frequency domain diagram, phase plane diagram, Poincaré section diagram, three-dimensional spectrum diagram, and spatial phase diagram, the nonlinear behavior of the system is described in detail, and the bifurcation evolution process of the system under the excitation frequency parameters of the external load is revealed. In addition, based on the theory of multi-scale method and considering the variables such as meshing stiffness, meshing damping, and load fluctuation, the stability equation of the primary resonance of the system is derived. The analysis of the stability of the system under different working conditions shows that the parameters are selected within a reasonable range, which effectively reduces the primary common amplitude value and enhances the overall stability of the system. The research content improves the previous system dynamics modeling method and provides a theoretical basis for the nonlinear dynamics modeling method and parameter optimization design of the planetary roller screw mechanism.

Numerical Simulation of the Behaviour of RC T-Beams Strengthened by EB-CFRP Composites Under Bending and Shear Effects

This article presents the results of numerical simulations performed using ABAQUS/CAE version 2019. The study aims to evaluate the structural integrity of reinforced concrete (RC) T-beams strengthened with externally bonded carbon fiber reinforcements polymer composite materials (EB) (CFRP), especially their response to bending and shear forces. The numerical model was validated by comparing the numerical and experimental results of eight RC T-beams. The numerical analysis was then extended to include various factors, including the impact of the tilt angle of the U-CFRP shell on the shear strength. The goal of this numerical extension is to implement a numerical model capable of simulating the nonlinear behavior of these beams accurately. A comparative analysis is also performed on the experimental and computational models, focusing on the damage modes and their load-induced deformation characteristics. The results showed a satisfactory level of agreement between the two sides. The average ratio of ultimate load to deflection in the numerical model simulation and experimental beam test is 1.004 and 1.046, respectively. The main finding is that inclined U-CFRP deformed at a 45° angle exhibits greater shear stiffness than beams embedded with vertical CFRP panels at a 90° angle, maintaining a constant CFRP panel spacing.

Analyzing dynamic patterns of information flow between bitcoin and economic uncertainty in light of public sentiments: A statistical behavior approach

Modeling and analyzing interrelationships within the Bitcoin market, as a prominent cryptocurrency, leads to understanding hidden structures, effective management and informed decision-making. Regarding this matter, numerous studies have analyzed the time-varying spillover patterns in this ecosystem. Although spillover network analysis can elucidate the nature and strength of correlations, it may not be adept at handling the conditional interdependencies within intricate non-linear and dynamic essential behaviors of financial time series. This research tries to address the mentioned challenges by presenting a novel analytical model to investigate the dynamic communication patterns among Bitcoin, United States Economic Policy Uncertainty (US EPU) and public sentiments. Following this objective, rather than directly exploring the effect of original data series on each other, the approach decomposes them into sequences of meaningful statistical behaviors, at different lag-lead horizons. Subsequently, considering the significance of conditional dependencies, we extract and analyze the rules and patterns of information flow among the observed behaviors. The findings not only unveil a distinct flow pattern compared to the spillover network, but also offer valuable insights into dynamic interactions and dominant behaviors under various scenarios. One observation suggests that as the historical range of predictors increases in predicting future changes, their effectiveness or reliability decreases, while their number simultaneously increases. Moreover, the trend slope of Bitcoin functions as a notable behavior in propagating information, directly influencing both economic uncertainty and investor sentiment. The proposed model enhances the understanding of interaction between financial time series and provides useful perspectives for analysis and risk management.

HE EFFECT OF LOADS SUPERPOSITION ON TECHNICAL STRUCTURES, ENVIRONMENT AND LIVING ORGANISMS

The current state of calculation the result of the superposition of loads, or their effects, on a material body is analyzed. The limits of the current calculation methods, based on strength theories, in the case of technical structures are shown. The results of experimental research that refer, in general, to the superposition of two loads of the same nature and without addressing problems of loads of a different nature (mechanical, chemical, electrical, magnetic, radioactive etc.), in the case of technical structures and the environment is analyzed. Starting from the principle of critical energy, which is based on the concepts of the total specific energies’ participation of the loads and of the critical participation, general relations are deduced for these concepts, in the case of the nonlinear behavior of matter, as a function of power. These results are applied to the calculation of the superposition of loads of different nature on a technical structure, the environment and living organisms, taking into account the deterioration of matter. The influence of the loading speed (static, shock ...) is taken into account based on the value of the exponent in the behavior law, which was not possible in the previous calculation methods. From the analysis of the results obtained in the paper, it is found the utility and the high degree of generality of the principle of critical energy and of the concept of the specific energy participation.

Semiparametric regression models under skew scale mixtures of normal distributions

Semiparametric models (SM) are an important tool in modeling environmental data where generally a covariate presents an unknown nonlinear behavior. Usually, the error component is assumed to follow a normal distribution. However, in some situations, the response variable is skewed and heavy-tailed. This paper aims to extend the SMs allowing the errors to follow a skew scale mixture of normal distributions, increasing the model’s flexibility. In particular, we develop the EM algorithm for the proposed model, diagnostic analysis via global, local influence, and generalized leverage. A simulation study is also conducted to evaluate the efficiency of the EM algorithm. Finally, a suitable transformation is applied in a data set on ragweed pollen concentration to illustrate the utility of the proposed model.

Assessment of non-linear critical pressure of MWCNT reinforced hybrid sandwich semi-ellipsoidal dome under hydrostatic pressure: A numerical and experimental study

The present study involves the numerical and experimental buckling response of MWCNT reinforced composite sandwich semi-ellipsoidal dome subjected to uniform hydrostatic external pressure. The skin of the composite sandwich dome is made up of MWCNT-GFRP composite layers and the PLA honeycomb core, which is reinforced with and without strips. Various honeycomb core configurations, such as SRHC-1 to SRHC-3, are formulated in such a way that the strips are reinforced between the regular honeycomb core in longitudinal and transverse directions to enhance the stiffness characteristics of the structure. The nonlinear buckling analysis of the MWCNT reinforced composite sandwich dome is formulated and solved through the commercially available software ANSYS®. The geometry and material non-linearity of the MWCNT reinforced sandwich dome structures are incorporated in the numerical model while solving the non-linear differential equations and identifying the critical pressure of the sandwich structures using arc length method. The testings were performed to obtain the various mechanical properties, the non-linear behavior of yield stress with a plastic strain of the MWCNT-reinforced GFRP skin and the transverse shear modulus of the various honeycomb core patterns. The efficiency of the present numerical modeling and buckling analysis is confirmed by comparing the critical pressure obtained through the experimental buckling analysis performed on the MWCNT-reinforced prototype sandwich dome and the results available in the literature. Various parametric studies are performed on the MWCNT-reinforced composite sandwich dome to examine the influence of MWCNT reinforcement on the skin, honeycomb core patterns, stacking sequence of skins, aspect ratio and slenderness of the shells and geometric imperfections on the critical pressure.

Mesh objective characteristic element length for higher-order finite beam elements

The use of fracture energy regularization techniques can effectively mitigate the mesh dependency of numerical solutions caused by the strain softening behavior of quasi-brittle materials. However, the successful regularization depends on the correct estimation of the crack bandwidth in Finite Element solutions. This paper aims to present an enhanced crack band formulation to overcome the strain localization instability especially for the higher-order elements developed in the framework of Carrera Unified Formulation (CUF). Besides, a modified Mazars damage method incorporating fracture energy regularization is employed to describe the nonlinear damage behavior of the concrete. To evaluate the efficiency of the proposed crack band formulation, three experimental concrete benchmarks are selected for the numerical damage analysis. By comparing numerical and experimental results, the proposed method can guarantee mesh objectivity despite varying finite element numbers and orders, indicating perseved fracture energy consumption within proposed higher-order beam models.

Molecular Dynamics Simulation of Cumulative Microscopic Damage in a Thermosetting Polymer under Cyclic Loading.

To develop durable composite materials, it is crucial to elucidate the correlation between nanoscale damage in thermosetting resins and the degradation of their mechanical properties. This study aims to investigate this correlation by performing cyclic loading tests on the cross-linked structure of diglycidyl ether bisphenol A (DGEBA) and 4,4'-diaminodiphenyl sulfone (44-DDS) using all-atom molecular dynamics (MD) simulations. To accurately represent the nanoscale damage in MD simulations, a bond dissociation algorithm based on interatomic distance criteria is applied, and three characteristics are used to quantify the microscopic damage: stress-strain curves, entropy generation, and the formation of voids. As a result, the number of covalent bond dissociations increases with both the cyclic loading and its amplitude, resulting in higher entropy generation and void formation, causing the material to exhibit inelastic behavior. Furthermore, our findings indicate the occurrence of a microscopic degradation process in the cross-linked polymer: Initially, covalent bonds align with the direction of the applied load. Subsequently, tensioned covalent bonds sequentially break, resulting in significant void formation. Consequently, the stress-strain curves exhibit nonlinear and inelastic behavior. Although our MD simulations employ straightforward criteria for covalent bond dissociation, they unveil a distinct correlation between the number of bond dissociations and microscale damage. Enhancing the algorithm holds promise for yielding more precise predictions of material degradation processes.

Optimization of structures subjected to earthquake excitation using two-point adaptive approximation with trust region strategy

This study presents a gradient-based method, TPAA-TR, for optimizing structures under earthquake excitation. The method develops an efficient algorithm that can converge quickly to the optimal solution under time history loading. It uses two-point exponential approximation with consistent intermediate variables to construct explicit linear sub-problems, and applies filter method and trust region strategy to solve them. Merit functions and filters are used to balance the trade-off between reducing objectives and satisfying constraints, and promote convergence. The method performs nonlinear response history analysis for seismic analysis to account for the nonlinear behavior of structures. The effectiveness of the proposed method is demonstrated by three numerical examples: a three-story shear frame, a six-story frame installed with nonlinear devices and a nine-story three-dimensional (3D) reinforced concrete (RC) nonlinear building. The results show that the proposed method can achieve optimal solutions with less computational time and fewer function evaluations than existing methods.

Solving nonlinear structural problems by associating line-search and path-following techniques

The demand for computational tools to simulate the nonlinear behavior of structures has intensified. Regarding nonlinear static or dynamic analysis, it is fundamental to use numerical strategies to trace the structure equilibrium paths, overcoming critical points (limit and bifurcations points). The nonlinear solvers must have a high level of efficiency in the two phases of the solution process (predictor and corrector), for each load step. In solving the nonlinear equations, it is quite common that Newton-Raphson's iterations do not converge or require an excessive number of iterations near equilibrium path critical points. Therefore, the line-search optimization technique appears as an additional sophistication. Basically, this technique aims to stagger the corrective displacements vector in the iterative phase, seeking to guarantee and accelerate the convergence of the process. This paper aims to verify the efficiency of the line-search technique coupled with Newton-Raphson iterations and different path-following methods and to verify their influence on the efficiency of the nonlinear solver. The effectiveness of the implemented line-search algorithm is verified by solving two slender structures with accentuated geometric nonlinearity. Such a resource is perceived to be triggered near load limit points (with more success when applied to structures with these critical points), accelerate the iterative process and increase the chances of convergence.

LMI feasibility analysis of 2DOF NATA model

AbstractPresent paper shows the different types of tensor product model based linear matrix inequality controller design and feasibility analysis of two degrees of freedom aeroelastic wing section model. The tensor product models are based on reducing or removing the nonlinear behavior of the system and weighting functions. The linear matrix inequality based method results globally asymptotically stable system. The goal of the paper is to examine that selecting and varying the transformation space influences the feasibility of the linear matrix inequality based controller. The paper gives a comparison between the different tensor product models in terms of controller performance. The linear matrix inequality gives feasible solution for the controller design if the transformation space is selected adequately.