Nonlinear Structural Response Research Articles

Nonlinear responses of longitudinally coupled slab tracks exposed to extreme heat waves

Structural responses of longitudinally coupled slab tracks (LCSTs) under extreme heat waves (EHWs) and the adaptability of track reinforcement measures to cope with EHWs-related issues have been unprecedentedly investigated in this study. A novel finite element model (FEM) to assess nonlinear mechanical behaviours of LCSTs exposed to temperature rise has been established. The nonlinearities of material constitutional properties, interfacial behaviours and temperature distribution are taken into account, and the FEM has been fully validated by experimental data. This paper is the world's first to highlight nonlinear structural responses of LCSTs such as slab arching and interface failure under EHWs and under normal temperature rises (NTRs). More importantly, effectiveness of track reinforcement measures (such as post-installed anchors and interface adhesives) in mitigating track damage under EHWs are demonstrated to determine whether those measures are capable of making LCSTs adapt to EHWs. The new findings reveal that: (1) vertical buckling of LCST can be caused by atmospheric temperature rises; (2) the interface area between the mortar layer and the track slab adjacent to the joint with initial defect can fail under NTRs, while the interface delamination incurs under EHWs; (3) vertical displacements of track slabs under EHWs can be reduced by 97.3 % when post-installed anchors are introduced; and (4) the bond strength of interface adhesives should be larger than 0.02 MPa and 0.048 MPa to retain the vertical displacements within the threshold of level III interfacial gaps under NTRs and under EHWs, respectively.

Foreword to the special issue on new developments in structural stability.

Foreword to the special issue on new developments in structural stability.

Damage assessment of concrete structures subjected to internal explosion under air-backed and water-backed conditions

There has been an increasing concern about the dynamic response and damage assessment of offshore structures under blast loads due to accidents and terrorist attacks. These concrete structures will face severe threats of internal explosions from powerful bombs. After the internal detonation of a bomb, the blast wave in the concrete structure will gradually propagate to two types of fluid-structure interfaces: the air-concrete interface or the water-concrete interface. The purpose of this paper is to investigate the nonlinear response and damage assessment of the concrete structures to internal explosion considering air-backed and water-backed conditions. Two types of blast tests are conducted to obtain the damage mechanisms and degrees of the concrete targets under internal explosion conditions. A fully coupled numerical approach is used to model the internal explosion and the fluid-structure interaction, and it is validated through comparing the test and the numerical results. The shock-wave and damage propagation of the concrete targets under air-backed and water-backed conditions are compared. The damage ranges of the concrete targets with various explosive weights, buried depths, and fluid-structure interfaces are presented. Its results are used to propose a damage assessment method for the concrete structures to internal explosion under air-backed and water-backed conditions.

Dynamic analysis of negative stiffness noise absorber with magnet

In the paper, the negative stiffness membrane absorber with magnet has been taken as a nonlinear noise absorber. The dynamic characteristics of the nonlinear noise absorber have been studied by nonlinear dynamics theory and numerical simulation. The dynamic equations of the system were established under harmonic excitation. The slow flow equations of the system are derived by using complexification averaging method, and the nonlinear equations which describe the steady-state response are obtained. Bifurcation diagram, amplitude frequency diagram and phase diagram are used to study the nonlinear response of structures under different excitation conditions. The effects of excitation amplitude, excitation frequency, nonlinear term and structural parameters on the nonlinear dynamic characteristics and sound absorption characteristics of the structure are studied. The resulting equations are verified by comparing the results which respectively obtained from complexification-averaging method and Runge-Kutta method. It is helpful to optimize the structural parameters and further improve the sound absorption performance to study the variation of the sound absorption performance of magnet negative stiffness membrane absorber system with its structural parameters.

Sensitivity of structural responses to the processing of near-fault ground motion records containing fling-step

Fling-step is one of the important characteristics of near-fault ground motions that is caused by a permanent static offset of the ground and appears as a one-sided velocity pulse and a large residual displacement at the end of the motion. Due to baseline errors in many ground motion records, they are processed (processing is a combination of baseline correction and filtering) before adding accelerograms to some earthquake databases whereby the residual displacements ( i.e., the permanent static offsets) in the fling records are typically eliminated. It is not clear to what extent the record processing can affect the nonlinear responses of structures subjected to fling-step records. To address this issue, the current study is conducted to investigate the sensitivity of the nonlinear structural responses to record processing. To achieve this goal, the seismic responses of three code-conforming reinforced concrete (RC) special moment-resisting frames with different heights subjected to two versions of fling-step ground motions including a processed version that static offsets are removed, and a baseline-corrected version with static offsets preserved are evaluated. The findings of this assessment indicate that even though the processing procedure does not preserve the static offsets of the fling-step ground motions, the seismic responses of the structures to the processed records may resemble those obtained under only the baseline-corrected ground motions (with static offsets preserved).

Simulation analysis of structural nonlinear seismic response

Faced with the difficulty of analyzing structural nonlinear seismic response, this study focuses on the reinforced concrete frame structure and designs a frame that meets the specifications. Artificial synthetic seismic records and natural seismic records were selected, and the acceleration response of the first story of the structure was used as the output sample for the study. On the basis of a nonlinear autoregressive moving average model with external inputs, a neural network model was constructed and nonlinear seismic response simulation analysis was conducted. These results confirm that the research method has good predictive performance and can effectively predict structural nonlinear seismic response. Under the action of artificial earthquake records, there is a small difference between them and the acceleration time history curve and acceleration response peak obtained from time history analysis. Under the action of artificial seismic record ACC12, when the time is 25 s, the calculation results of time history analysis and research methods are 1.715 m/s2 and 1.403 m/s2, respectively, with the former being 0.312 m/s2 smaller than the latter. In natural earthquake records, with a characteristic period of 0.30 s, under the action of natural earthquake record USA00668, the relative energy of time history analysis is 4.997 m2/s when the time is 30 s, which is 0.938 m2/s higher than the research method. The research method can accurately analyze the nonlinear seismic response of the results.

Survey on non-linear cyclic responses of Unreinforced Masonry buildings by means of commercial finite-element codes

This work presents a comparison about the nonlinear cyclic response of unreinforced masonry structures obtained by using commercial calculation codes and on the base of the type of modeling approaches currently available. In particular, several elasto-plastic modeling methodologies are considered, representative of a good part of the state of the art for this type of construction: mechanical-based concentrated plasticity macro-element (Tremuri), macro-element with diffuse fiber-based plasticity for flexure and concentrated springs for shear (SeismoStruct) and macro-element with phenomenological-based concentrated plasticity (NextFEM Designer). The purpose of the present research is to evaluate the ability of the different codes to represent the proper hysteretic response of masonry structures. To this aim, several experimental tests from literature are analyzed and compared; two different masonry panels, characterized by different resistant mechanisms, and an entire perforated wall have been studied through nonlinear cyclic static analyses. The reported comparison, mainly focused on the numerical cyclic behaviour exhibited by each computer program, is conducted on the basis of the path of the cycles obtained and on the amount of dissipated energy.

Thermo-mechanical large deformation characteristics of cutout borne multilayered curved structure: Numerical prediction and experimental validation

The numerical modeling of static large-deformation behavior of the multilayered flat/curved panels with cutouts subjected to thermo-mechanical load is presented in this work. The numerical model includes third-order displacement polynomials. The large-deformation characteristic of the multilayered panel is incorporated using two nonlinear strains (Green–Lagrange and von-Karman). The governing equation is formulated using Hamilton’s principle, and approximate numerical solutions are obtained using the selective integration scheme (Gauss-Quadrature) associated with Picard’s direct iterative method. A generic computational algorithm is developed in MATLAB using isoparametric finite element (FE) steps. The solution accuracy is verified with the published results and experimental data by utilizing the available/fabricated lab-scale test rig. The role of cutout parameters, including the various geometrical parameters on the nonlinear structural responses, is studied for a clear insight into the damaged structural modeling using the temperature-dependent elastic properties of the laminate. In addition, the effect of nonlinear strain terms on the final structural responses is presented. Based on the observation, the applicability of the full geometrical (Green–Lagrange) strain–displacement relation is established.

Post-buckling analysis of shell-like structures using an implicit dynamic time integration scheme

PurposeThis paper aims to investigate post-buckling responses of shell-like structures using an implicit conservative-decaying time integration dynamic scheme.Design/methodology/approachIn this work, the authors have proposed the use of a four-node quadrilateral flat shell finite element with drilling rotational degree of freedom within the framework of an updated Lagrangian formulation mutually with an implicit conservative-dissipative time integration dynamic scheme.FindingsSeveral numerical simulations were considered to evaluate the accuracy, robustness, stability and the capacity of the considered time integration scheme to dissipate numerical noise in the presence of high frequencies. The obtained results illustrate a very satisfying performance of the implicit conservative-dissipative direct time integration scheme conjointly with the quadrilateral flat shell finite element with drilling rotation.Originality/valueThe authors have investigated the potential of the implicit dynamic scheme to deal with unstable branches after limit points in the non-linear post-buckling response of shell structures with no need for structural damping. The capability of the studied algorithm to study buckling and post-buckling behaviour of thin shell structures is illustrated through several numerical examples.

Random response analysis of nonlinear structures with inerter system

Most researches on inerter focused on the mechanism or deterministic vibration analysis, and some studies lied in the random vibration of linear structures. However, many structures exhibit the nonlinear characteristics under a large excitation, and the effects of inerter system on additional properties and probabilistic distribution of random response of nonlinear structure under random excitation have rarely been considered at present. Based on the enhancement effect of inerter system on nonlinear structure, the influence of various components of inerter system on the response suppression of nonlinear structure is investigated from the probability level, and a developed response analysis method suitable for inerter system is proposed in this paper. The stochastic differential equation of nonlinear structure with inerter is established in this work, in which both the nonlinear structure without hysteresis and the hysteretic structure are considered. The probability density function of structural response is obtained by the exponential polynomial closure (EPC) method combined with the state-space-split technique. In terms of nonstationary random excitation, a scheme of equivalent stationary excitation is proposed to split the state space vector. Meanwhile, the EPC method is developed through the reduction of undetermined coefficients in the probabilistic solution, which significantly improves the efficiency. Numerical results show that the response suppression effectiveness of inerter system is robust to nonlinear structures, and the inerter system mainly provides additional damping for the primary structure, thereby achieving the vibration mitigation. However, an excessively rigid inertia system may lead to a negative additional stiffness for the primary structure and inhibit the vibration mitigation.

Approximating nonlinear response to harmonic base-excitation using fixed-interface quasi-static modal analysis

The recently developed quasi-static modal analysis (QSMA) technique approximates the amplitude dependent modal characteristics of large-scale finite element models with frictional contact at preloaded interfaces. The nonlinear natural frequencies and damping ratios offer insight into the dynamic behavior of assembled structures, particularly the amount of frictional damping and stiffness loss introduced from an isolated modal oscillation due to the joints. This work presents an approach to approximate the nonlinear steady-state response of a base-excited structure using the nonlinear frequency and damping estimates from QSMA. A Hurty/Craig-Bampton transformation allows for the base-excited system to be expressed in terms of the fixed-interface modal coordinates, thus allowing the extension of previously developed analytical approximations using the prescribed base acceleration and the nonlinear, fixed-interface modes from QSMA. The accuracy and relevance of this non-intrusive approach rely on the applicability of Masing's hypothesis within QSMA to approximate the hysteresis curves from the initial loading curve. The limitations are investigated by considering both Masing and non-Masing joint models. A comparison to reference solutions demonstrates the accuracy of the approximation to efficiently obtain nonlinear steady-state solutions of large-scale models with frictional interfaces for cases that satisfy Masing's hypothesis.

Influence of the angle of seismic incidence of long-period pulse-like ground motion on an irregular base-isolated building

In general, isolators and dampers used in seismically isolated buildings are designed to be isotropic in any horizontal direction. However, in the case of buildings with plan irregularities, their nonlinear responses depend on the direction of seismic loading. To discuss the influence of the angle of seismic incidence (ASI) on the nonlinear response of irregular building structures, it is important to define the angle of the critical axis of the horizontal ground motion. One possible choice is the “principal axis of ground motion” proposed by Arias (A measurement of earthquake intensity, 1970). However, because this principal axis is independent of the natural period of a structure, it could be complicated to use for seismically isolated structures with long natural periods. In this study, the influence of the ASI of long-period pulse-like seismic input on an irregular base-isolated building is investigated. First, the angle of the principal axis of ground motion is defined in terms of the cumulative energy input. Then, a nonlinear time-history analysis of a five-story irregular base-isolated building is performed using 10 long-period pulse-like ground motion records considering various ASIs. The results show that, compared with the principal axis of ground motion proposed by Arias, defining the principal axis of ground motion in terms of the cumulative energy input is more suitable for discussions concerning the influence of the ASI on the response of an irregular base-isolated building.

Investigations on Nonlinear Dynamic Modeling and Vibration Responses of T-Shaped Beam Structures

A novel nonlinear dynamic modeling approach is proposed for the T-shaped beam structures widely used in the field of aerospace. All of the geometrical nonlinearities including the terms in the deformation of the beams, the terms at the connections, and the free ends of beams are considered in the dynamic modeling process. The global mode method is employed to determine the natural frequencies and global mode shapes of the linearized system. The validity and accuracy of the derived model are verified by comparing the natural frequencies obtained with those calculated from FEM. Adopting the Galerkin truncation procedure, a set of reduced-order nonlinear ODEs is obtained for the structure. A study on the variation of dynamic responses taking the different numbers of global modes into account is performed to determine the number of modes taken in nonlinear vibration analysis. A comparison between the responses of the system with linear or nonlinear matching and boundary conditions is given to evaluate the importance of neglecting and reserving the nonlinear terms in matching and boundary conditions. It is shown that ignoring the nonlinear terms in both matching and boundary conditions may significantly alter the responses while developing the discretized governing ODEs of the structure.

Virtual modelling technique for geometric-material nonlinear dynamics of structures

This paper presents a virtual modelling technique for dynamic safety assessment of practical structures undergoing geometric and material blended nonlinearities. The variational inputs of systematic properties are treated within the 3D dynamic geometric-elastoplastic analyses. To circumvent numerical challenges in solving the coupled nonlinear problems, a freshly developed dynamic virtual modelling (DVM) technique is employed to determine the inherent relationship between the variational input data and the nonlinear structural response by using a new clustering based extended support vector regression (C-XSVR) algorithm with a novel T-spline polynomial kernel function. The virtual modelling models can be constructed at each time step within the Newmark’s time integration procedure, which then can be used to predict deflection, force, and stress of the concerned structure at different periods. The DVM is capable of visibly forecasting potential large deformation nonlinear behaviours in an efficient manner, based on the explicit relationship functions. To demonstrate the accuracy and effectiveness of the proposed framework, nonlinear behaviours of two practical applications under future forecasted working conditions are predicted and validated in the numerical investigations.

Effects of Parameters on Non-Linear Seismic Analysis of Fixed Offshore Platform

Fixed offshore structures in seismically active zones are likely to have deformations large enough to exceed the elastic limits of materials under strong ground motions. Therefore, investigation of nonlinear response of offshore structures under dynamic loadings is very interesting to structural engineers. Nonlinear behavior of structures is highly related with the soil properties and soil behavior. The main purpose of this study is to investigate and show the methodology for inelastic dynamic analyses of fixed-offshore structures under the 10,000-year earthquake loadings. The investigation in this study includes the effect of soil radiation damping, soil-pile gapping, and soil degradation on fixed offshore structures. Additionally, the effect of the direction of earthquake is included in this study. An offshore structure model ‘Platform A’ is modeled in CAPFOS. 10,000-year earthquake events are considered and for this purpose, two different earthquakes are used: Hector Mine Earthquake (1999) and Landers Earthquake (1992). These ground motion records are scaled to have a resulting earthquake that has a return period of 10,000-year. CAPFOS software is used to complete time-history analyses with these earthquakes. Results indicate that: (i) Considering the soil radiation damping negligible is not correct, because without the radiation damping, the total damping ratio is estimated as % 3, while including radiation damping raises the ratio to % 4.5, (ii) soil-pile gapping and soil radiation damping generate adverse effects on analyses outcome, and (iii) using high values of soil degradation factors is not always conservative.

Hybridizing machine learning with metaheuristics for preventing convergence failures in mechanical models based on compression field theories

Some materials, such as reinforced concrete (RC), introduce non-linear constitutive relationships into structural models. The characterization of their structural load–strain response is usually approached by using iterative strategies, such as Newton-type methods. However, these iterative strategies may not predict the non-linear structural response of RC elements (beams) due to convergence problems (non-consistent elements). In this work we propose a novel solution to overcome the convergence failures of RC structural elements subjected to shear force modeled by Compression Field Theories (CFTs). First, a Coral Reef Optimization with Substrate Layers (CRO-SL) metaheuristic is used to solve a fitting problem between numerical and experimental results on a set of real beams tested in shear, for which the system is solvable. Then, the outputs of the CRO-SL, plus the mechanical and geometric parameters of the RC beams, are used to train different Machine Learning (ML) regression methods. These regressors are then able to predict the tensile strains of the non-consistent RC elements. The characterization of such strains allows modifying the parameterization of the system of equations, overcoming thus the convergence problem of Newton-type methods in these cases. Experiments over a set of 72 real RC beams have shown the good performance of our approach. In them we have carried out a comparison among different ML regressors including Multi-Layer perceptrons, Support Vector Regression and Random Forest, plus feature reduction techniques such as PCA.

An explicit time-domain method for non-stationary random analysis of nonlinear frame structures with plastic hinges

In this study, a novel approach for random vibration analysis of nonlinear frame structures under seismic random excitations is developed. The explicit time-domain method is improved in this approach by integrating the plastic hinge model, which can simulate the nonlinear behaviors caused by material property changes. Specifically, the hysteretic system’s equation of motion is constructed using auxiliary differential equations that govern the plastic rotational displacements and their corresponding hysteretic displacements. Additionally, by introducing the concept of equivalent excitations, an explicit iteration scheme for solving the equation of the hysteretic system is developed, in which the auxiliary differential equations are solved under the assumption that the plastic rotational velocity changes linearly with time between two adjacent time instants. Finally, by combining the Monte Carlo simulation method and the proposed explicit time-domain method, the non-stationary random responses of nonlinear frame structures can be obtained. As illustrated by numerical examples, the proposed method achieves satisfactory solution accuracy and efficiency when applied to nonlinear frame structures with plastic hinges. Moreover, the proposed iterative method resolves equations involving displacements describing the frame’s global state, plastic rotational displacements, and corresponding hysteretic parameters, introducing a novel concept for solving problems with nonlinear coupled variables of multiple types.

FREQUENCY OF NON-LINEAR DYNAMIC RESPONSE OF A POROUS FUNCTIONALLY GRADED CYLINDRICAL PANELS

In this article, a nonlinear dynamical investigation of porose functionally graded cylindrical panels using a proposed analytical model is carried out. The material's properties are considered to be porosity-dependent and graded in the thickness direction, corresponding to a power-law distribution. The classical shell theory, with the geometrical shape of nonlinear in von Karman–Donnell, is employed to get the Lagrange motion equations. By applying the Galerkin procedure, the system of nonlinear dynamic vibration equations is found. The natural frequencies and dynamic amplitude vibrations are obtained by using the fourth-order Runge–Kutta approach. In numerical analyses, the effects of porosity factor, power-law index, porous FGM thickness, frequency–amplitude relation, and excitation force on the dynamic response of thin functionally graded porous cylindrical panels are investigated. Through the obtained results, it is discovered that the porosity coefficients have important effects on the natural frequencies and amplitude of the nonlinear dynamic response of the FG structures. It leads to a reduction in natural frequencies by 5.74 % at 10% pores.

Variable-kinematic finite beam elements for geometrically nonlinear dynamic analyses

This article investigates the dynamic nonlinear response of three-dimensional structures using variable-kinematics finite beam elements obtained with the Carrera Unified Formulation. The formalism enables one to consider the three-dimensional form of displacement–strain relations and constitutive law. The deformation mechanisms and the associated couplings are described consistently with the selected kinematic model. The Hilbert–Hughes–Taylor method and the iterative Newton–Raphson scheme are adopted to solve the motion equations derived in a total Lagrangian scenario. Various models have been obtained by using Taylor- and Lagrange-like expansions. The capabilities of the beam elements are assessed considering isotropic, homogeneous structures with compact and thin-walled sections.

Optimum sizing design of steel frame structures through maximum energy dissipation of friction dampers under seismic excitations

This paper focuses on optimum sizing design of steel frame structures equipped with friction dampers (FDs) in order to prevent the vulnerable effect of an earthquake. The fundamental concept is to maximize the energy dissipation of implemented FDs under different seismic excitations. The FDs utilized as passive energy dissipation devices in a steel structure increase the energy dissipation capacity of the structure by decreasing the seismic demand during an earthquake. In this context, the Pall friction dampers (PFDs) are implemented as diagonal damped brace members in investigated structures. Three different earthquake records (Kobe, Kocaeli-Duzce, Erzincan) are utilized to acquire nonlinear dynamic responses of the steel frame structures through time-history analyses. The open application programming interface (OAPI) functions are used to integrate a finite element modelling based structural analysis program, SAP2000, with a design optimization algorithm encoded in MATLAB for achieving the exact structural behaviours by synchronously data transferring. As an optimizer, one of the recent nature-inspired metaheuristic techniques, so-called Grey Wolf (GW) algorithm is used. Initially, under effect of seismic excitations, the steel frame structures are optimally sized for attaining minimum design weights without implementing the PFD elements by subjecting only strength, displacement, drift, and geometric structural design constraints taken from AISC-LRFD practice code provisions. Afterward, in order for optimally modelling the PFD elements, the frames are equipped with PFDs to calculate optimum yield strengths that is defined as slip load of a PFD. To do so, the GW algorithm ensures the maximizing of the dissipated energy and controls the yield strengths between the stories since the shear force due to the earthquake increases towards the base of the structure. Eventually, the provisions-based sizing design optimizations of the steel frame structures equipped with optimally modelled PFD elements are conducted under seismic excitations for conclusive evaluations.