Present Nonlinear Model Research Articles

Supervised machine learning computing paradigm to measure melting and dissipative effects in entropy induced Darcy–Forchheimer flow with ternary-hybrid nanofluids

This study investigates the change in thermophysical characteristics of Darcy–Forchheimer flow of tri-hybrid nanofluid (THNF) over stretchable porous skin. Machine learning (ML) technique is employed to compare thermal exchange of water-based hybrid nanofluid (HNF), composed of aluminum oxide (Al2O3) and silicon dioxide (SiO2) with THNF by introducing copper oxide (CuO) nanoparticles in HNF. Flow rate profile, dissipation effect, and entropy generation are analyzed with novel, time, and cost-effective evaluation technique. By using similarity parameters, the governing system of partial differential equations (PDEs) is transformed to a system of ordinary differential equations (ODEs). Finite difference method is used for dataset generation by the aid of Python environment, then neural fitting computation technique is utilized for optimized results. Turbulence and randomness are incorporated in the present nonlinear mathematical model which is tackled by artificial intelligence (AI)-based Levenberg Marquardt Neural-Network Algorithms (LMNA), to produce optimized outputs. Velocity, temperature, and entropy profile are evaluated against various influencing factors, such as Forchheimer value, porosity, melting parameter, radiation, Prandtl, Eckert, and Brinkmann coefficient. Numerical and AI-generated outputs and errors graphs with complete neural network training scheme, are portrayed to draw the effective concluding inferences. Enhanced results are beneficial for industrial and engineering production units, for efficient thermal management.

Numerical modeling on wave–current flows and bed shear stresses over an algal reef

AbstractCurrents in coastal zones under multiple mechanisms in terms of tides, waves, wind, and high roughness are difficult to model; bed shear stresses under wave–current flows are particularly challenging yet not being well studied. Few studies reported the modeling and validation of the bed shear stress in reef environments. In this paper, we present the first direct assessment of numerical modeling on depth-averaged currents and bed shear stresses over an algal reef using a coupled wave–current model (Delft-3D). The modeled results were validated and compared to the field observed data. The model considers hydrodynamic forcing in terms of tides, waves, wind stresses, and bed friction. Results show that the model generally reproduces the depth-averaged currents and bed shear stresses when considering all the mechanisms. Two numerical cases with and without wind forcing were tested to examine the effects of the winds. We found that the tide is mostly the primary factor driving the current, even in shallow waters within a depth of 3 m; however, the currents are also significantly affected by wind speeds and wind directions during high-wind events. When the wind direction is in the same direction as the tidal current, the current speed increases, suggesting the importance of the wind stress on the coastal currents. In addition, two models were chosen to study the nonlinear enhancement of bed shear stress by waves. We found a significant difference between the two models in predicting the bed shear stresses compared to the observed data. Nonlinear contribution from wave enhances the magnitude of bed shear stresses, which reduces the model error. The results highlight the nonlinear interaction between waves and currents is meaningful in predicting the bed shear stresses during high-wave-orbital motions; improvement of the present wave-current nonlinear interaction model for predicting the bed shear stresses may be needed.

Non-linear sloshing characteristics of liquid inside a chamfered bottom tank with submerged internal object under near-and far-fault earthquakes

Cylindrical and rectangular-shaped tanks have a concentration of stagnant impulsive liquid at the bottom corners that do not participate in sloshing. While used as tuned liquid dampers (TLDs), this non-participating fluid adds extra liquid mass to the tank but does not have any role in the vibration control aspect. In the present study, to decrease the stagnant impulsive liquid, a chamfered bottom-shaped tank with a submerged internal object is demonstrated. Due to the high-energy velocity pulse present in near-fault earthquakes, there is a possibility of violent liquid sloshing which may cause unwanted structural damage to the tank. Hence, the present study focuses on the influence of near- and far-fault earthquakes on the non-linear seismic behavior of the tank with submerged internal object. The non-linear sloshing is modeled using the finite element method based on a combined Eulerian-Lagrangian approach. The accuracy of the present non-linear numerical model is checked by verifying the results with the previously published results. In addition to the absolute response, the dynamic convective and impulsive response components are quantified. The proposed non-linear finite element scheme can be utilized in the context of structure-mounted chamfer bottom TLDs in the future.

Design, fabrication, nonlinear analysis, and experimental validation for an active sandwich beam in strong electric field and thermal environment

In the present work, an efficient one-dimensional finite element (1D-FE) framework considering layerwise mechanics with full electro-mechanical coupling has been developed for the laminated smart sandwich beams submitted to active damping. Nonlinear constitutive relations of piezo-thermo-elasticity at large electric field with temperature-dependent material properties have been considered. The efficient layerwise theory (ELWT) considers the normal deformation of the piezoelectric sensing/actuating patches/layers due to the more significant value of piezoelectric strain coefficient d33. The electric potential variation across the thickness of the PZT sensor/actuator has been assumed quadratic. The state space format of the dynamical system has been constructed based on a reduced order model in modal space. The feedback linearization approach has been applied to the nonlinear system of equations to design an equivalent linear optimal control strategy. An experimental facility has been developed to test the accuracy of the present nonlinear FE model. This facility consists of a thermal chamber with a heating system, air gun, actuation & sensing units with band-pass filters, a smart sandwich beam equipped with PZT-SP5H patches, a data acquisition system, and a computer with LabVIEW software. Open- and closed-loop responses from the present 1D-FE model have been compared with those obtained through experimentation at different temperatures. It has been observed that the current nonlinear FE model correctly captures the dynamic behavior of the vibrating smart sandwich beam at different operating temperatures and strong electric field. The study shows a strong dependence of the PZT materials on thermal chamber temperature and actuation field. New results for a smart sandwich beam are also presented to study the performance of PZT-SP5H patches as sensors/actuators for nonlinear active shape and vibration control in a thermal environment. The effect of piezoelectric actuator/sensor thickness, patch size, position, and applied mechanical load on the active shape and vibration control has been discussed.

Non-linear finite element analysis of seismically excited sloped wall tank

The non-linear seismic behavior of a ground-supported sloped wall tank is analyzed in the present study using a finite element model. A combination of three-node triangular and four-node quadrilateral finite elements is used to discretize the liquid domain. The velocity potential formulation is adopted for the liquid domain with a mixed Eulerian-Lagrangian scheme. By comparing the current numerical results with the existing experimental results, the competency of the present non-linear model is verified. The fundamental sloshing frequencies obtained from the present non-linear model are found closer to the experimental results compared to the linear counterpart. Non-linear seismic characteristics of liquid sloshing inside a ground-supported sloped wall tank are investigated under six different earthquakes categorized as low-, intermediate-, and high-frequency contents. Also, the dynamic impulsive and convective response components of hydrodynamic base shear force and pressure are quantified successfully. The comparison of the non-linear hydrodynamic response with the linear counterpart shows a significant difference in results which reasonably clarifies the limited capabilities of the linear model for response prediction as well as designing sloped wall tanks subjected to seismic excitation. The developed non-linear numerical model in the present study can be utilized for tuning and designing structure-coupled sloped wall TLDs.

An analytical nonlinear model for plain-woven composites under off-axis loads

Woven composite is a kind of thin-wall structure that is widely used in the structural strengthening for constructions. A deep understanding of the nonlinear behavior of a woven composite is essential for its application to complex load cases. An analytical model is presented to describe the nonlinear behavior of a plain-woven composite under off-axis loads. The model is developed by combining a discrete method of a plain-woven RVE and a novel nonlinear three-phase micromechanical bridging model of a unidirectional composite. Specifically, a plain-woven RVE is firstly divided into several sub-cells. Then, each sub-cell is seen as a micro-laminate consisting of at most two unidirectional composite layers and two pure matrix layers. Further, a three-phase micromechanical bridging model is applied to simulate the nonlinear behavior of the unidirectional composite layer, where the matrix elastoplastic behavior and the interface damage are involved. The matrix deformation is described by a J2 flow rule with consideration of stress concentration factors. The interface damage is simulated by interphase with progressive stiffness degradation. The present nonlinear model is validated by comparing with experimental data of three kinds of plain-woven composites under off-axis tensile or compressive loads.

Vibration control studies of a high-aspect-ratio wing with geometric nonlinearity

Many challenges of vibration problems due to structure nonlinearity are growing while high-aspect-ratio wings are being widely used. Feasible vibration control method is an effective way to decrease such challenges. At the beginning, a new high-aspect-ratio flexible wing model with swept-back angle and control surface was designed and manufactured. Numerical simulation was employed to find basic dynamic characteristics of the wing. Ground experiments could provide vibration test results of this wing. The numerical method of computational flutter velocity of the wing including geometric nonlinearity was applied to study this wing. Then the open-loop flutter dynamic pressure and the closed-loop flutter speed were compared, it is found that the control law designed by linear quadratic Gaussian theory can increase the flutter speed of the present geometric nonlinear wing model. The computational results of flutter vibration show that the geometric nonlinear flutter speed is lower than the linear flutter speed, and the change in torsional mode is the critical reason for the decrease in flutter speed. Both numerical and experimental method proposed in this paper could be applied to predict the approximate flutter effect of such complex elastic high-aspect-ratio wing via structural nonlinearity.

Lie symmetry analysis and invariant solutions for (2+1) dimensional Bogoyavlensky-Konopelchenko equation with variable-coefficient in wave propagation

This work aims to present nonlinear models that arise in ocean engineering. There are many models of ocean waves that are present in nature. In shallow water, the linearization of the equations requires critical conditions on wave capacity than it make in deep water, and the strong nonlinear belongings are spotted. We use Lie symmetry analysis to obtain different types of soliton solutions like one, two, and three-soliton solutions in a (2 + 1) dimensional variable-coefficient Bogoyavlensky Konopelchenko (VCBK) equation that describes the interaction of a Riemann wave reproducing along the y-axis and a long wave reproducing along the x-axis in engineering and science. We use the Lie symmetry analysis then the integrating factor method to obtain new solutions of the VCBK equation. To demonstrate the physical meaning of the solutions obtained by the presented techniques, the graphical performance has been demonstrated with some values. The presented equation has fewer dimensions and is reduced to ordinary differential equations using the Lie symmetry technique.

Presenting innovative ensemble model for prediction of the load carrying capacity of composite castellated steel beam under fire

The main aims of this study are related to present nonlinear analysis and prediction model for evaluating and predicting the performance of composite castellated steel beam (CCSB) under fire and static load. This study includes two parts, including parametric study and the prediction models. The beam size, concrete thickness, temperature, and beam length are considered as the independent variables in the parametric study. Among considered independent variables in this study, the increasing concrete thickness has a negligible positive effect on the load carrying capacity. In addition, gene expression programming (GEP), three regression models such as multiple linear regression (MLR), principal component regression (PCR), and multiple Ln equation regression (MLnER), the combination of GEP and MLR, and the combination of GEP, MLnER, and MLR are used to predict the load carrying capacity of the castellated beam. The maximum positive and negative errors, mean of absolute percentage error (MAPE), and statistical parameters such as the coefficient of determination, root mean square error (RMSE), normalized square error (NMSE), and fractional bias are utilized to evaluate and compare the performance of the models. According to the results of these parameters, the two best models specify. In addition, a distribution error table is used to specify the best model. Based on the results of this table and statistical parameters, the combination of GEP and MLR is considered as the best model for predicting the load carrying capacity of CCSBs.

Quantification of thermal energy generation in annular hyperbolic porous-finned heat sinks using inverse optimization

The present paper introduces an accurate numerical procedure to assess the internal thermal energy generation in an annular porous-finned heat sink from the sole assessment of surface temperature profile using the golden section search technique. All possible heat transfer modes and temperature dependence of all thermal parameters are accounted for in the present nonlinear model. At first, the direct problem is numerically solved using the Runge–Kutta method, whereas for predicting the prevailing heat generation within a given generalized fin domain an inverse method is used with the aid of the golden section search technique. After simplifications, the proposed scheme is credibly verified with other methodologies reported in the existing literature. Numerical predictions are performed under different levels of Gaussian noise from which accurate reconstructions are observed for measurement error up to 20%. The sensitivity study deciphers that the surface temperature field in itself is a strong function of the surface porosity, and the same is controlled through a joint trade-off among heat generation and other thermo-geometrical parameters. The present results acquired from the golden section search technique-assisted inverse method are proposed to be suitable for designing effective and robust porous fin heat sinks in order to deliver safe and enhanced heat transfer along with significant weight reduction with respect to the conventionally used systems. The present inverse estimation technique is proposed to be robust as it can be easily tailored to analyse all possible geometries manufactured from any material in a more accurate manner by taking into account all feasible heat transfer modes.

Nonlinear Traveling-Wave Vibration of a Ring-Stringer Stiffened Cylindrical Shell

The nonlinear traveling-wave vibration of a ring-stringer stiffened cylindrical shell is analyzed. Using Donnell’s nonlinear shell theory and Lagrange equations, the nonlinear dynamic model of the ring-stringer stiffened cylindrical shell is derived. Galerkin’s method based on multi-mode instead of single-mode approximation is used to discretize the shell’s displacements. Two types of orthogonal circumferential modes with same frequency are used and the interaction between them is considered in the analysis of the shell’s nonlinear traveling-wave vibration. The harmonic balance (HB) method, along with the pseudo-arc length continuation algorithm, is adopted to solve the forced vibration responses of the shell. The stability of the solution is determined by the Floquet theory. Through comparison with the results available in the literature, the correctness of the present nonlinear dynamic model and its solution process are validated first. Next, the mode selection rules are determined through a convergence study. Finally, the nonlinear traveling-wave vibration of the ring-stringer stiffened cylindrical shell is studied. Also, the paper investigates, in detail, the effects of stiffener parameters on the nonlinear dynamic characteristics of the stiffened shell.

A numerical solution of nonlinear DPL bioheat model in biological tissue due to laser irradiations

In this study, the numerical solutions of the thermal damages of biological tissue by nonlinear dual-phase-lag theory under different boundary conditions are constructed for the medicinal treatment of tumors cell. The volumetric heat source component in nonlinear dual phase lag bio-heat transfer model such as the metabolic heat generation is considered an experimentally temperature-dependent function. Due to the nonlinearity of the governing relations, the finite element schemes are used to get the solutions of these problems. The numerical outcomes for temperature are given graphically. Furthermore, the comparison between the linear and nonlinear results displays the present nonlinear mathematical models effective tools to estimate the bio-heat transfer in the living tissue.

Influence of Large Amplitude Vibration on Geometrically Imperfect Sandwich Curved Panels Embedded with Gradient Metallic Cellular Core

This study investigates the influence of large amplitude vibration on geometrically imperfect sandwich curved panels embedded with gradient metallic cellular (GMC) core using an efficient nonlinear finite element formulation based on higher-order shear deformation theory (HSDT). The cores of the sandwich curved panels are assumed to have three distinct porosity distributions. The material properties of the sandwich curved panel’s GMC core layer vary in the thickness direction as a function of porosity coefficient and mass density. The present nonlinear finite element model is validated with limited results available in the open literature, and few new results are also computed that can be used as a benchmark solution. The influence of porosity coefficient, porosity distribution type, amplitude ratio, imperfection amplitude, and curvature ratio on the free vibration characteristics of the geometrically imperfect sandwich curved panels with the GMC core are studied in detail.

A nonlinear model for a self-powered electromechanical actuator using radioactive thin films

This paper presents a nonlinear model for the self-powered electromechanical actuator using radioactive thin films. The theoretical formulations are based on Hamilton principle and include the effects of geometric nonlinearity due to nonlinear curvature and load nonlinearity due to radioactive source. Two models which named as constant coefficient collector current model (CCM) and variable coefficient collector current model (VCM), respectively, are presented to formulate the electrostatic force. The nonlinear governing equations based on the CCM and VCM are solved using Galerkin principle and iterative method. The present nonlinear model is validated through direct comparisons with the experimental results in open literature. Numerical results show that the CCM is valid for small initial distance only whereas for large initial distance, the VCM must be used for accurate analysis. The effects of initial distance, cantilever beam length and thickness on the drop-down time of the self-powered electromechanical actuator are also discussed.

Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes

This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates and panels using a finite element method. Based on the first-order shear deformation theory (FSDT), the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type. A C0 isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations. By adopting the extended rule of mixture, the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters. Four carbon nanotube (CNT) distributions, labeled uniformly distributed (UD)-CNT, FG-V-CNT, FG-O-CNT, and FG-X-CNT, are considered. The solution procedure is carried out via the Newton-Raphson incremental technique. Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model. The effects of the CNT distributions, their volume fractions, and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.

Tensile properties of microtubules: A study by nonlinear molecular structural mechanics modelling

A nonlinear molecular structural mechanics (MSM) model is proposed in this paper for studying the tensile properties of microtubules (MTs). In the nonlinear MSM models, the interactions between tubulin monomers in MTs are treated as nonlinear axial and torsional springs, whose stiffness coefficients are extracted from all-atom molecular dynamics simulations. The Young's modulus and fracture properties of MTs under tension extracted from the present nonlinear MSM models are found to agree well with the existing simulation and experiment results, which shows the efficiency and accuracy of the proposed nonlinear MSM models. In addition, the nonlinear MSM models are also extended to investigate the tensile properties including Young's modulus and fracture strain of MTs possessing lattice defects. The results obtained from nonlinear MSM models are utilized to develop a predictive equation for quickly predicting the tensile properties of MTs with different lattice defect levels.

Deployment dynamical behavior of planetary rover mast mechanism considering geometric nonlinearity and laminated structure characteristics

In this paper, the precise deployment dynamical behavior is studied for a planetary rover mast mechanism of spacecraft undergoing large attitude adjustment motion. In the conventional dynamic formulation, flexible appendages of mast attached to spacecraft are taken as linear deformations with isotropic material, and it can result in improper responses. Therefore, the present model takes into account the coupling relations between geometric nonlinearity and laminated structure characteristics. Accordingly, by introducing the nonlinear constitutive relation of laminated materials based on the higher-order shear deformation theory, the nonlinear dynamic model of the planetary rover mast mechanism composed of laminated composite material is deduced based on the virtual work principle including geometric nonlinearity and material nonlinearity. By comparing the experiments results and those of present nonlinear model, the correctness and accuracy of present nonlinear model are verified. Furthermore, numerical examples are presented to investigate the nonlinear laminated material effect on deployment dynamical behavior of the planetary rover mast mechanism using different laying angles and curvature radii, and the results also testify the accuracy and efficiency of the formulation. The conclusions have important theoretical value and practical engineering significance for the dynamic characteristics and vibration control of attitude adjustment of planetary rover mast mechanism.

The use of a general convected time derivative to compute the Reynolds stress tensor for a compressible turbulent flow

This paper deals with the turbulence closure problem associated with the Reynolds-averaged Navier–Stokes equations for compressible flows. Due to the known limitations faced by the turbulent closure model based on the Boussinesq hypothesis, additional tensors are needed in order to capture the complete Reynolds stress tensor. Models such as this are in the group of the so-called nonlinear eddy viscosity models. The methodology here presented consists mainly in translating the coefficients obtained via orthogonal projection of the Reynolds stresses that are calculated from a large eddy simulation onto a given basis of tensors. In addition, these coefficients can be seen as turbulent parameters which have analogous interpretation in a class of non-Newtonian fluids. The proposed closure, expressed in terms of the mean strain-rate and its Gordon–Schowalter convected derivative, has a concise and clear physical interpretation. In addition to the turbulent viscosity, parameters associated with the Gordon–Schowalter convected derivative are incorporated to help the interpretation of the nonlinear turbulent model. The methodology is applied to a compressible flow through a narrow channel with a series of holes of cylindrical shape. This configuration is representative of what is generally found in a Hole-Pattern turbomachinery seal. Different number of holes are tested in order to evaluate the influence of neighborhood holes in the analysis. The comparison between the Boussinesq hypothesis and the extended model shows how the latter one outperforms the former. Even though the nonlinear model has shown some limitations, there are still tensorial subspaces of the Reynolds stress tensor obtained from the LES approach that the present nonlinear model could not reach. In addition, the physical coefficients did not present strong similarities for the different configurations tested, what can be a challenge for constructing a complete closure model.

Tuning electronic energy band in a piezoelectric semiconductor rod via mechanical loading

Based on the k·p model with 8 × 8 band Hamiltonian, we demonstrate that the electronic energy band in a wurtzite piezoelectric semiconductor (PSC) rod can be tuned by a pair of uniaxial mechanical tractions. This tuning is achieved by solving two sub-problems: the electro-mechanical fields induced by a pair of axial tractions applied at the two ends of the rod, and the band energy based on the calculated strains and electric potential via the k·p model. Numerical results indicate that, when the magnitude of the applied load is relatively small, the induced PSC fields predicted by the linear model in the rod generally agree with those based on the present rigorous nonlinear model. Otherwise, the linear model will be invalid and the present nonlinear model has to be used to characterize correctly the intrinsic nonlinear property in the PSC rod. It is the first time that the heavy hole (HH), light hole (LH), spin-orbit split-off (SO) and conduction band (CB) in ZnO and GaN rods are all analyzed in details at different locations of the rod under different magnitudes of the applied traction. It is shown that the mechanical load could significantly affect the energy band edges, particularly near the ends of the rod where the loads are applied. Furthermore, the coupling effect of the valence band (VB) and CB is discussed in an InN rod where the material has a narrow bandgap. This work provides a unique opportunity in nanodevice design where nano energy is a key parameter.

Experiments and computations of solitary wave interaction with fixed, partially submerged, vertical cylinders

This paper presents the development of a three-dimensional fully nonlinear wave model to simulate the hydrodynamic interactions between a solitary wave and a fixed vertical cylinder which is partially submerged in water of constant depth. The governing Laplace equation and free-surface boundary conditions in a transient curvilinear coordinate system are solved by a mixed explicit and implicit finite difference scheme. The interaction processes described by a time sequence plots of free-surface elevations are presented, where a series of outward-scattered waves can be observed. Additionally, laboratory tests were carried out with recorded wave elevations to verify the present nonlinear wave model. The numerically generated wave elevations are found to match well with the experimental measurements. The horizontal and vertical force coefficients with different draft conditions are calculated and presented. It is found that with larger submergence of the vertical cylinder: (1) the horizontal force increases, and (2) the vertical force decreases.