Nonlinear Analytical Model Research Articles

Experimental and nonlinear analytical investigation of the flexural performance of single-box double-chamber steel–bamboo composite beams

Steel–bamboo composite structures present excellent and stable engineering performance. This study presents a novel single-box double-chamber steel–bamboo composite beam consisting of cold-formed thin-walled steel and bamboo scrimber. Nine single-box double-chamber steel–bamboo composite beams were prepared with various section parameters. A four-point bending test was conducted to evaluate the flexural behaviour of the beams. The failure mode, deflection deformation, and load-carrying capacity were analysed based on the test phenomena and data; the influences of the various parameters on the flexural behaviour were explored. Finally, nonlinear analytical models were developed considering the nonlinear constitutive law of beams and the influence of the steel–bamboo interface slip. The results indicated that lateral instability and local buckling behaviours were effectively avoided, and two failure modes were identified. The bending resistance was improved by reducing the flange bamboo width–thickness ratio, steel height-thickness ratio, and increasing the height of the web. The bending capacity depended more on the bamboo than that on steel. The nonlinear analytical models provided accurate predictions for the beams with tensile failure. Discrepancies between the experimental and analytical results were less than 8.6%.

Equivalent Nonlinear Beam Model for Static and Free Vibration Analysis of the Beamlike Truss

Equivalent Nonlinear Beam Model for Static and Free Vibration Analysis of the Beamlike Truss

Micro-vibration modeling and analysis of single-gimbal control moment gyros

Micro-vibration modeling and analysis of single-gimbal control moment gyros (SGCMGs) are conducted in this study. Considering the rotation and support effect of the low-speed gimbal, a nonlinear time-varying dynamic model for micro-vibration analysis of an SGCMG is established using the energy theorem. By considering the Hertzian contact, elastohydrodynamic lubrication, and surface waviness, the nonlinear supporting forces and moments of the angular contact ball bearings on the high-speed rotor and low-speed gimbal are derived, and accordingly, an iterative solution method is proposed. Based on a three-axis dynamic force measurement platform, the dynamic characteristics of a real SGCMG are tested to verify the rationality of the proposed micro-vibration model. Subsequently, the effects of unbalance mass, surface waviness amplitude, gimbal lock angle, and rotation angular speed of the gimbal on the three-axis gimbal bearing transmission forces are discussed. The findings of this study provide insights for clarifying the micro-vibration characteristics and provide a theoretical basis for the working state design and structural optimization of SGCMGs.

Iterative piezo response function-based optimization for static shape control of cantilever beam using nonlinear piezoactuators

Shape control of complex structures by optimizing the electrode potential is not achievable directly by analytical solutions and piezo response function base-optimization techniques due to the nonlinear response of piezoactuators. In the present work, a metaheuristic iterative piezo response function (iPRF)-based optimization technique is developed to achieve the arbitrary shape of piezoelectric unimorph (PU) using nonlinear piezoactuators. In this regard, a PU is fabricated using APC 850 piezoactuator to verify the nonlinear response in bending mode and nonlinear analytical model of PU. After verification, length of the inactive layer and number of piezoactuators in PU are modified to study the shape control. iPRF-based technique is used for the optimization of electric potential to achieve the target shape of modified piezoelectric unimorph (MPU) with various piezoactuators. The results of iPRF-based technique are compared with the results of simulated annealing (SA)-based direct optimization technique. Unlike SA-based direct optimization technique, prior knowledge of nonlinear coefficients of piezoactuator is not required in iPRF-based technique. Optimum values obtained from both the direct nonlinear solution- and iPRF-based optimization methods are same for all MPUs. Furthermore, the number of iterations of iPRF-based optimization approach is not affected by the number of piezoactuators used to achieve the desired shape.

Rate-dependent constitutive model of high-strength reinforcing steel HTRB600E in tension

High-strength reinforcing steel HTRB600E has significant potential application in reinforced concrete (RC) structures because of its high strength and ductility. Under the risk that structures with HTRB600E are subjected to severe dynamic loadings, the rate-dependent behavior and constitutive model of HTRB600E need to be investigated to provide a basis for the structural analysis. A series of tension tests were carried out to acquire the engineering stress–strain curves of HTRB600E in the strain rate range from 0.00025 to 590 s−1. Moreover, a hybrid experimental–numerical converse method was used to obtain the true stress–strain curves beyond the necking of HTRB600E at different strain rates. The test results indicate that the strain rate significantly affects the mechanical properties of HTRB600E. The effect of strain rate on yield and ultimate tensile strength, uniform elongation, and yield to tensile ratio of HTRB600E was discussed. Three commonly-used models were calibrated or modified to predict the dynamic increase factors (DIFs) for yield and ultimate tensile strength of HTRB600E. A rate-dependent constitutive model for the engineering stress–strain curves modified from the Mander model was presented for the structure's analytical model based on the section analysis technique. A new rate-dependent constitutive model for the true stress-plastic strain relationship with necking behavior was proposed for the structure's nonlinear finite element analysis model. The formulations of DIFs and constitutive models agree with the test results well.

Linear, nonlinear, parametric and nonparametric regression models for nonstationary flood frequency analysis

In recent years, nonstationary flood frequency analysis (NFFA) has become an active area of research. It is crucial for water resources management and hydrologic engineering design to cope with the changing environment. Finding suitable and effective models could help perform better flood frequency analysis and make reliable estimates under the nonstationary environment. This study assesses different modelling techniques for nonstationary flood frequency analysis, including linear, nonlinear, parametric and nonparametric models using an extensive data set of 161 catchments across the UK. It identifies that rejection rates are generally higher for precipitation-informed NFFA models than time-varying NFFA models. For both time-varying and precipitation-informed NFFA, rejection rates for linear and cubic polynomial models are the highest. The models with the fewest rejections are fractional polynomial models followed by cubic spline models. Because of the flexibility, parsimony, and user-friendly features, fractional polynomial models could be a potential alternative for modelling the nonstationary behaviour of flood series. To investigate whether the seasonal flood variation and catchment characteristics influence the goodness-of-fit, a quantified seasonality index was calculated to illustrate the degree of seasonal variation of flooding for each catchment. It was found that the southeast of the UK has more significant seasonal flood variation than the northwest, and most of the catchments with high seasonality indexes are close to the Scotland and England border. Nevertheless, the correlation analysis shows insufficient evidence to conclude that catchment characteristics and seasonal flood variation impact the goodness-of-fit of the NFFA models.

Nonlinear 3D Finite Element Model for Round Composite Columns under Various Eccentricity Loads

Composite columns are often used in constructing high-rise structures because they can reduce the size of a building's columns while increasing the usable area in the floor plan. This research aimed to develop a nonlinear 3D finite element analysis model using the ABAQUS, version 6.13-4, of various round composite column designs with varied multi-skin of tubes for solid and hollow columns subjected to various eccentricity loads (90, 180 mm). Extended data to another 12 specimens of composite columns by numerical method, based on six references experimental data of composite columns. The results of ABAQUS data in this study show that; increasing eccentricity for applied loads causes a decrease in loads to fail for composed columns. The ultimate load of hollow composite sections under eccentricity is lower than solid composite sections under different eccentricity loads. Also, the same results indicated fort eccentricity loads. The same results indicated an increased number of steel layers. The stiffness of concrete is greatly influenced by its strength. When the concrete strength rises, the stiffness of the composite column rises as well. The ratios of concrete compressive strength values according to the reference column (CC1S00 with fc’=31.96 MPa) were (-4.4, 3.1, and 6.5) percent for the specimen (CC1S00) with (fc’=25, 35, and 40) MPa, respectively. The method utilized is in the nonlinear analysis, and the finite element results are in good agreement with the experimental results.

Nonlinear analysis of flat slab‐column connections to optimize the use of HPFRC under monotonic vertical loading

AbstractNumerous studies have shown that incorporating fibers in concrete can improve its mechanical properties, including tensile strength and toughness. Due to these outstanding properties, the use of fiber‐reinforced concrete (FRC) composites has been investigated for applications in structural members subjected to shear, in which brittle failure mode may occur. An example of this type of application is the use of high/ultrahigh‐performance fiber‐reinforced concrete (HPFRC/UHPFRC) in flat slab‐column connections as an alternative to shear reinforcement. The experimental results revealed that the use of advanced concrete materials led to an increase in the punching shear and deformation capacities. Despite these advantages, the use of HPFRC/UHPFRC in practical design is somehow limited by the lack of guidelines in codes for this type of new material. Furthermore, the study of constitutive models for nonlinear finite element analysis is also necessary. In this regard, this article addresses the simulation of two‐way slabs with HPFRC, subjected to concentrated monotonic vertical loading, tested in a previous experimental study, where the HPFRC was used only in a limited slab region around the column, and the rest of the slab was cast with normal strength concrete. The numerical models were developed in the commercial finite element software DIANA. The concrete nonlinear behavior was modeled by a total strain‐based constitutive model, in which the HPFRC softening is represented by a tensile stress‐crack width (σ − w) relationship. The validity of the numerical model is checked by the comparison with the experimental results and a punching shear mechanical model, leading to the formulation of a closed‐form equation. Finally, a parametric study was conducted to extrapolate the results obtained in the experimental campaign and to optimize the use of HPFRC to obtain a more economical and sustainable solution.

Nonlinear analytical modeling of mass-timber buildings with post-tensioned rocking walls

Nonlinear analytical modeling of mass-timber buildings with post-tensioned rocking walls

Geometric nonlinear model and optimization of vortex-induced energy harvester with variable beam width

This paper proposes a geometric nonlinear analytical model of a vortex-induced energy harvester (VIEH) with variable beam width in order to improve the output performance. The analytic method is adopted to establish the geometric nonlinear model of VIEH. Based on the geometric nonlinear analytical model, the beam structure is then optimized to improve the output. The results show that the harvested power and average power density within a specific resistance range can be increased through the beam width variation of the VIEH. Nonlinear hardening behaviors can be observed in the outputs varied by the flow velocity of a VIEH with variable beam width.

Nonlinear transverse vibrations of a jointed structure with two slightly curved beams connected by complex elastic joints

The research of jointed structures has attracted extensive attention and most of the current research focuses on the dynamic modeling and analysis of straight-beam jointed structures, while sometimes the jointed structures are composed of curved beams in engineering practice. Therefore, this paper aims to propose a novel nonlinear dynamic modeling method regarding a jointed structure with two slightly curved beams (SCBs) connected by complex elastic joints. Firstly, the nonlinear dynamic analytic model of a single SCB is established as one part of the jointed structure. Secondly, the idea of the global mode method is used to establish the entire nonlinear dynamic analytic model of a two-SCB jointed structure and obtain its natural frequencies and mode shapes. The dynamic characteristics of the complex elastic joints are subsequently introduced into the entire nonlinear dynamic analytic model of the jointed structure by applying the equilibrium conditions and boundary conditions. Thirdly, a procedure to calculate the forced vibration responses of the two-SCB jointed structure is proposed by successively using the Galerkin truncation method, harmonic balance method and pseudo arc-length method. Finally, the proposed nonlinear dynamic modeling method is validated by carrying out case studies and the results calculated by the proposed method are in good agreement with the results of finite element analysis, which demonstrates the accuracy of the proposed nonlinear dynamic modeling method. Furthermore, the effects of stiffness at the complex elastic joints, external excitation amplitude, and initial curvature on the nonlinear dynamic characteristics of the jointed structure are also analyzed by the comparative case studies.

(Digital Presentation) A Constant Deformation Modulus for the Simulation of Gas Diffusion Layer

The deformation of gas diffusion layer(GDL) directly affects gas diffusion and electron transfer in the fuel cell. The modulus of stress-strain relationship is the basic parameter in the process of deformation. In this paper, based on beam bending theory and geometric probability analysis, a nonlinear analytic model of stress-strain with physical meaning is established, and a constant deformation modulus of GDL is given. Based on the deformation modulus, we further simulate the inhomogeneous deformation of GDL within a half channel-rib model. The results indicate that the uneven deformation with deformation modulus is more significant than that with linear elastic modulus in the same condition. Finally, a shape-dependent bending radius design for the rib edge is proposed, in which the inhomogeneous deformation of GDL becomes smoother as the radius increases, thereby improving the service condition of GDL and prolonging its service life.

Matrix equations models for nonlinear dynamic analysis of two-dimensional and three-dimensional RC structures with lateral load resisting cantilever elements

In control engineering and structural dynamics, mathematical models such as the state-space representation, equation of motion, and the phase plane are matrix equations describing the system equilibrium. This paper develops novel matrix equations models for linear/nonlinear dynamic analysis of reinforced concrete (RC) buildings with cantilever elements lateral load resisting systems (e.g., RC shear wall, RC core). The models offer a new approach for introducing two-dimensional and three-dimensional cantilever structures to control the theory’s state-space representation and structural dynamics’ equation of motion. The development primarily addresses the stiffness and mass matrices. The proposed displacement-related stiffness matrix of cantilever elements satisfies the necessary conditions of symmetricity and elemental boundary conditions. The nonlinear matrix structural analysis employs a smooth hysteretic model for deteriorating inelastic structures, referring to the relation between the bending moment and the bending curvature through the bending stiffness. The parameters controlling the cyclic behavior regard a composite RC cross section subject to gravitational load and bending simultaneously. The paper includes four examples that exemplify the practical utilization of the matrix equations models in analyzing two-dimensional and three-dimensional structures of linearly elastic and inelastic properties. The four examples demonstrated the idealized applicability of the matrix equations models for modal analysis, pushover analysis, and inelastic earthquake response analysis.

An analytical nonlinear dynamic model for linear guide with carriage flexibility

Accurate estimation of vibration characteristics of linear guide is imperative for sophisticated structural performance of linear motion equipment. It has been illustrated that flexible model considering carriage deformation is a more precise description of realistic system. However, few dynamic model of carriage flexibility is found for vibration analysis when complex external load is applied. This paper proposes an analytical model to analyze the nonlinear vibration behavior of flexible linear guide system under multidirectional harmonic excitations. The outward deformation of flexible carriage skirt region is calculated by the classical deformation formula of vertical loaded cantilever beam. A lumped dynamic model accounting for segmented restoring force is proposed by coupling the vertical, lateral and rolling displacement and outward deformation. Dynamic responses of rigid and flexible models are compared, and the condition that neglects carriage flexibility is obtained. Numerical simulation exhibits abundant and fascinating nonlinear phenomena when the effects of external excitation, preload and carriage weight are discussed. Additionally, excitation experiments are performed to verify the proposed model. The developed theoretical model is promising for structure optimization of linear guide.

Performance of Rocking Shallow Foundations and the Evolution of Beam-on-Nonlinear-Winkler Foundation Modeling

The nonlinear behavior of shallow bridge and building foundations under large-amplitude seismic loading is an important aspect of performance-based earthquake engineering. Soil yielding beneath foundations can be an effective energy dissipation mechanism; however, this yielding may lead to excessive permanent deformations. The research and engineering community has established decades of model testing and analytical modeling to understand foundation nonlinearity and uplift. Physical model testing provides insight into the mechanisms at work in rocking, shallow foundations, while analytical modeling and simulation are validated against these experiment results such that modeling recommendations can be applied in practice. This body of work led to the current design procedures in industry, such that the benefits and consequences of foundations allowed to rock under seismic events can be understood and implemented in practice generally for design of proposed structures, as well as retrofit of existing structures. While there are various established analytical modeling approaches, this paper presents a summary of both the elastic and nonlinear Winkler analytical modeling approaches used to approximate observations from experiment, the status of codified design procedures incorporating rocking, and includes speculation on the future of research and design in this field.

Parametric investigation of GFRP-RCC jute fibre-reinforced recycled aggregate concrete elements

Large quantity of recycled aggregate concrete (RAC) attained from demolishing old infrastructures needs to be disposed of appropriately for sustainable construction. The current work has attempted to investigate the axial compressive effectiveness of jute fibre-reinforced RAC columns having glass fibre-reinforced polymer (GFRP) bars. Nine GFRP bars RAC circular compressive members (GJFC columns) and nine steel bars RAC compressive members (SJFC columns) with the size 1200 mm × 300 mm were investigated under concentric and eccentric conditions. The axial strength (AST), axial deformations, ductility, loading eccentricity, and failure patterns of members were assessed. A nonlinear three-dimensional finite element analysis (3D-FEA) model is proposed for a comprehensive parametric study of GJFC columns. The results depicted that the SJFC members had a higher AST up to 23 % and a lower deformation capacity up to 16 % compared with GJFC members. The eccentric loading produced similar declines in AST for both GJFC and SJFC members. The moment interactions diagrams showed higher values of moments and AST for SJFC columns than for GJFC columns. The parametric study results depicted that the impact of enhancing the crushing strength of jute fibre-reinforced concrete and the longitudinal reinforcement ratio led to a substantial improvement in the AST of GJFC members.

Non-Renewable and Renewable Energies, and COVID-19 Pandemic: Do They Matter for China’s Environmental Sustainability?

Since the emergence of the COVID-19 pandemic, people all around the globe have seen its effects, including city closures, travel restrictions, and stringent security measures. However, the effects of the COVID-19 pandemic extend beyond people’s everyday lives. It impacts the air, water, soil, and carbon emissions as well. This article examines the effect of energy and the COVID-19 pandemic on China’s carbon dioxide emissions in light of the aforementioned context, using the daily data from 20 January 2020 and ending on 20 April 2022. Using the nonlinear autoregressive distributed lag model for empirical analysis, the findings indicate that COVID-19 pandemic confirmed cases and renewable energy advance environmental sustainability due to their negative effects on carbon dioxide emissions, whereas fossil fuel energy hinders environmental sustainability due to its positive effect on carbon dioxide emissions. Moreover, these results are also supported by the results of the frequency domain causality test and the Markow switching regression. In light of these results, there are several policy implications, such as vaccination, renewable energy utilization, and non-renewable energy alternative policies, which have been proposed in this paper.

An equivalent spring-based model to couple the motion of visco-hyperelastic dielectric elastomer with the confined compressible fluid/air mass

Soft materials exhibiting large voltage-induced deformation under external stimuli have gained increasing attention in the recent past owing to their potential applications in soft transducers. Dielectric elastomer actuators (DEAs) coupled with a fluid/air mass have proved to undergo considerable voltage-induced deformation. This article presents a framework to couple the motion of an inflated Dielectric elastomer (DE) membrane with a confined compressible fluid/air mass and develops a nonlinear dynamic analytical model to predict the polar region deflection of an inflated DE membrane attached to an airtight chamber (namely bulging actuators) stimulated by an electric field. In order to derive the differential equations which determine the dynamic behavior of the membrane coupled to an airtight chamber, the Euler–Lagrange equation is employed, which takes into account the effects of membrane pre-stretch, initial inflation pressure, membrane viscoelastic behavior, and transient electric loading. A hypothesis of pseudo-air-spring is incorporated to consider the effect of the volume of the confined fluid/air mass. The experimental investigation conducted for various geometrical and loading conditions in both depressurized and pressurized states of actuation shows that the developed nonlinear model satisfactorily predicts the influence of fluid/air mass on the dynamic response of the considered DE membrane undergoing small voltage-induced deformation. Finally, the proposed framework is incorporated for building insights on several effecting parameters such as inflation pressure, quality, and quantity of the confined fluid mass, etc., on the electrodynamic behavior of the actuator. The results reveal that the volume of the air column appreciably alters the nonlinear dynamic behavior of the bulging actuator. Poincaré plots along with phase diagrams are presented for analyzing the periodicity of the nonlinear oscillations of the actuator. The underlying theoretical framework and the obtained inferences of the present article can be implemented effectively in the design of a futuristic class of structures whose motion is coupled with compressible fluid/ air mass subjected to time-dependent actuation.

Convolution/Volterra Reduced-Order Modeling for Nonlinear Aeroelastic Limit Cycle Oscillation Analysis and Control

A methodology for leveraging a combination of linear (through convolution integrals) and nonlinear (through Volterra series) reduced-order modeling (ROM) development was demonstrated on both a two- and three-degree-of-freedom (2-DOF and 3-DOF, respectively) aeroelastic system. The linear/nonlinear ROM approach was demonstrated against previous work in the field for a 2-DOF system and subsequently extended to a 3-DOF (flapped airfoil) system. Excellent agreement was demonstrated at limit cycle oscillation (LCO) onset (flutter) prediction between computational fluid dynamics, linear ROMs, and nonlinear ROMs. Although linear ROMs were sufficient to predict LCO onset, the nonlinear Volterra correction was required to estimate the amplitude of post-LCOs. Corrections that accounted for more coupling between degrees of freedom predicted the amplitudes more accurately. A study was undertaken to determine the minimal training set required to produce reasonable LCO amplitude estimates of the 3-DOF airfoil. A controller was also implemented in an effort to mitigate LCO onset and flutter divergence and to demonstrate the usefulness and power of leveraging the ROM for control design. A full-state feedback controller, tuned via a linear quadratic regulator (LQR), was shown to be effective in controlling the system below LCO onset. However, beyond LCO onset, this specific linear controller structure was observed to be ineffective in controlling the system. Future work will evaluate nonlinear control methods in which the ROM can be deployed as a part of the control system to update the LQR gains in a fully coupled approach.

Least-distance approach for efficiency analysis: A framework for nonlinear DEA models

We propose a class of nonlinear data envelopment analysis (DEA) models, including variants of the Russell graph measure (RM), BRWZ measure, slack-based measure (SBM), and geometric distance function (GDF). Based on linear programming, this class of DEA models provides a monotonic maximum efficiency measure and an efficient target that achieves the least Manhattan distance from the weakly efficient frontier of the production possibility set. We show that the maximum efficiency measure in this class can be explicitly expressed as a decreasing function of the least Manhattan distance. Furthermore, by adding certain consistent weight restrictions to this class of DEA models, the maximum efficiency measures satisfy strong monotonicity.