Nonlinear Structural Analysis Research Articles

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).

A Cartesian spatial discretization method for nonlinear dynamic modeling and vibration analysis of tensegrity structures

For vibration analysis of a tensegrity structure, the development of a dynamic model is a key step. A common issue in the traditional dynamic modeling methods for vibration analysis of tensegrity structures is that structural members are oversimplified. Member internal displacements, including those in longitudinal directions for bar and cable members and those in transverse directions for cable members, were neglected. This oversimplification would inevitably prevent the dynamic model of a tensegrity structure so developed from revealing accurate responses, especially for those in the high-frequency domain. To resolve this issue, a new method called the Cartesian spatial discretization method is developed for nonlinear dynamic modeling and vibration analysis of tensegrity structures. This method can successfully incorporate member internal displacements in dynamic modeling of a tensegrity structure by defining positions of structural members as a summation of internal terms and boundary-induced terms in a global Cartesian coordinate system. The proposed method is applied to vibration analysis of a planar Snelson’s X tensegrity structure, a three-dimensional tensegrity tower, and an irregular tensegrity grid in simulation, and compared with the Lagrangian method based on generalized coordinates, the commercial finite element analysis software ANSYS and the finite element analysis method in literatures, respectively. Results show that the proposed method is accurate in predicting dynamic responses of tensegrity structures, especially for vibration analysis in the high-frequency domain. It is also demonstrated that the proposed method is applicable to both simple and complex tensegrity structures, and computationally efficient as it converges in a super-linear rate by using only a small number of internal terms of member displacements.

SHAKER: A selector of consistent and energetically equalized natural ground motions using the Italian earthquake database

Input motion set selection for nonlinear dynamic structural analysis is commonly based on spectral compatibility, obtained through the uniform scaling of natural signals. Due to the aleatory nature of the expected time history, alone spectral compatibility requirement appears very weak to guarantee scaled ground motions that suit local seismic hazard. Magnitude-Distance interval pairs to control selection and scaling factor thresholds do not always provide input motions with adequate energy levels. In order to tackle these critical issues, a novel computer-aided selection method based on consistency analysis to provide conservative energy levels has been developed. The method equalizes the ground motions subject to the spectral compatibility process to the modified Housner Intensity of the hazard spectra. A multi-parametric consistency analysis based on statistic confidence is performed on the equalized (by uniform scaling) ground motion set by comparing it with the larger regional natural dataset on the same Magnitude-Distance pairs. The consistency analysis involves multiple ground motion parameters taken into relation with the focal mechanism too. Sensitivity tests show the capability of the method to reach high spectral compatibility joined with high consistency degrees by multi-parametric calibration. Compared with the traditional ones, this method also shows greater performance in composing ground motion sets close to real occurrences with a more assorted spectral frequency distribution.

3D printing concrete with recycled sand: The influence mechanism of extruded pore defects on constitutive relationship

Recycled sand (RS) as an environmental-friendly building material, has shown great prospects for the digital construction of buildings. In this study, 3D printed recycled sand concrete (3DPRSC) mixed with RS was prepared, and the related compressive strength and constitutive relationships were investigated on different RS replacement ratios and construction methods. The geometric characteristics and spatial distribution of pore defects were analyzed by the combined X-CT and MIP, and the microscopic morphology of RS and natural sand was analyzed by SEM. The results showed that the compressive strength and constitutive curves have apparent anisotropic characteristics. With the increase in the RS replacement rate, the compressive strength tended to decrease. The ellipsoidal pore geometry's arrangement of 3DPRSC extruded pore defects differs in different printing directions, and the pore defect distribution characteristics vary with the accumulated height of the filaments and the printing direction. The mechanism of the formation and distribution of extruded pore defects on the compressive strength and constitutive relationship was analyzed, and a model of the constitutive curve based on extruded pore defects and anisotropy was established, which provided a theoretical basis for the nonlinear analysis of the engineering structure of 3DPRSC.

Nonlinear dynamic thermal-mechanical behaviors of framed structures under temperature variations

An abnormal change in dynamic characteristics is considered an indicator of structural damage and can help the optimal design of structures suffering from dynamic loads, but these characteristics are also affected by ambient temperature. Therefore, a novel advanced computational method based on the fiber-based approach is proposed for the first time to predict the nonlinear dynamic behaviors of frames under environmental temperature changes with linear and nonlinear profiles by using Fortran programming language. The cross-section will be divided into a matrix of fibers, and by assigning the different temperatures to each fiber, all linear and nonlinear temperature gradients in both vertical and horizontal directions will be operated. The material nonlinearity is traced by the distributed plasticity model using the same mesh as the fiber-based approach whereas the effects of geometric nonlinearity due to member curvature and member chord rotation are considered by using the stability functions and a geometric matrix, respectively. A sequential nonlinear thermal incremental-iterative solution scheme based on the Newton-Raphson algorithm and Newmark-β method is also developed to address the nonlinear dynamic problems due to temperature variations. The accuracy and computational performance of the proposed method are validated by comparing the obtained results with those from experiments and the Abaqus. Results obtained show that the proposed method is exact for the nonlinear inelastic dynamic thermo-mechanical analysis of framed structures. It would offer a tool for thermal-structural design practice instead of using time and cost-consuming commercial software.

Cross-Sectional Shape Optimization of Cylindrical Elastomer Spring for Sensitive Cargo Container

High-value sensitive cargoes are often damaged by low-frequency vibration and shock of containers during land and rail transport processes or mixed transport processes. Therefore, a dedicated cylindrical elastomer spring that absorbs vibration transmitted into the container has been developed. This study developed an optimal shape using a polyurethane material instead of the existing rubber spring. Elastomer spring requires an optimal design that satisfies the design target stiffness and strength by nonlinear finite element analysis. In order to develop an elastomer spring for a cargo container, the material constant was obtained by a hyperelastic behavior test of natural rubber, and based on this, the necessary optimal material constant of the new spring was predicted. In addition, nonlinear structural analysis was performed using ABAQUS to obtain the optimal shape of the spring, and optimal design was performed with I-SIGHT software. As a result of the sum of squared difference minimization with the comparison algorithm, it was found that the polyurethane material constant C10, C20, and C30 with the same characteristics as natural rubber was obtained. In addition, analysis using three optimization algorithms, Hooke–Jeeves algorithm, multi-island genetic algorithm, and optimal Latin hypercube, yielded a maximum principal strain of 0.244 of the spring obtained through the optimal cross-sectional shape design. It was found that this value was about 39% lower than the natural rubber spring in use. As a result of the compression load-displacement test of the actually developed product, it was confirmed that the correlation coefficient between the predicted value and the measured value was 0.928.

An Accurate, Controllably Dissipative, Unconditionally Stable Three-Sub-Step Method for Nonlinear Dynamic Analysis of Structures

An implicit truly self-starting time integration method for nonlinear structural dynamical systems is developed in this paper. The proposed method possesses unconditional stability, second-order accuracy, and controllable dissipation, and it has no overshoots. The well-known BN-stability theory is employed in the design of algorithmic parameters, ensuring that the proposed method can stably solve nonlinear structural dynamical systems without restricting the time step size. The spectral analysis shows that compared to existing second-order accurate time integration methods, the proposed method enjoys a considerable advantage in low-frequency accuracy. For nonlinear problems where the currently popular Generalized-[Formula: see text] method and [Formula: see text]-Bathe method fail, the proposed method shows strong stability and accuracy. Further, for nonlinear problems in which all methods’ results are convergent, the proposed method has greater accuracy, efficiency, and energy-conservation capability.

Determination of the change in the structural performance of an RC building due to a nearby deep excavation

In this study, the structural performance of an existing thirteen-story reinforced concrete building is evaluated and compared to the case caused by the ground motion due to a nearby deep excavation. Accordingly, the effects of this event on structural safety emerge. First of all, the structural system details, geometry, layout, and material properties of the existing building are determined by field surveys and laboratory studies. Secondly, the structure is modelled with finite element software, and nonlinear structural analyses are carried out with pushover analyses, taking into account various loading conditions, which consist of four cases: vertical and seismic loading with and without ground displacements caused by the event. The nonlinear behaviour is defined, and deformation values in the cross-sections of the structural elements are obtained by using fiber hinges in vertical structural elements and lumped hinges on the beams. Finally, the seismic performance levels of the building are found before and after excavation, taking into account the latest Turkish Building Earthquake Code (TBEC 2018). This case study provides a methodology for engineering practice in evaluating the structural performance and modelling of reinforced concrete (RC) buildings affected by a similar deep excavation event.