Nonlinear Behavior Research Articles

Theoretical investigation of threshold pressure gradient in hydrate-bearing clayey-silty sediments under combined stress and local thermal stimulation conditions

Due to the characteristics of smaller grain size and higher clay mineral content, the threshold pressure gradient (TPG) exists in multi-phase flow within hydrate-bearing clayey-silty sediments (HBCSS), which significantly affects the gas production from hydrate reservoirs. However, multi-phase flow through HBCSS relates to thermal-hydrological-mechanical coupling, leading to the understanding of TPG in HBCSS with complex pore structures and hydrate distribution is unclear. In this study, a theoretical TPG model of HBCSS is developed by considering the combined influences of effective stress, temperature increase, pore structures, hydrate saturation and its growth patterns. The proposed TPG model has been thoroughly validated using available experimental data. Moreover, the parameter sensitivity analysis is conducted based on this derived model, revealing a positive correlation between TPG and both effective stress and temperature increase. While TPG generally increases with higher hydrate saturation when other parameters are held constant, the relationship between TPG and hydrate saturation is non-monotonic. This observation suggests that TPG is impacted not only by hydrate saturation but also by other factors, including hydrate growth patterns and pore structures. The findings of this study establish a theoretical foundation for characterizing the nonlinear flow behavior during hydrate exploitation.

Online motion accuracy compensation of industrial servomechanisms using machine learning approaches

This paper addresses the crucial aspect of position error modeling and compensation in industrial servomechanisms with the aim to achieve accurate control and high-performance operation in industrial robots and automated production systems. The inherent complexity and nonlinear behavior of these modules, usually consisting of a servomotor and a speed reducer, often challenge traditional analytical modeling approaches. In response, the study extensively explores the design and implementation of Machine Learning (ML) algorithms to obtain a comprehensive model of the Transmission Error (TE) in rotating vector reducers, which is a main source of robot motion accuracy errors. The ML models are trained with experimental data obtained from a special purpose test rig, where the reducer is tested under different combinations of input speed, applied load and oil temperature. In the second part of the work, the resulting predictive model, tailored to capture the intricate dynamics of the analyzed reducer, is imported into a programmable logic controller to enable online compensation strategies during the execution of custom motion profiles. Experimental tests are conducted using two distinct motion profiles: one generated with a cycloidal law, typical of industrial machinery, and the other extrapolated from the joints of an industrial robot during a pick-and-place task. The results demonstrate the effectiveness of the proposed approach, enabling accurate prediction and substantial reductions (over 90%) in the overall reducer TE through the implemented predictive model.

Remarkable enhancement of the nonlinear optical behavior towards asymmetric substituted D-π-A dithiophene-based compounds.

Nonlinear optics (NLO) is an interesting field that discloses the interaction between intense light and matter, leading to a deeper understanding of NLO phenomena. Organic chromophores are considered as promising materials for NLO due to their exceptional structural versatility, ease of processing, and rapid response to NLO effects. Functional materials based on thiophene have been indispensable in advancing organic optoelectronics. Specifically, dithiophene-based compounds display weaker aromaticity, reduced steric hindrance, and additional sulfur-sulfur interactions. Hence, by utilizing dithieno[2,3-d:2',3'-d']benzo[1,2-b:4,5-b']dithiophene (DTBDT) as the core structure, designing of a set of organic compounds with D1-π-D2-π-A-type framework, namely ZR1D1-ZR1D8, was carried out in this study. The analysis of frontier molecular orbitals (FMOs) revealed that compound ZR1D2 has the lowest band gap of 1.922eV among all the investigated chromophores. The correlation of global reactivity parameters (GRPs) with the band gap values indicates that ZR1D2 displays a hardness of 0.961eV and a softness of 0.520eV-1. Among the studied compounds, ZR1D2 demonstrated a broad absorption spectrum that extended across the visible region. The maximum absorption wavelengths were observed at 766.470nm for ZR1D2 and 749.783nm for ZR1D5. These DTBDT-based dyes exhibit a remarkable NLO response with exceptionally high first hyperpolarizability (βtot) values. Among them, compound ZR1D2 stands out with the highest average linear polarizability (⟨α⟩ = 3.0 × 10-22 esu), first hyperpolarizability (βtot = 4.1 × 10-27 esu), and second hyperpolarizability (γtot = 7.5 × 10-32 esu) values. In summary, this investigation offers valuable insights into the potential use of DTBDT-based organic chromophores, particularly ZR1D2, for advanced applications in NLO. These findings suggest promising opportunities for researchers to synthesize these molecules and utilize these compounds in hi-tech NLO-based applications. The density functional theory computations were performed at the M06/6-311G(d,p) functional to explore their structural effects on electronic and NLO findings. Various analyses like highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps, absorption maxima, density of states, open circuit voltage, binding energies of electrons and holes, and transition density matrix are employed to investigate photovoltaic efficiencies of the derivatives. Different software packages like Avogadro, Multiwfn, Origin, GaussSum, PyMOlyze, and Chemcraft were used to deduce conclusions from the output files.

On measuring climate risks using attention search and testing the clean energy-climate hypothesis

ABSTRACT We measure physical and regulatory climate risks as innovations in several attention to climate change indexes that we construct using search volume data in Google Trends. The intention is to use the constructed risk indexes to test the empirical validity of the clean energy-climate hypothesis, which posits that clean energy prices fall (rise) following a drop (rise) in attention to climate risks. We test the empirical validity of this hypothesis at the macro (market level) using regime switching models and at the micro (firm level) using time-series regressions across clean energy sub-sectors. The macro analysis reveals that our hypothesis is only valid for climate pledges and physical climate risks. When attention to climate pledges drops or when physical climate risks are low, investors become reluctant to hold clean energy assets and vice-versa. Climate policy and climate solution risks have no impact on the nonlinear dynamic behaviour of clean energy prices. These results mean that investors and the public believe that climate policies lack credibility and climate solutions are not effective. The firm-level analysis confirms the findings of the macro analysis and reveals the heterogeneity of climate risks across clean energy sub-sectors.

A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

Viscoelastic flows play an important role in numerous engineering fields, and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids. However, traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time, and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids. In this paper, a universal multiscale method coupling an improved smoothed particle hydrodynamics (SPH) and multiscale universal interface (MUI) library is presented for viscoelastic flows. The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain. We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows. In the first example, the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions. The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain. In the second example, the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics (DPD) method. The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain. Moreover, transferring different physical quantities has an important effect on the numerical results.

A comprehensive unsteady RANS numerical investigation to unveil the influence of wave steepness on the motion dynamics and added resistance of a ship in waves

In this study, we investigate the influence of wave steepness on both ship motions and added resistance in regular head waves by conducting simulations at three distinct wave steepness levels using unsteady RANS method. Numerical results show that, when wavelength comparable to the ship length, the interaction of body nonlinearity and wave nonlinearity results in highly nonlinear behavior in the time history of added resistance. The study illustrates, step-by-step, the hydrodynamic pressure distribution on the hull during an encounter period, highlighting the time-varying nature of the added resistance. Examining the visualised results, it is observed that in certain instances, high pressure may be exerted on the flat bottom of the trimmed ship and contribute significantly to the added resistance. It is observed that, when wavelength is comparable to ship length, the added resistance coefficient decreases with increasing wave steepness. Specifically, at λ/LPP = 1.15, |CAW,H/λ=1/30−CAW,H/λ=1/60|CAW,H/λ=1/60 = 27.1%. In relatively short waves the diffraction phenomena dominate and the resulting added resistance exhibits limited nonlinearity. However, obtaining stable results in such cases proves challenging. Finally, the influence of wave steepness on added resistance is quantified. The results are useful for improving the transparent methods for predicting the added resistance in wave.

Nonlinear behavior of existing pre-tensioned concrete beams: Experimental study and finite element modeling with the constitutive Serial-Parallel rule of mixtures

The performance of existing prestressed concrete (PC) beams and their time-dependent behavior have been concerns for bridge maintenance services. In this paper, laboratory tests of three PC void slab beams taken away from an obsolete bridge were conducted and an alternative more efficient finite element (FE) method was developed. In preparing the three beam specimens, two retained their original reinforced concrete (RC) overlay and one chiseled off its RC overlay. Through the four-point loading tests, the load response plots of the beams from elastic to plastic failure were carefully documented, including the strains along the mid-span section, the strains of longitudinal rebars and strands, and the mid-span deflection. The test results showed that no interface slip was observed between the RC overlay and the top of void slab during the whole loading process, and the yield load of the test beams with the overlay was approximately 45 % higher than that without the overlay. Regarding the proposed nonlinear numerical formulation, the modelling process avoided the treatment of complex reinforcement and prestressing tendon layouts. The prestressed concrete was simulated as a composite material whose behavior is depicted by a constitutive serial-parallel rule of mixtures (SP-RoM). The generalized Maxwell model and generalized Kelvin model were applied to calculate the time-dependent losses of prestress. All the developments have been implemented within the open-source FE code Kratos-Multiphysics environment and are fully available. Compared with the test outcomes, it shows that the numerical results are in good agreement with the solutions in terms of stiffness, load-deflection curves, and damage evolution. The differences between the experimental and numerical values of ultimate load for the specimens with and without RC overlay were all within 10 %. Furthermore, the proposed nonlinear models can also predict the time-dependent prestress losses of existing PC beams.

The modified Swift constitutive model of 304L stainless steel at the cryogenic temperature based on the Olson–Cohen model

The nonlinear behavior of austenitic stainless steel (ASS) is significantly affected by the temperature and strain during plastic deformation. However, the conventional constitutive model is often inadequate to accurately describe its mechanical properties, particularly at cryogenic temperatures. Therefore, the development of a constitutive model for ASS at cryogenic temperatures is of paramount importance in order to fully understanding the performance of liquefied natural gas (LNG) membrane tank structures under such conditions. In this study, we have derived a modified constitutive model using 304L stainless steel that incorporates a phase transition model through theoretical derivations. First, the stress and strain data for 304L stainless steel within the range of 108–293 K have obtained from quasi-static tensile experiments. Subsequently, the XRD test results are utilized to calculate the volume fraction of martensite across various temperatures and strains. Next, a modified constitutive model is proposed by combining the Olson–Cohen phase transition model and the Swift constitutive model. Finally, the accuracy of the modified Swift constitutive model is verified through experimental data. The results demonstrate that the modified Swift constitutive model is precise for characterizing the properties of 304L stainless steel across a wide range of temperatures. Furthermore, multiple case studies have proven the feasibility of using the modified Swift constitutive model to predict the properties of various austenitic materials. By incorporating the Olson-Cohen phase transition model, the modified Swift constitutive model showcases its wide applicability and potential in designing and assessing the safety of ASS structures.

Nonlinear dynamic analysis of high-speed precision grinding considering multi-effect coupling

The aerostatic spindle is widely used in the field of precision grinding because of its excellent machining stability and machining accuracy. The spindle is jointly affected by multiple excitation effects in the high-speed grinding process. In order to study the dynamic characteristics of the aerostatic spindle under high-speed precision machining, it is necessary to analyse the nonlinear response of the aerostatic spindle with multi-physical field coupling. In this paper, the nonlinear dynamic model of the aerostatic spindle system under multi-effect coupling is established by considering three aspects: fluid-structure coupling, mass eccentricity excitation coupling, and vibration-grinding force coupling. Firstly, the instantaneous nonlinear air film force excitation is calculated by the derivation of the dynamic air film thickness model with multi-degree-of-freedom vibration responses coupling. The mass eccentricity excitation considering dynamic deflection angle is derived through the eccentric-load relationship. Afterwards, the dynamic precision grinding force model under the full surface of the tool is established based on judging the material removal mode, which considers the grain-workpiece interaction relationship under the influence of the nonlinear vibration. Finally, the accuracy and effectiveness of the coupled model is verified by high-speed precision grinding experiments, and the nonlinear dynamic behaviour under different operating parameters is analysed.

Emergence of chaos in an electroactive artificial muscle PVC gel under state-varying electromechanical parameters

The deformation mechanism of artificial muscle materials based on the natural method has always been one of the frontier topics in the field of biophysics. Electroactive PVC gel is a composite material that mimics the response of natural muscles, making it highly advantageous for various bionic mechanical applications. The existing literature primarily focuses on enhancing the performance and exploring applications of PVC gel, with particular emphasis on optimizing its ability to simulate muscle deformation. However, the existing literature lacks research on the theoretical mechanism and modeling of large deformation, particularly regarding the investigation of nonlinear dynamic behavior under state-varying electromechanical parameters. The present research establishes a novel theoretical model for PVC gel and investigates its dynamic response to voltage, mechanical force, and inertia force. Firstly, the electromechanical constitutive model of PVC gel actuator was elucidated, and the nonlinear dynamics control equation of PVC gel actuator was established based on the Gent model. Secondly, we investigate the vibration characteristics of PVC gel material by analyzing four key parameters: size, tensile strength, applied voltage amplitude, and excitation frequency. Through this analysis, we determine the relevant parameters and operational range of the PVC gel actuator when subjected to voltage excitation. Meanwhile, the phase trajectories and Poincaré maps were generated based on the control equation calculation results to investigate the vibration stability and chaotic characteristics of the PVC gel actuator under electromechanical coupling conditions. The deformation of PVC gel is influenced by various nonlinear factors, wherein the alteration in frequency induces harmonic, subharmonic, and super-harmonic resonance phenomena within the frequency response. By revising the size, voltage, and frequency of these three factors, with particular emphasis on regulating the frequency, chaotic behavior in the PVC gel will be facilitated. Finally, the bifurcation analysis of the electromechanical vibration behavior of the PVC gel actuator was carried out, and the stability of the PVC gel vibration was further quantitatively determined by the Lyapunov exponent.

Second harmonic generation and reverse saturable absorption in electrospun picric Acid-PMMA nanofibers

Picric acid (PA) – polymethyl methacrylate (PMMA) nanofibers were synthesised using electrospinning technique by optimising all the required parameters. The nonlinear optical behaviour of the synthesised nanofibers was investigated along with their preliminary characterisations like morphological, structural, thermal, mechanical, dielectric and linear optical studies. The nanofibers with average diameter around ∼800 nm, were found to crystallise in Pca21 space group under the orthorhombic crystal system. The incorporation of Picric acid nanocrystals inside the PMMA nanofibers enhanced their tensile strength. Second harmonic generation imaging of picric acid embedded PMMA nanofibers was done by nonlinear microscopy and the emission was confirmed by power dependence as well as Kurtz – Perry powder technique. Nonlinear absorption studies by Z – scan technique were conducted with a Q – switched Nd: YAG laser and the nanofibers exhibited reverse saturable absorption nature at all the input intensities (0.616 × 1012 W/m2, 1.23 × 1012 W/m2 and 2.46 × 1012 W/m2) and the value of the nonlinear absorption coefficient increased corresponding to an increase in input intensity (0.98 × 10−10 m/W, 1.39 × 10−10 m/W and 1.61 × 10−10 m/W) owing to a sequential two photon absorption. Using the transmittance data optical limiting properties of the nanofibers were also analysed and the limiting threshold values (1.92 × 1012 W/m2, 1.80 × 1012 W/m2 and 1.54 × 1012 W/m2) at respective intensities were extracted. The low optical limiting threshold obtained in the present case confirms that picric acid – PMMA nanofibers can be an assured contender as optical limiters in laser safety devices.

Nacelle optimisation through multi-fidelity neural networks

PurposeAerodynamic shape optimisation is a complex problem usually governed by transonic non-linear aerodynamics, a high dimensional design space and high computational cost. Consequently, the use of a numerical simulation approach can become prohibitive for some applications. This paper aims to propose a computationally efficient multi-fidelity method for the optimisation of two-dimensional axisymmetric aero-engine nacelles.Design/methodology/approachThe nacelle optimisation approach combines a gradient-free algorithm with a multi-fidelity surrogate model. Machine learning based on artificial neural networks (ANN) is used as the modelling technique because of its ability to handle non-linear behaviour. The multi-fidelity method combines Reynolds-averaged Navier Stokes and Euler CFD calculations as high- and low-fidelity, respectively.FindingsRatios of low- and high-fidelity training samples to degrees of freedom of nLF/nDOFs = 50 and nHF/nDOFs = 12.5 provided a surrogate model with a root mean squared error less than 5% and a similar convergence to the optimal design space when compared with the equivalent CFD-in-the-loop optimisation. Similar nacelle geometries and aerodynamic flow topologies were obtained for down-selected designs with a reduction of 92% in the computational cost. This highlights the potential benefits of this multi-fidelity approach for aerodynamic optimisation within a preliminary design stage.Originality/valueThe application of a multi-fidelity technique based on ANN to the aerodynamic shape optimisation problem of isolated nacelles is the key novelty of this work. The multi-fidelity aspect of the method advances current practices based on single-fidelity surrogate models and offers further reductions in computational cost to meet industrial design timescales. Additionally, guidelines in terms of low- and high-fidelity sample sizes relative to the number of design variables have been established.

Development of enhanced force models to analyze the nonlinear hysteresis response of miniaturized pneumatic artificial muscles

Miniaturized pneumatic artificial muscles (MPAMs), designed to replicate natural muscle actuation, offer unique attributes such as a high power-to-weight ratio, flexibility, easy integration, and compactness, making them favourable for many applications. The present paper aims at the development of an accurate semi-analytical force model considering the effect of the bladder material and friction terms to predict the nonlinear force-deformation response of MPAMs during contraction and expansion cycles. Existing force models for MPAMs exhibit limitations to accurately capturing the force-deformation behaviours due to several simplification factors. This study enhances these models by integrating correction terms to accurately address the nonlinearity and frictional effects exhibited by MPAMs. An analysis of the hysteresis loops resulting from the cyclic loading and unloading of MPAMs under specific pressures is undertaken to compare different methodologies in order to determine the most accurate correction terms. To investigate the nonlinear behaviour of MPAMs, the stress-strain relationship of the bladder material and results from force-deformation experimental tests on the entire actuator are considered and for the effect of friction term, theoretical and empirical approaches are investigated. Results suggest that the theoretical force model based on analytical and empirical friction forces, respectively, slightly overestimates and underestimates the force experienced by MPAMs during contraction while slightly underestimate and overestimates during expansion, respectively. A comparative analysis between MPAMs featuring Ecoflex-50 silicone and Ecoflex30 + PDMS mixture as bladder materials has also been conducted to further investigate the effect of bladder materials on their force and contraction outputs under inlet pressures ranging from 0 kPa to 300 kPa. It is shown that the MPAM feauting Ecoflex-50 bladder, exhibits lower dead-band pressure and an overall reduced blocked force in comparison to MPAM with bladder made of Ecoflex30 + PDMS while exhibiting a substantially enhanced free contraction capacity.

Destroying Phantom Jams with Connectivity and Automation: Nonlinear Dynamics and Control of Mixed Traffic

Connected automated vehicles (CAVs) have the potential to improve the efficiency of vehicular traffic. In this paper, we discuss how CAVs can positively impact the dynamic behavior of mixed traffic systems on highways through the lens of nonlinear dynamics theory. First, we show that human-driven traffic exhibits a bistability phenomenon, in which the same drivers can both drive smoothly or cause congestion, depending on perturbations like a braking of an individual driver. As such, bistability can lead to unexpected phantom traffic jams, which are undesired. By analyzing the corresponding nonlinear dynamical model, we explain the mechanism of bistability and identify which human driver parameters may cause it. Second, we study mixed traffic that includes both human drivers and CAVs, and we analyze how CAVs affect the nonlinear dynamic behavior. We show that a large-enough penetration of CAVs in the traffic flow can eliminate bistability, and we identify the controller parameters of CAVs that are able to do so. Ultimately, this helps to achieve stable and smooth mobility on highways. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: This work was supported by the University of Michigan’s Center for Connected and Automated Transportation [U.S. DOT Grant 69A3551747105]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0498 .

Dynamic stability of a nitinol Langevin ultrasonic transducer under power and current tracking conditions

The Langevin transducer is widely used in medical and industrial ultrasonics, typically comprising a piezoelectric ceramic stack preloaded between two end-masses. A principal operational challenge is that, depending on the target application or operational environment, piezoelectric ceramics commonly experience elevated temperatures promoting nonlinear dynamic behaviours, often reducing operational performance. Transducers can be operated via burst excitation to mitigate this, but such methods can have limited efficacy, particularly at elevated temperatures. A novel emergent approach is the incorporation of shape memory Nitinol into the transducer, where its temperature-dependent microstructural phase transformations can compensate for changes in the mechanical properties of the piezoelectric ceramics. However, the ability to maintain dynamic stability under power and current tracking, common methods used to ensure stability of Langevin transducers in practical applications, remains unknown. In this research, a cascaded Nitinol Langevin transducer is used to demonstrate its practical application potential. Dynamic stability is assessed whilst power and current levels are tracked in operation. Stable operating frequency, electrical impedance, and vibration amplitude are shown, using a combination of methods including electrical impedance analysis and laser Doppler vibrometry. This research demonstrates the practical application of Langevin transducers incorporating shape memory materials, including with dynamic stability at elevated temperatures.

Enhancing the Range and Reliability of the Spacer Layer Imaging Method

The spacer layer imaging method (SLIM) is widely used to measure the thickness of additive and lubricant films, in lubricant development and evaluation, and for fundamental research into elastohydrodynamic lubrication and tribofilm formation mechanisms. The film thickness measurement, as implemented on several popular tribometers, provides powerful, non-destructive in-situ mapping of film topography with nanometre-scale height sensitivity. However, the results can be highly sensitive to experimental procedure, machine condition, and image analysis, in some cases reporting unphysical film thickness trends. The prevailing image analysis techniques make it challenging to interrogate these errors, often hiding their multivariate nonlinear behaviour from the user by spatial averaging. Herein, several common ‘silent errors’ in the SLIM measurement, including colour matching to incorrect fringe orders, and colour drift due to the optical properties of the system or film itself, are discussed, with examples. A robust suite of novel a priori and a posteriori methods to address these issues, and to improve the accuracy and reliability of the measurement, are also presented, including a novel, computationally inexpensive circle-finding algorithm for automated image processing. In combination, these methods allow reliable mapping of films up to at least 800 nm in thickness, representing a significant milestone for the utility of SLIM applied to elastohydrodynamic contact.Graphical abstract

Modified lap shear test for intralaminar shear failure of fiber reinforced composites

This work presents a modification of the lap shear test for application to the intralaminar shear failure of fiber reinforced composites. The proposed method involves an S-shaped double-cracked specimen loaded under uniaxial in-plane compression. The resulting loading is akin to a lap shear test but inducing intralaminar shear failure (not interlaminar). Elastic stress analysis confirms a shear dominated stress state in specimen ligament, and numerical contour-integral confirms a mode II dominance in the near tip region. Experimental results for an epoxy/carbon twill woven composite are presented, demonstrating the ease of the test method. Nonlinear quasi-ductile behavior is observed, as expected, and necessitates the use of elastoplastic fracture mechanics to interpret the fracture toughness. The estimated initiation toughness values are successfully verified via cohesive crack simulations. The presented test represents a simple and repeatable method to characterize the intralaminar shear failure of fiber-reinforced composites.

Investigating the bending and buckling behaviors of composite porous beams reinforced with carbon nanotubes and graphene platelets using a TRPIM path following mesh-free approach

The aim of the present work consists in investigating the nonlinear behavior of porous beams reinforced with graphene platelets (GPL) and supported carbon nanotubes (CNT), termed functionally graded graphene platelets reinforced composite beam (FG-GPLRC) and functionally graded nanotube carbon reinforced composite beam (FG-CNTRC), respectively. Notably, the distribution of GPL/CNT is explored in both uniform and non-uniform patterns across the beam's thickness. What sets this research apart is its utilization of a refined beam model as enhanced FSDT incorporating nonlinear shear terms which is a crucial advancement in accurately capturing the post-buckling response in certain boundary conditions, a feature lacking in the existing FSDT literature. Innovatively, the post-buckling load-deflection relationship is derived through the solution of governing equations incorporating cubic nonlinearity. This is achieved by employing Galerkin's method alongside a non-iterative high-order continuation technique based on the asymptotic numerical method coupled with the Tchebychev-radial point interpolation method (TRPIM), using a path-following where the solutions are obtained branch-by-branch by eliminating the need for iterative processes. In essence, this research underscores the pivotal role of porosity and GPL/CNT reinforcement in shaping the post-buckling configuration of both perfect and imperfect nanocomposite beams, thereby advancing our understanding of structural behavior in porous nanocomposite materials. The findings of this study illuminate the significant influence of parameters such as porosity coefficient, porosity distribution, GPL/CNT distribution, and GPL-weight/CNT-volume fraction on the nonlinear buckling behavior of porous beams.

Simulation and parameterization of nonlinear elastic behavior of cables

AbstractThis work contributes to the simulation, modeling, and characterization of nonlinear elastic bending behavior within the framework of geometrically nonlinear rod models. These models often assume a linear constitutive bending behavior, which is not sufficient for some complex flexible slender structures. In general, nonlinear elastic behavior often coexists with inelastic behavior. In this work, we incorporate the inelastic deformation into the rod model using reference curvatures. We present an algorithmic approach for simulating the nonlinear elastic bending behavior, which is based on the theory of Cosserat rods, where the static equilibrium is calculated by minimizing the linear elastic energy. For this algorithmic approach, in each iteration the static equilibrium is obtained by minimizing the potential energy with locally constant algorithmic bending stiffness values. These constants are updated according to the given nonlinear elastic constitutive law until the state of the rod converges. To determine the nonlinear elastic constitutive bending behavior of the flexible slender structures (such as cables) from the measured values, we formulate an inverse problem. By solving it we aim to determine a curvature-dependent bending stiffness characteristic and the reference curvatures using the given measured values. We first provide examples using virtual bending measurements, followed by the application of bending measurements on real cables. Solving the inverse problem yields physically plausible results.

Numerical Procedure for Solving the Nonlinear Behaviour of a Spherical Absorber

The aim of the paper is to perform numerical simulations for a system of nonlinear differential equations that describe the behaviour of a spherical absorber placed in a support bowl and to describe the applied techniques. The motion of the sphere is constrained to a plane problem. The derived system of equations is numerically solved using the continuation method and the modified secant method. The absorber's response to different harmonic excitation forces is simulated to demonstrate the applicability of these techniques in its analysis. The dependence of the response amplitude on the angular frequency of excitation is presented graphically. The results also include a response stability analysis using the Routh-Hurwitz criteria.