Nonlinear Structural Behavior Research Articles

Sparse Uniform Traversal of Model Parameter Space for Estimating the Nonlinear Displacement Response of Instrumented Buildings to Earthquakes

ABSTRACTThe displacement response of a building structure to earthquake excitations is crucial for assessing its seismic damage, which is usually accompanied by structural nonlinear behavior. This study proposes an efficient method of quickly estimating the nonlinear displacement responses of seismically damaged buildings. By designing a set of sparsely and uniformly distributed samples in the multi‐dimensional parameter space, this method traverses all these samples to find the best set of parameters for a parametric numerical model of the building that minimizes the error between the simulated and the measured responses. Compared to existing model‐driven methods, the proposed method can efficiently match the high‐dimensional parameters of the assumed parametric model without tedious and less robust iterative optimization, even if the instrumented building sustains severe seismic damage and deviates significantly from its initial state. The shaking table test data of a full‐scale four‐story reinforced concrete moment‐resisting frame structure is used to justify the advantage of the method over the state‐of‐the‐art optimization‐based model‐driven method. The proposed method successfully estimated the structural responses of all the stories of the building with an average error of 4.6% for the maximum inter‐story drift across the five earthquake loading runs. It took only approximately 19 min to complete the calculation on a personal computer, which could be greatly accelerated given more computation cores because the traversal is inherently friendly to parallel computation.

Reinforced concrete plates: cracking and ultimate load through Lumped Damage Mechanics

In structural analysis, it is crucial to accurately characterize the nonlinear behavior of structures. This behavior may result on strain localization phenomena, that may lead to collapse processes. Lumped Damage Mechanics (LDM), one of the more recent nonlinear theories, has shown promise for a variety of applications. It is applied to frame elements, for static and dynamic analysis, in reinforced concrete, plain concrete or steel structures, or in continuous media, with plate elements for plain concrete or bending plate elements, for reinforced concrete slabs. This paper presents the study of reinforced concrete slabs using LDM. Damage and plastic rotations are the internal variables of the problem that characterize concrete cracking and reinforcement yielding, respectively. The results numerically obtained were confronted with experimental ones. It was observed that the model is highly accurate in describing the initiation and propagation of cracks, as well as identifying the collapse mechanism, in addition to precise Load vs. Deflection results, close to the experimental values.

Exploring the nonlinear behavior of solitary wave structure to the integrable Kairat-X equation

This study presented various types of soliton solutions for the nonlinear integrable Kairat-X equation by utilizing the improved F-expansion technique with symbolic computational software Mathematica. Explored results for the nonlinear integrable Kairat-X equation are interesting, novel, and more general with different physical structures of solitary waves and solitons, such as kink wave, mixed dark–bright, peakon, anti-kink wave, bright, anti-kink dark, periodic, and dark solitons. With numerical simulations, the secured soliton solutions visualized in two-dimensional, three-dimensional, and contour graphs represent the physical phenomena of the demonstrated results. The explored soliton solutions will be helpful to comprehend interesting physical structures in fiber optics, nonlinear optics, ferromagnetic dynamics, and many other scientific fields. The extracted soliton structure sheds light that the enhanced technique is effective, powerful, concise, and reliable. We can also investigate the soliton results of other nonlinear integrable partial and fractional equations.

Nonlinear Finite Element Simulation and Analysis of Steel Frame Structures Considering Nonlinear Behavior

This paper focuses on investigating the nonlinear behavior of steel frame structures in practical engineering applications. Utilizing finite element analysis, the study simulates the response of structures under extreme loads such as strong earthquakes. By incorporating nonlinear material properties and contact effects, the numerical simulation and analysis explore phenomena such as plastic deformation, yield, and instability in frame structures. The research outcomes contribute to a deeper understanding of the energy dissipation and safety performance of these structures.

Efficient deep learning based models for rapid prediction of RC shear wall responses under monotonic and cyclic loading

The seismic response of reinforced concrete (RC) shear walls is of paramount importance in earthquake-resistant design. While traditional techniques such as finite-element-based modeling and experimental testing provide comprehensive insights into shear wall behavior, they often require significant computational resources and time. In response, this study investigates the efficacy of various Deep Neural Networks (DNNs), including Convolutional Neural Networks (CNNs), Bidirectional Long Short-Term Memory (Bi-LSTM) networks, and LSTM-Based Autoencoders, in predicting the behavior of RC shear walls under monotonic and cyclic loading conditions. Through training on a diverse dataset encompassing various geometric configurations, material properties, and loading scenarios, the proposed approach generalizes well to unseen cases, enabling rapid estimation of shear wall responses without extensive numerical simulations. This approach offers several advantages, including faster design iterations, improved assessment of existing structures, and potentially higher accuracy. Extensive comparative analyses against experimental tests and numerical simulations evaluate the performance of the deep learning models. Results demonstrate that the proposed approach achieves superior accuracy in prediction of hysteresis and pushover curves, effectively capturing the nonlinear structural behavior of RC shear walls subjected to static and cyclic loading conditions. Validation using a comprehensive experimental database of 160 specimens shows that the model achieves less than 10 % error in maximum lateral load predictions for specimens within the training data range; while simultaneously reducing computational time Overall, this study contributes to the evolving landscape of structural engineering by showcasing the potential of DNNs as efficient tools for predicting the behavior of RC shear walls.

Nonlinear free vibrations of a structurally tailored anisotropic pre-twisted thin-walled beam subjected to large deformations

It is essential to understand the nonlinear free vibration behaviour of a thin-walled composite structure as they find their applications in harsher environments prone to large deformations. Further, these structures made of fibrous materials, have directional properties for different fibre orientations resulting in a diversified and a complex nonlinear behaviour. In this regard, present work provides a comprehensive mathematical formulation on nonlinear vibration of pre-twisted thin-walled anisotropic box beam. The mathematical model is derived as coupled (flap-lag-extension-torsion) model considering shear deformation and green's strain tensor for large displacements in order to study the influence of nonlinear couplings on the dynamic behaviour. The derived energy equations are presented depending on degree of nonlinearity. These nonlinear equations those derived are nondimensionalized and solved with in the frame work of energy method using classical Ritz approximation. An iterative method is used to solve the nonlinear equations pertaining displacement terms. This nonlinear behaviour is evaluated for two important types of structural tailoring techniques available for thin-walled composite beams namely Circumferentially Asymmetric Stiffness (CAS) and Circumferentially Uniform Stiffness (CUS). It is found that CAS layup experiences significantly severe nonlinear effects compared to CUS due to the presence of 3rd degree nonlinear coupling terms. The variation of nonlinear frequency ratios over different ply angles showing the influence of nonlinearity on fibres orientation is presented for the first time for the two ply lay ups. The influence of degree of nonlinearity on the accuracy of the nonlinear frequencies is evaluated and presented. Moreover, the impact of nonlinearity on the pre-twisted beam is presented for different pre-twist angles.

Comparative analysis of seismic response and vulnerability of laminated bamboo frame structure under near-field and far-field earthquake actions

The study offers an evaluation of seismic response and vulnerability for a five-story laminated bamboo frame structure, assessing the effectiveness of seismic intensity measures across various damage thresholds and the modeling uncertainties involved. A structural finite element model was developed in OpenSees software, utilizing the Pinching4 model to accurately represent the non-linear characteristics of T-shaped steel connections in beam-column joints. Two collections of earthquake records, one consisting of pulse-like near-field and the other of far-field events, were utilized to examine the structure's nonlinear behavior. Additionally, vulnerability curves for various damage states were generated using the multiple stripe analysis technique, applied to both ground motion datasets. The applicability of 24 seismic intensity measures was also analyzed across various damage limit states. The modeling uncertainty under different seismic actions was further estimated using a first-order second-moment method. Ultimately, the annual collapse probability of the structure are elucidated. Research indicates that due to the influence of joint stiffness, the overall structure demonstrates dynamic characteristics that are predominantly of the first mode shape. The spectral acceleration associated with the fundamental period achieves a reduced logarithmic standard deviation in the vulnerability analysis across various limit states. Other IMs considering higher mode effects or softening period actions no longer predominate. In most cases, the modeling uncertainty under far-field seismic action is higher than that under near-field, especially at the severe damage limit states by using an efficient intensity measure. The laminated bamboo frame structure faces a much higher collapse risk in near-field than in far-field conditions.

Reinforced concrete structures under hard projectile impact: penetration and perforation resistance

AbstractReinforced concrete (RC) structures are mainly designed to withstand both static and dynamic loads. However, due to the highly nonlinear behavior of RC structures subjected to extreme dynamic loads, these structures have a very complex damage behavior under dynamic impact loading. In fact, current existing methods for damage‐simulation and prediction are generally based on either empirical data, simplified mechanical approaches or complex numerical simulations mainly using the finite element method. In this regard, empirical and semi‐empirical models can be considered to calculate the load‐bearing capacity in a simplified way with only a few input parameters. Hence, using current experimental test data, this paper aims to analyze and assess existing empirical and semi‐analytical approaches that are established in standards and guidelines. Accordingly, a functional relationship in terms of an impact factor is found. Based on the obtained results, different approaches are also developed to describe the resistance to projectile penetration of RC structures as well as the force interaction between projectile and RC structures.

On the Nonlinear Behavior of Composite Structures under Multiple Earthquakes Considering Soil–Structure Interaction

On the Nonlinear Behavior of Composite Structures under Multiple Earthquakes Considering Soil–Structure Interaction

Nonlinear dynamic study of FG-GFRC-NPR structures

The functionally graded glass fibre-reinforced polymer composite(FG-GFRC) is one of the contemporary sophisticated materials that may be employed for a variety of technical purposes. The shock absorption capacity of FG-GFRP laminates can be improved by incorporating auxetic property (i.e., negative Poisson's ratio NPR) in the structures, which can be attained by a particular stacking sequence of glass fibres (GF) and a different percentage of GF distribution along the thickness direction within the FG-GFRP structure. The nonlinear dynamic behaviour of such structures must be investigated. The clamped-clamped FG-GFRP-NPR structure is stimulated under a uniform transverse load distribution in the current work. Based on the higher-order shear deformation theory (SDT), the displacement field and nonlinear stress–strain relationship are derived. The nonlinear differential equation with cubic non-linear components were derived using Hamilton’s principle and transformed using Galerkin’s technique and obtained governing equation of motion. MATLAB has been used to conduct all numerical simulations. A time series, a phase picture and a Poincare diagram (PCM) were generated to characterize the vibration behavior of such auxetic structures.

Performance Prediction of GFRP-Reinforced Concrete Deep Beams Containing a Web Opening in the Shear Span

This study aimed to investigate the nonlinear structural behavior of concrete deep beams internally reinforced with glass fiber-reinforced polymer (GFRP) reinforcing bars and containing a web opening of various sizes and locations within the shear span. Three-dimensional (3D) numerical simulation models were developed for large-scale GFRP-reinforced concrete deep beams (300 mm × 1200 mm × 5000 mm) with a shear span-to-depth ratio (a/h) of 1.04. Predictions of the numerical models were validated against published experimental data. A parametric study was conducted to examine the effect of varying the opening size and location on the shear response. Results of the numerical analysis indicated that the strength of the deep beam models with an opening in the middle of the shear span decreased with an increase in either the opening width or height. The rate of the strength reduction caused by increasing the opening height was, however, more significant than that produced by increasing the opening width. Placing a web opening in the compression zone close to the load plate was very detrimental to the beam strength. Conversely, a negligible strength reduction was recorded when the web opening was placed in the tension side above the flexural reinforcement and away from the natural load path. Data of the parametric study were utilized to introduce simplified analytical formulas capable of predicting the shear capacity of GFRP-reinforced concrete deep beams with a web opening in the shear span.

Simulation and parameterization of nonlinear elastic behavior of cables

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

Earthquake Performance Analysis of a Masonry School Building's Retrofitted State by the Equivalent Frame Method

Nonlinear analyses of masonry structures are frequently used in both engineering practice and academic studies. Due to the dominant nonlinear behaviour of masonry structures, complex and extensive finite element models are required to obtain accurate analysis results. While masonry walls are usually modelled using fine-meshed shells or solid elements in such structures, high computing power in modelling, analyzing, and post-processing results is necessary for the analyses of large structures. In recent years, the equivalent frame method, as a solution to this problem has been developed and presented in the literature. In this study, the equivalent frame method is used in a masonry structure modelling, and the axial force-bending relationship is represented by force-based fiber elements. The multi-linear load-deformation relationship reflects the shear behaviour of the walls. Within the scope of the study, an existing masonry school building is modelled using the equivalent frame elements with OpenSees software. Seismic performance analyses are done considering the existing and retrofitted states of the structure, and the results are discussed in a comparative manner.

THD improvement of piezoelectric MEMS speakers by dual cantilever units with well-designed resonant frequencies

In this study, a piezoelectric MEMS (Micro-Electro-Mechanical-System) speaker with thoughtfully selected resonant frequencies of dual cantilever units is designed and implemented. Based on the lead zirconium titanate (PZT) thin film with superior piezoelectric coefficient, the cantilever diaphragm is designed through the modal analysis. In the 1.5 mm by 1.5 mm cantilever array, a high-frequency actuation unit with resonance of 13.1 kHz and a low-frequency actuation unit with resonance of 6.35 kHz constitute the proposed piezoelectric MEMS speaker. The boost of sound pressure level (SPL) due to the resonant mode of low-frequency actuation unit reduces the total harmonic distortion (THD) around the subharmonic frequency of high-frequency actuation unit. Meanwhile, the asymmetric triangle diaphragm reduces the maximum stress in the structure when operating at the resonant frequency, thereby mitigating the THD spikes resulting from the nonlinear structural behavior. In pressure-field measurements, the proposed design can reach SPL ≥ 70.0 dB from 2.7 kHz to 15.0 kHz with only 0.179 Vrms input. At the same time, THD remains below 3.0 % from 3.2 kHz to 20 kHz. The outstanding performance under larger input signal and bias voltage is also verified. Actuated by 0.354 Vrms and 2 VDC bias, the maximum SPL achieves 111.9 dB and the SPL is higher than 80.0 dB from 3.3 kHz to 14.1 kHz. Furthermore, THD is lower than 3.0 % from 1.0 kHz to 8.9 kHz. A promising solution of piezoelectric MEMS speaker for in-ear applications is demonstrated in this study.

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.