Nonlinear Structural Analysis Research Articles

Field testing for structural behavior of a stratified monumental complex over time: Palazzo Colonna-Barberini and Templum Fortunae Praeneste

The use of recent technology in heritage conservation incremented the knowledge on structures and materials, reducing the number of uncertainties. There are different activities required for an accurate structural assessment, the interconnection and coordination of the tasks and their results are the main challenges for the optimal exploitation of information. This research presents a holistic methodology to assess the seismic behavior of a complex and stratified historical construction. The assessment methodology includes historical survey, onsite testing for mechanical characterization, geometrical survey, visual inspection and recording to define a three-dimensional model and perform nonlinear structural analysis. The specific contribution of the paper is in the mechanical characterization through the integration of field local testing, as well as sonic tomography, double flat jacks, endoscopy, with virtual inspection assisted by photogrammetry. In this work, the methodology was applied to the Palazzo Colonna-Barberini in the Templum Fortunae Praeneste in Palestrina, Italy. The geometrical model of the actual complex was defined in the Building Information Model environment based on available survey and visual recordings. The structural model was derived from the geometry and integrated with the in-situ testing results, finally it was analyzed considering the nonlinear response of the materials.

A constrained solid-shell model for the geometric nonlinear finite-element analysis of laminates with alternating stiff/soft layers. Applications to laminated glass

Solid-shell models are developed for the geometrically nonlinear analysis of multi-layered composite structures made of alternating layers with large difference in material properties. Exemplificative applications are presented for laminated glass, in which a number of stiff plies of glass are permanently shear-coupled by soft interlayers. The sectional warping due to significant transverse shear strains in the soft layers makes theories of laminated plates based on the plane-section hypothesis unreliable. The proposed approach is based on a geometrically exact solid-shell finite element model with one element per layer in the thickness direction, as alternative to solid discretization. The element approximation is based on the displacement nodal values at the top and bottom surfaces of the layers, with a natural C0 continuity. An alternative solid-shell model with fewer parameters is derived imposing the equal finite rotation of the stiff layers at each surface point by a local rotation-free re-parametrization of the nodal displacements and enforcing the plane stress condition. The approach permits an easy coupling with a fully solid discretization, e.g. to model connections, and is based on a simple strain measure quadratic in the displacement unknowns and suitable for finite strains. Extensive numerical examples for laminated glass plates and curved shells susceptible to large deflections and buckling are provided, comparing the results with those from a fully solid approach.

Geometric Nonlinear Analysis of Self-Supporting Structures for Overhead Transmission Lines

Geometric Nonlinear Analysis of Self-Supporting Structures for Overhead Transmission Lines

Seismic Performance of Reinforced Concrete Buildings with Joist and Wide-Beam Floors during the 26 November 2019 Albania Earthquake

Beams with width greater than their depth and depth equal to the depth of the slab (concealed wide beams) are widespread in Reinforced Concrete (RC) buildings in Albania. A large number of RC buildings with wide beams were hit by a strong Mw6.4 earthquake on 26 November 2019. The earthquake hit two of the most densely populated areas in Albania and caused widespread damage to these buildings. This paper aims to provide an updated view on the seismic performance of buildings with wide beams in light of the new field data following the 26 November 2019 Albania earthquake. To this end, a thorough literature review including experimental and field observations from past earthquakes is presented and data from field visits in Albania are described. It was found that damage to the joists and wide beams themselves was limited, even when the buildings suffered significant non-structural or structural damage in other elements as a result of the earthquake. A discussion on the behavior of wide beam–column frames based on nonlinear structural analyses and tests from the literature is presented. Furthermore, the implications of the results of the analysis for the seismic performance of RC buildings are discussed and confronted with observations from the 2019 Albania earthquake. Based on the literature review, further experimental research on wide beams with longer and more realistic span lengths is recommended.

An Efficient Reduced-Order Multi-Scale Simulation Approach for Nonlinear Analysis of Frame Structures with Nonlinear Localization

ABSTRACT This paper presents a reduced-order multi-scale simulation approach for nonlinear analysis of structures with local nonlinearities. Using it, the traditional global structural analysis can be changed to that of a reduced-order system where only nodal displacements of nonlinear elements are solved using the Newton–Raphson method in a single iterative procedure. Meanwhile, two nonlinear force/stiffness correctors are introduced based on the stress decomposition to describe material nonlinearities of frame members. In addition, two simulation ways are used to deal with the nonlinearities of the yielding frame members. Finally, the static and transient structural systems are simulated to verify the approach.

Development of numerical model capturing cyclic behavior of Two-Side clamped infill plates

This study aims to propose a simple numerical model methodology for two-side clamped infill steel plates with various aspect ratios, slenderness ratios and even different steel grades. The modeling element constructed using the methodology expects to be directly implemented into computer structural software for nonlinear time-history analyses of structures employing two-side clamped infill plates. The suggested model is constructed with their force–displacement relation including nonlinear and cyclic effects which can be defined by modeling parameters evaluated from empirical equations. The empirical equations are developed using regression analyses to agree with the parametric analysis results with detailed finite element models of two-side clamped infill plates. A proposed numerical model including the hysteretic characteristics was validated by comparison with existing experimental results conducted by other studies. It is confirmed to utilize the proposed numerical model that can accurately represent cyclic behavior over entire response ranges including buckling, tension field action representing the post-buckling behavior, and fracture of steel plates.

A novel data-driven analysis for sequentially formulated plastic hinges of steel frames

Although many different nonlinear analysis techniques for steel frame structures, they causes the increase in total computational cost. A data-driven approach can then be used to substitute the classic finite element nonlinear analysis including second order methods and inelastic modelling. In this paper, a novel data-driven method using ensemble learning models for geometric and material nonlinear analyses of frame structures is proposed. For this approach, the data acquisition process and machine learning-based models are needed to train a large amount of dataset, which is collected from the nonlinear analysis and a yield surface equation. Ensemble learning algorithms are then used to build the data-driven models. After training, the sequence of plastic hinge formation in steel frame structures can be predicted without any nonlinear analysis process. In that situation, the data-driven model is more effective, especially in practical cases with the lack of experimental information due to limited sensors. The validity of the proposed method has been demonstrated by several numerical examples.

Synthesis, structural, spectral and third-order nonlinear optical analysis of solution-grown 4-methylbenzylammonium oxalate hydrate: a novel organic crystal for laser applications

Synthesis, structural, spectral and third-order nonlinear optical analysis of solution-grown 4-methylbenzylammonium oxalate hydrate: a novel organic crystal for laser applications

Nonlinear Analysis of Structures by Total Potential Optimization Using Metaheuristic Algorithms (TPO/MA)

Nonlinear Analysis of Structures by Total Potential Optimization Using Metaheuristic Algorithms (TPO/MA)

Nonlinear analysis of a typical nonlinear beam structure based on experimentally extracted dynamical characteristics

Measuring nonlinear characteristics of a flexible structure is difficult and complicated since the nonlinear phenomena often exhibits several special features such as unstable vibration and bifurcation. The purpose of this paper is to propose a novel computing method for extracting dynamical characteristics of a typical nonlinear beam structure. Through comparing with the experimental data derived from modal experiments, the accuracy and feasibility of nonlinear normal modes function can be validated. Afterwards, the dimensionless dynamical equation that can indeed analyze nonlinear characteristics of the system is deduced, and the associated nonlinear frequency response is calculated based on Harmonic Balance method. According to comparisons between numerical simulations and experimental harmonic frequency response of the structure from a swept-sine experiment, the accuracy of the deduced dimensionless dynamical equation can be certified and the nonlinear analysis of the system is believed to be realized. Finally, the nonlinear attractor and bifurcation phenomena are discussed, and the stable condition is validated based on the Lorenz-like system.

Impact of ground-motion duration on nonlinear structural performance: Part I: spectrally equivalent records and inelastic single-degree-of-freedom systems

In current seismic performance-based assessment approaches, nonlinear dynamic analysis of structures generally relies on ground motions selected based on their pseudo-spectral accelerations, with little or no consideration for ground-motion duration. Part I of this study, presented in this article, attempts to comprehensively quantify the impact of ground-motion duration on the nonlinear structural performance of case-study inelastic single-degree-of-freedom systems for shallow-crustal seismicity conditions. The effect of duration is decoupled from that of ground-motion amplitude and spectral shape by assembling sets of spectrally equivalent long- and short-duration records. Such sets are employed in incremental dynamic analyses of a wide range of computational models incorporating in-cycle and cyclic strength and stiffness deterioration. The structural response is quantified in terms of peak- and cumulative-based engineering demand parameters. Formal hypothesis testing is used to assess the statistical significance of duration’s impact on the median structural capacity of the considered structural systems. Furthermore, the derivation of duration-dependent fragility and vulnerability relationships demonstrates that ground-motion duration effectively impacts the nonlinear structural performance of various systems, and it should be accounted for in current practice. The fragility median values for highly deteriorating structural systems under long-duration ground motions are found to be up to 21% or 34.0% smaller than the short-duration counterpart if a peak- or cumulative-based engineering demand parameter is adopted, respectively.

Cyclic elastoplastic constitutive model for stainless steels compatible with multiple strengths

The application of stainless steel materials in civil engineering has begun to attract attention over the last decade. Nevertheless, most studies of stainless steel structures still use the oversimplified Chaboche model. Therefore a more accurate constitutive model is needed to describe the cyclic elastoplastic behavior of stainless steel. The model should be able to simulate stainless steel of varying strengths and should be easily calibrated for practical engineering purposes. This paper proposes a compatible constitutive model that meets these objectives. The constitutive model combines two forms of hardening, is dominated by isotropic and kinematic hardening, and accounts for the strain memory effect and the average stress relaxation effect. A complete numerical implementation scheme for the constitutive model is proposed and coded in the user material subroutine (UMAT) based on the implicit return mapping algorithm. Furthermore, simplified methods and recommendations for the calibration of material parameters are given. The simulation results of a detailed finite element model are compared with the results of the cyclic loading tests, and good agreements are obtained. The proposed constitutive model can be further used in seismic or other dynamic nonlinear analyses of stainless steel structures to correctly predict their strength, deformation, and energy dissipation capacity.

Novel methods for reliability study of multi-dimensional non-linear dynamic systems

This research presents two unique techniques for engineering system reliability analysis of multi-dimensional non-linear dynamic structures. First, the structural reliability technique works best for multi-dimensional structural responses that have been either numerically simulated or measured over a long enough length to produce an ergodic time series. Second, a novel extreme value prediction method that can be used in various engineering applications is proposed. In contrast to those currently used in engineering reliability methodologies, the novel method is easy to use, and even a limited amount of data can still be used to obtain robust system failure estimates. As demonstrated in this work, proposed methods also provide accurate confidence bands for system failure levels in the case of real-life measured structural response. Additionally, traditional reliability approaches that deal with time series do not have the benefit of being able to handle a system's high dimensionality and cross-correlation across several dimensions readily. Container ship that experiences significant deck panel pressures and high roll angles when travelling in bad weather was selected as the example for this study. The main concern for ship transportation is the potential loss of cargo owing to violent movements. Simulating such a situation is difficult since waves and ship motions are non-stationary and complicatedly non-linear. Extreme movements greatly enhance the role of nonlinearities, activating effects of second and higher order. Furthermore, laboratory testing may also be called into doubt due to the scale and the choice of the sea state. Therefore, data collected from actual ships during difficult weather journeys offer a unique perspective on the statistics of ship movements. This work aims to benchmark state-of-the-art methods, making it possible to extract necessary information about the extreme response from available on-board measured time histories. Both suggested methods can be used in combination, making them attractive and ready to use for engineers. Methods proposed in this paper open up possibilities to predict simply yet efficiently system failure probability for non-linear multi-dimensional dynamic structure.

Post-fire nonlinear vehicle–bridge interaction analysis considering hysteretic material behavior

Deteriorating bridges and potential vulnerabilities are crucial in the structural assessment of railroad bridges. Among various hazards that a bridge may encounter, evaluating the bridge after a fire is important because it may change the behavior of the bridge. More specifically, the post-fire bridge exhibits structural stiffness degradation, residual stress accumulation, and residual deflection. Due to those residual responses further affecting the dynamics of the bridge, analyzing the post-fire behavior of a bridge subject to normal traffic usage becomes important. Thus, this paper proposes a framework that assesses the dynamic behavior of a post-fire bridge considering the material hysteresis due to thermal loads and vehicle-bridge interaction (VBI). The proposed model is different from previous approaches in that the nonlinear VBI analysis is analyzed in an integrated system equation. So far, most related works exchange the data between separate finite element analysis software and in-house codes, intrinsically facing convergence problems. Instead, by adopting the augmented representation approach, the proposed framework becomes computationally efficient. Herein, nonlinear structural fire analysis is performed to obtain post-fire responses of the bridge. Then, the dynamic analysis is realized by incorporating material hysteretic behavior and VBI systems. The proposed framework is validated against the linear VBI model under gravity load. Subsequently, parametric studies are presented to represent various fire scenarios and long-term serviceability. The results demonstrate that the proposed model provides an effective tool for evaluating post-fire bridge dynamics by including material hysteresis under cyclic traffic loads. Moreover, the proposed framework can easily accommodate various types of hazards as well that cause the nonlinear behavior of the system.

Nonlinear vibration and stability analysis of a flexible beam-ring structure with one-to-one internal resonance

The nonlinear dynamic characteristics of a flexible beam-ring structure under fundamental harmonic excitation are systematically investigated. The nonlinear partial differential governing equations of motion for the beam-ring structure are derived by using Hamilton's principle and discretized into two coupled ordinary differential equations including quadratic and cubic nonlinearities by Galerkin's technique. The potential internal resonance relationship of the beam-ring structure is recognized through analyzing the mode shapes and linear frequencies. The method of multiple scales is utilized to approximately analyze the dynamic system and yield a set of autonomous equations under the case of 1:1 internal resonance and a primary resonance. The amplitude-frequency characteristics and the stability of the steady-state responses are studied numerically. The frequency-response curves show that some parameters of the amplitude-frequency equations have significant contributions to the nonlinear responses near resonance of the beam-ring structure. Finally, the bifurcation diagram is obtained and the Poincare map, power spectra and the largest Lyapunov exponent are used to identify the nonlinear dynamic behaviors of the beam-ring structure. From the numerical simulations, it is found that there exist typical nonlinear phenomena such as multi-value solutions, jumps, bifurcations, multiple periodic and chaotic motions in the beam-ring system. This work also proposes a reference for nonlinear modeling and dynamic analysis of similar complex structures.

Impact of ground-motion duration on nonlinear structural performance: Part II: site- and building-specific analysis

This study’s Part I proved that ground-motion duration could play an important role when assessing the nonlinear structural performance of case-study inelastic single degree-of-freedom systems. However, quantifying duration effects in many practical/more realistic engineering applications is not trivial, given the difficulties in decoupling duration from other ground-motion characteristics. This study’s Part II, introduced in this article, explores the impact of duration on nonlinear structural performance by numerically simulating the structural response of realistic case-study reinforced concrete bare and infilled building frames. Advanced computational models incorporating structural components’ cyclic and in-cycle strength and stiffness deterioration, and destabilizing [Formula: see text] effects are used. The proposed methodology relies on the generalized conditional intensity measure approach to select ground motions. This allows selecting records consistent with the seismic hazard at a target site, both in terms of spectral shape and duration. Those are employed as input to cloud-based nonlinear structural response analyses. Variance analysis is used to quantify the impact of duration on structural response. Furthermore, vector-valued fragility and vulnerability models alternatively using peak- and cumulative-based engineering demand parameters are derived. Results show that higher damage/loss estimates can be attained as ground-motion duration increases. Relative differences up to 44% are found in fragility median values for a pre-code reinforced concrete infilled frame when comparing scalar and vector-valued fragility models conditioned on average pseudo-spectral acceleration and significant durations up to 35 s.

The two-level probabilistic description of the compressive constitutive parameters of concrete

The constitutive model of concrete is the critical basis for the nonlinear analyses of concrete structures. Due to the fact that the mechanical behavior of concrete exhibits remarkable randomness, the probabilistic modeling of the key parameters of the concrete constitutive model is of paramount significance. In the present study, a two-level probabilistic model is proposed to describe the dependent random constitutive parameters based on the compressive test results of several batches of concrete specimens of different strength grades. Both the local probabilistic dependence, i.e., the dependence of the parameters of intra-batch specimens, and the global probabilistic dependence, i.e., the dependence of the parameters of inter-batch specimens, are captured by the proposed method. To this end, the constitutive parameters of concrete are first standardized by their means and coefficients of variation (COVs). In this way, the local dependence can be represented by the same copula model for the concrete of different strength grades. The global dependence is expressed as the empirical formulae in terms of the means and COVs of the parameters. The full probabilistic model can then be obtained by synthesizing the local and global dependence models. The effectiveness of the proposed approach is demonstrated by comparing the generated samples with the test results. To illustrate the effect of the probabilistic dependence of the compressive constitutive parameters on the structural evaluation result, the nonlinear stochastic dynamic response analysis of a reinforced concrete frame is carried out. The results indicate that the probabilistic dependence of the constitutive parameters of concrete has a non-negligible effect on the structural response and reliability, and should be reasonably considered in practice.

Structural, spectral, and third-order nonlinear optical analysis of solution-grown allylammonium hydrogen oxalate hemihydrate crystal for laser applications

Structural, spectral, and third-order nonlinear optical analysis of solution-grown allylammonium hydrogen oxalate hemihydrate crystal for laser applications

Dynamic response analysis of nonlinear structures with hybrid uncertainties

The physical systems of nonlinear structural dynamics are usually expressed mathematically as ordinary differential equations. When hybrid uncertainties are in the system, it is necessary to understand the effects of uncertainties in the system response to accurately predict its behavior using mathematical models. To address the hybrid uncertainty of random and interval parameters often encountered in engineering applications, we propose the nonlinear structural dynamics analysis with hybrid uncertainty (NSDAHU) method. The expressions for calculating the statistical characteristics (i.e., mean and variance) of nonlinear structural dynamic responses with hybrid uncertainties are derived using random interval moment and random interval perturbation methods. The applicability, accuracy, and efficiency of the NSDAHU method are verified using Monte Carlo simulation method (MCSM). The NSDAHU method can not only solve hybrid random interval problems but also solve single interval, single random, and linear structural dynamics problems.

A Mathematical Model for Non-Linear Structural Analysis Reinforced Beams of Composite Materials

The beams are frequently utilized in construction as well as in the fabrication of vehicles like as trains, ships, and airplanes. Depending on the necessary working circumstances, several materials may have been utilized in the production of these beams, from high fatigue resistance, high corrosion resistance, strong earthquake resistance, and other aspects. As a result, composite beams made of glass or carbon fibers are increasingly commonly employed. This is a result of its strong collapse resistance, light weight, and strong fatigue stress resistance. In order to compare the models' resistance to deformations, stresses, and strains that they are exposed to during loading, this article focuses on constructing a variety of models using a variety of composite materials and shapes. The outcomes demonstrate a rise in the rate of deformation. against beams with linear shapes in those with non-linear shapes. Additionally, the findings demonstrate an increase in stresses and strains in regions with curves (i.e., areas that are nonlinear).