Nonlinear Structural Behavior Research Articles

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

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

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

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

Development of a novel fractional magneto-viscoelastic dynamic model for an adaptive beam featuring functional composite magnetoactive elastomers: Simulations and experimental studies

Recently, the rapid emergence of functional composite magnetoactive elastomers with integrated hard magnetic particles (known as hard magnetoactive elastomers) has attracted significant interest in fields such as soft robotics and material science. It is of paramount importance to develop an efficient model that can accurately predict the nonlinear dynamic behavior of adaptive structures for their practical application and the synthesis of effective control strategies. In this study, a novel nonlinear fractional magneto-viscoelastic model of an adaptive cantilevered beam featuring hard magnetoactive elastomers has been developed. This model effectively characterizes the beam’s nonlinear and rate-dependent response behavior under magnetic stimuli of varying frequencies and magnitudes. Considering the fractional Kelvin-Voigt energy dissipation model and large deformation nonlinearity, the governing equations for the cantilevered hard-magnetic soft beam were derived using the Hamilton principle. The finite difference method, combined with the Galerkin modal decomposition scheme, was subsequently utilized to discretize the time and space domains, respectively. A hardware-in-the-loop experimental framework was finally designed to experimentally investigate the beam’s nonlinear response behavior and validate the simulation results. The simulated nonlinear quasi-static responses of the beam, subjected to magnetic loading up to 30 mT, exhibited excellent agreement with the experimental data collected. Moreover, the simulated dynamic responses of the beam, subjected to various amplitudes of the applied magnetic field and magnetic frequencies up to 2 Hz, were thoroughly investigated. These included time-histories, phase-plane, and hysteretic responses, all demonstrating strong alignment with the experimental observations.

Numerical Modelling simulation technology of Nonlinear Multi-Field Coupled Ground Foundation

Contemporary civil engineering practices demand sophisticated computational tools to navigate the complexities of structural systems and their interactions with the ground. This paper introduces a novel numerical modelling simulation technology tailored for nonlinear multi-field coupled ground foundations. Ground foundations, pivotal interfaces between structures and underlying soil, undergo intricate interactions influenced by various physical phenomena, including soil-structure interaction, soil-structure-fluid interaction, and thermal effects. Traditional analytical methods often falter in capturing the nuanced nonlinear behavior of these coupled systems. Consequently, this paper proposes a comprehensive numerical modelling framework integrating advanced computational techniques to accurately simulate the complex interplay of multiple fields within ground foundations. The methodology incorporates finite element analysis, multi-physics coupling algorithms, and advanced constitutive models to capture the nonlinear behavior of soil, structure, and fluid interactions. Through detailed case studies and validation against experimental data, the efficacy and accuracy of the proposed simulation technology are demonstrated, emphasizing its potential to revolutionize the design and analysis of ground foundation systems in civil engineering applications. This paper represents a foundational contribution towards advancing the state-of-the-art in numerical modelling simulation technologies for nonlinear multi-field coupled ground foundations, fostering innovation and optimization in civil engineering practice.

Predicting shear strength in UHPC beams through an innovative neural network with SHAP interpretation

Ultra-High performance concrete (UHPC) has garnered considerable attention in the construction industry due to its exceptional mechanical properties and durability. In the design of UHPC beams, accurately predicting shear strength is crucial. Inspired by the dense blocks in DenseNet, this paper proposes a novel neural network for predicting the shear strength of UHPC beams. A comprehensive database of UHPC beams was initially established through extensive literature data collection, amassing 619 experimental data samples. Preprocessing was subsequently conducted using mahalanobis distance (DM) to eliminate outliers. Subsequently, the database underwent detailed parameter analysis. In practical testing, the novel neural network model exhibited superior accuracy in predicting the shear strength of UHPC beams, surpassing traditional machine learning (ML) models and empirical formulas. Furthermore, it demonstrated excellent generalization capabilities, achieving an R2 value of 0.988 in the training set and 0.964 in the test set. The study introduced the shapley additive explanations (SHAP) method to conduct global and local interpretability analysis of the network model, demonstrating the contributions of each input parameter to the model predictions. Finally, based on this network model, a graphical user interface (GUI) was developed for researchers engaged in UHPC beam design, enabling users to easily input relevant parameters and obtain shear strength predictions. The findings of this study are expected to promote the application of ML models in predicting the complex nonlinear behavior of UHPC structures, providing strong support for engineering practice.

Nonlinear stochastic behavior of soft-core sandwich panels

The nonlinear stochastic behavior of soft-core sandwich panels and the evolution of uncertainty along the nonlinear path are investigated. The paper focuses on the way the geometrically nonlinear and unstable behavior is affected by uncertainty and considers, for the first time, the evolution of uncertainty along the unstable structural response. The structural modeling relies on the EHSAPT and its integration into the geometrically nonlinear stochastic regime. A tailored nonlinear FE model that is based on a variational formulation and an arc-length solution scheme are developed. The stochastic analysis adopts the Perturbation-based SFEM and its generalization for the evolution of uncertainty along the process axis. A numerical study demonstrates the stochastic methodology and explores the impact of uncertainty on the nonlinear structural behavior. The evolution of the stochastic stress resultants at the displaced end is studied along the two axes of evolution. The differences between the two representations and their physical and engineering significance are highlighted revealing significant changes to the uncertainty evolution pattern with the shift from global buckling to localized wrinkling instabilities. The representation of the stochastic results along the process axis also quantifies the level of uncertainty near critical and singular points where conventional analyses diverge.

Identifying Damage in Structures: Definition of Thresholds to Minimize False Alarms in SHM Systems

In recent years, the development of quick and streamlined methods for the detection and localization of structural damage has been achieved by analysing key dynamic parameters before and after significant events or as a result of aging. Many Structural Health Monitoring (SHM) systems rely on the relationship between occurred damage and variations in eigenfrequencies. While it is acknowledged that damage can affect eigenfrequencies, the reverse is not necessarily true, particularly for minor frequency variations. Thus, reducing false positives is essential for the effectiveness of SHM systems. The aim of this paper is to identify scenarios where observed changes in eigenfrequencies are not caused by structural damage, but rather by non-stationary combinations of input and system response (e.g., wind effects, traffic vibrations), or by stochastic variations in mass, damping, and stiffness (e.g., environmental variations). To achieve this, statistical variations of thresholds were established to separate linear non-stationary behaviour from nonlinear structural behaviour. The Duffing oscillator was employed in this study to perform various nonlinear analyses via Monte Carlo simulations.

Nonlinear behavior of dust acoustic periodic soliton structures of nonlinear damped modified Korteweg–de Vries equation in dusty plasma

In this article, the nonlinear plasma model known the damped modified Korteweg–de Vries equation under consideration on the base of analytical technique to know the novel behavior of this nonlinear model. We formulated the nonlinear plasma model by utilizing the RP (reductive perturbation) technique with basic set of fluid system which consisted on cold negative charge dust fluid, immobile background neutral charges, positive charge ion fluid, fast (ionized) electrons and thermally electrons. We also constructed various kinds of novel soliton solutions including kink wave solitons, periodic solitary waves, anti-kink wave solitons for the damped modified KdV equation. The determined soliton solutions are novel, interested and did not determined in the previous research. The physical interpretation of demonstrated solutions represent in contour, two-dim and three-dim with computational software. The study prove that our proposed approach is powerful, efficient and can also be fruitful for study of other nonlinear models.

Non-Linear Behaviour and Analysis of Innovative Suspension Steel Roof Structures

Suspension structures are one of the most effective roof load-bearing structures for medium to long spans. Their shape under symmetric loads is usually a square parabola or a curve close to it. The biggest drawback of such structures is their increased deformability under asymmetric loads. So-called rigid cables are used to solve this problem. However, the production of such rigid cables with a curvilinear shape is complicated, and their maintenance also has drawbacks due to the above-mentioned shape. To avoid these shortcomings, straight-line suspension structures have been used. This paper proposes a new form of combined suspension roof structures consisting of main load-bearing straight suspension elements supported by cable struts. For the main suspension elements, the bending stiffness is accepted, taking into account the operational requirements of the structure. This article analyses the behaviour of such a combined suspension structural system in symmetric conditions with an innovative approach. The arrangements of this system are discussed. The calculation of the forces and displacements of this structure and its elements is presented, taking into account the geometrical nonlinear behaviour. The distribution of the forces in the rigid elements and node displacements of the structure are discussed. The proposed new form of a combined cable-supported roof structure was shown to be more effective in terms of weight than the standard parabolic-shaped suspension structure.

A multistable composite hinge structure

A composite tape-spring (CTS) structure is a thin-walled open slit tube with fibres oriented at ±45°, which is stable in both extended and coiled configurations. The governing factors of its bistability include composite constitutive behaviour, initial geometrical proportions, and geometrically non-linear structural behaviour. Its bistable principle can be employed to produce a flexible multistable hinge structure with tailorable stability. This is achieved by introducing variable stiffness design within a cylindrical shell structure, where folding stability is dependent on central functional patch region, and then connected to linking ploy regions. Thus, a novel multistable composite hinge structure can be designed with positive Gaussian curvature deformation, and its multistability is highly tailorable: a lengthy one-dimensional mechanical arm can be designed to coil and fold multiple times to enable large folding ratio. An analytical model was established based on the strain energy principle, in order to determine effects from functional tape length; the typical structural stability and stable configurations were then predicted with respect to regional length of the functional layer. It is found that the stability of a multistable composite hinge structure is dependent on geometry and combination of both the functional patch region, and connecting ploy region; the stable criteria are then proposed and show good agreement with experimental observations and FE analysis. These enrich the diversities of functional deployable structures to benefit novel requirements for various deployable mechanisms, and enable customised design, as well as smart driving for flexible and multifunctional mechanical composite hinge applications.

Nonlinear free vibrational behavior of temperature-dependent two-directional functionally graded truncated cone-like shells in thermal environment

This article investigates nonlinear free vibrations of temperature-dependent two-directional functionally graded (TDTDFG) cone-like shells in thermal environment. The structure material is a combination of ceramic and metal with temperature-dependent mechanical characteristics varying continuously in the thickness and longitudinal directions. Initially, the thermomechanical dynamic equations of the system are modeled based on the first-order shear deformation theory (FSDT) and the strain-displacement relations of von Kármán. Afterward, the final governing equation for the structure’s transverse motion is obtained using the Galerkin discretization method. Finally, the governing equation is solved using improved Lindstedt-Poincaré method as an analytical technique, resulting in an equation for calculating the nonlinear frequencies of the shell. To validate the research’s results, the system frequencies are calculated under different conditions and compared with the results of previous studies. After ensuring the accuracy of the results, a parametric study is performed to evaluate the effects of various parameters on the linear and nonlinear frequencies of the TDTDFG cone-like shell in thermal environment. The results of this study have demonstrated that gradient indices, geometric ratios, and thermal environment have a significant influence on the nonlinear vibration behavior of structures.

Forced resonance of a buckled beam flexibly restrained at the inner point

Restraints along slender structures, such as pipes conveying fluid and beams, play important roles in enhancing their bending stiffness. The current work investigates the influence of the midpoint restraint on the buckled axial force and dynamic characteristics for the first time. A continuous model is introduced by treating the midpoint restraint force as a concentrated force using Dirac function. The influence of the midpoint restraint is discussed based on modal expansion, and a partitioned model is proposed for validation. The conclusion is that the continuous model has good accuracy. Based on this model, it finds out two stable buckled states changing with the midpoint stiffness. The first stable buckled state occurs under weak midpoint restraint and has a cambered shape. The zero- and double frequency components occur in symmetric modal shapes and the response is softened along the whole beam. However, in the second stable buckled state, it turns into a whole sine function shape. The zero- and double frequency components just occur in the second modal shape, and the soften phenomenon doesn’t occur at the midpoint. With increasing excitation amplitude, a bubble appears on the primary resonance peak while another resonance peak emerges nearby it. This work explains the influence of midpoint stiffness on nonlinear resonance and enhances the study of the nonlinear behavior of buckled slender structures.

Thermo-electro-mechanical effects on nonlinear dynamics of smart dielectric elastomer minimum energy structures

Minimum energy structures made up of smart electro-active polymers (SEAPs) have attracted significant attention in the field of soft robotics and actuators due to their exceptional property of undergoing large deformations when subjected to electric fields. In general, temperature also plays a crucial role in modeling of SEAPs because it affects the mechanical, electrical, and thermal properties of the polymer. These properties, in turn, determine the performance of smart polymer-based devices. Motivated by these ongoing advancements, this study investigates the effects of temperature on the nonlinear dynamic behavior of a smart dielectric elastomer-based minimum energy structure (SDEMES) actuator. The governing dynamic equation of the actuator is derived using the standard Euler–Lagrange’s equation. Through the utilization of time-evolution diagrams, Poincaré plots, and phase portraits, the study comprehensively evaluates the effects of temperature on the stability, periodicity, and resonant behavior of the actuator. The results highlight the significant influence of temperature on the stiffness of the elastomer within the SDEMES actuator, directly impacting its actuation performance. The frequency response of the actuator demonstrates a distinct increase in resonant frequency as the temperature rises. These findings shed light on the crucial role of temperature in shaping the stiffness and nonlinear dynamic behavior of smart dielectric elastomer minimum energy structures.

Simple Nonlinear Numerical Modeling for Unreinforced and FRP-Reinforced Masonry Domes

This paper presents a new method to model the nonlinear behavior of double-curvature masonry structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. The method is meant to be used in professional design, especially for assessment and retrofitting purposes, based on the exploitation of the simplest nonlinear finite elements available in commercial software, namely, trusses with elasto-fragile and elasto-ductile behavior (Cutoff Bars, according for instance to the definition provided by Strand7 R3.1.3a). Numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and by lumping nonlinearities on joints. These are assumed, in turn, to be elastic–brittle and elastic–plastic by using 1D elements, namely, Point Contacts, under the No-Tension Material hypothesis, and Cutoff Bars, respectively, assigning a small tensile resistance to the material. The reinforcement, realized with FRP hooping strips, is successfully modeled in a similar fashion, i.e., by applying perfectly bonded elastic–plastic Cutoff Bars at the extrados of the dome, where debonding is accounted for in a conventional way, limiting the tensile strength according to Italian Standards’ indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison. After an in-depth analysis of the obtained results, in terms of capacity curves, the robustness and accuracy of the proposed approach are assessed.

Circular steel tube-confined ultra-high performance concrete beam-column: Database, modeling, and design

The fiber beam element (FBE) model is widely used to simulate and predict the nonlinear behavior of structures owing to its simplicity and high computational efficiency. The accuracy of the FBE simulation of ultra-high-performance concrete (UHPC) filled steel tubular (UHPCFST) members is mainly dependent on the input materials and interactions between the steel tubes and concrete, such as second-order effect, yielding of steel tubes and passive confinement effect to the UHPC. This work proposes uniaxial effective stress-strain models of UHPC confined by circular steel tubes based on existing experimental data that are integrated into the FBE model to predict the nonlinear behavior of UHPCFST members. The robustness and reliability of the proposed material models are comprehensively verified against a database encompassing a wide range of materials and geometric parameters under different loading conditions (monotonic and cyclic loading). Furthermore, the application of existing design codes for computing ultimate bending strengths is assessed using an established experimental database. Finally, the ultimate bending strengths of circular UHPCFSTs are calculated using a novel and simplified N–M interaction equation. It is demonstrated that the developed material models could predict the nonlinear behaviors of circular UHPCFST members with good satisfaction, and that current design codes, to some extent, underestimate the ultimate bending strengths of circular UHPCFST columns, the proposed practical method in this study is highly accurate, with a mean value of 1.00.

Nonlinear seismic response and damage evolution of a mountain tunnel: Multi-scale simulation by IBEM-FEM coupled method

Studying dynamic response and damage assessment of mountain tunnels is paramount in earthquake engineering. This paper proposed a novel method, the indirect boundary element method-finite element method (IBEM-FEM) coupled method, aimed to concurrently simulate the amplification effect of kilometer-scale mountain topography and the damage evolution in a centimeter-scale lining tunnel section. The proposed method involves two fundamental steps. Initially, the input motion on the truncation boundary within the mountain is accurately determined using the indirect boundary element method (IBEM). Subsequently, the nonlinear dynamic behavior of the tunnel structure and its adjacent area is analyzed by the finite element method (FEM) based on the results from the previous step. This study numerically simulates the seismic damage and failure mechanisms of a mountain tunnel considering three influence factors: incident wave types, incident wave intensities, and surrounding rock mass grades. The results indicate that mountain topography amplifies the seismic response, thereby affecting the dynamic behavior of the tunnel. Under the incidence of SV-waves and P-waves, the dynamic damage distribution patterns of the tunnel lining are significantly different. Moreover, as seismic wave intensity increases, the peak values of tunnel stress exhibit a non-monotonic increasing trend. The surrounding rock mass grade also significantly affects the dynamic response and damage distribution of the mountain tunnel. Overall, the proposed IBEM-FEM coupled method can effectively consider complex mountain topography and is applicable for evaluating the nonlinear seismic response of mountain tunnels.

Machine learning-based multiscale framework for mechanical behavior of nano-crystalline structures

In this paper, a computational atomistic-continuum multiscale framework is developed based on the machine learning (ML) architecture to capture the nonlinear behavior of nano-crystalline structures. The dataset of the ML process is derived from analyzing the atomistic representative volume element (RVE) through the molecular dynamics method under various deformation paths. A comprehensive investigation is performed on the influential parameters of the atomistic RVE that leads to the determination of an appropriate atomistic RVE for reproducing the mechanical characteristics from fine-scale to coarse-scale level. The multilayer perceptron neural network approach (MLP–ANN) is employed in the optimization algorithm of the ML process to train the atomistic dataset. The performance of the ML model is validated by predicting the response of atomistic RVE under various deformation gradients. Finally, the proposed computational algorithm is employed for the simulation of several mechanical benchmark problems, including the uniaxial tensile test, pure shear test, pure torsion test, and nano-indentation problem. Numerical simulations are validated by comparing the results of machine learning-based multiscale analysis with the fully atomistic model and experimental data. It is shown that the proposed ML-based method enhances the multiscale analysis to capture the nonlinear behavior of nano-crystalline structures without computational complexities associated with conventional multiscale methods. The results highlight that the proposed multiscale framework can be utilized as a constitutive model for the large-scale analysis with a great accuracy and unique efficiency.

The generalized E-DVA method: a new approach for multi-modal pushover analysis under multi-component earthquakes with local variables maximization

Pushover analysis is a common nonlinear static procedure, performed to evaluate seismic response of civil structures. This approach allows considering the structural nonlinear behavior under earthquake loading in a simplified yet effective way; however, in its classic formulation, it is limited by restrictive and unrealistic assumptions. Thus, the basic method is inadequate for the accurate analysis of buildings without a vertical plane of symmetry and/or for multi-component earthquakes, where torsion effects cannot be neglected. Furthermore, standard pushover analysis only comprises one dominant mode of vibration; higher modes, and therefore their effects, are not accounted for. For all these reasons, the standard technique is generally not considered suitable for the assessment of buildings at high risk of natural-technological (NaTech) events, such as nuclear facilities in areas of high seismic activity. To overcome these limitations, a multi-modal pushover analysis procedure is here tested and validated on the data from a non-symmetric structure (the SMART case study) under multi-component earthquakes. In detail, the procedure applies a linear combination of modal load patterns, defined according to the well-established Direct Vectorial Addition (DVA) method. With respect to other existing multi-modal pushover analysis techniques, elliptical response envelopes are employed to calculate the corresponding combination factors. Innovatively, the identification of the dominant modes for the load pattern is not limited to the classic maximization of the forces at the basis of a structure but rather generalized to shear and displacement maximization at different heights and locations throughout the whole structural frame.

Linear vs nonlinear structural vibration behavior of steel-timber composite building elements

Composite structures including wood are increasingly coming into focus due to rising demand for sustainability and, at the same time, high-rise buildings, and long-span components. In this context, steel-timber hybrid building elements are gaining more attention since they offer sufficient load-carrying properties. However, such lightweight structures increase vibration levels and sound transmission. Accurate understanding of the structures is therefore indispensable. Consequently, herein, a novel steel-timber composite building element is studied concerning its vibrational behavior numerically and experimentally. Especially the influence of the joints between steel and timber components is investigated by considering nonlinear behavior due to frictional effects. Therefore, amplitude-dependency regarding eigenfrequencies and damping properties as well as multi-harmonic responses are studied. Hence, nonlinearities are revealed by slight amplitude-dependency and the occurrence of higher harmonics.

Correction Factor Method As A Substitute For Sequential Construction Analysis Of Buildings

Abstract: Within the sphere of structural analysis, a method of paramount importance emerges - the Correction Factor Method. Unlike conventional approaches, this method stands as a stalwart against the complexities of non-linear structural behavior. It pioneers a path that diverges from the linear norm, offering precision and insight where others falter. The structural parts of the building are analyzed in one step using linear static analysis method by assuming that the structure will be subjected to full load after the finishing of the construction completely. In reality things work in other way the dead load from each structural members and finishing materials are imposed in different stages as the structure is constructed storey by storey. Similarly the stability of frame changes at every stage of construction. Because of this changes the loads assumed in conventional analysis vary in the construction process and the results obtained in the traditional analysis will be unstable. Thus the structural frame should be analyzed in every structural construction stage by keeping variation of loads. This process is called as Construction Stage Analysis this process considers all the uncertainties precisely. This process is a time consuming process as the analysis is a complex process. Thus Correction factor method can be introduced where the analysis time can be reduced and the results will be accurate to Construction Stage Analysis. In this project multistoried reinforced concrete building frames with different number of floors are analyzed using ETABS, and then Construction Stage Analysis of each building model is done. A comparative study of Bending moments, axial forces, twisting moments and shear forces are carried out at every stage of the structural frame. These values are compared with linear static analysis and Construction Stage Analysis. From the values obtained correction factors are derived. From this method we can get results which has a maximum error of 2% and this proves that correction factor can be used as a substitute for sequential construction analysis