Response Analysis Of Nonlinear Structures Research Articles

Simulation of soil-structure interaction using inelasticity-separated finite element method

The soil–structure interaction (SSI) effect is nonnegligible during the nonlinear seismic response analysis of large-scale or underground structures. However, the computation of nonlinear response of a structure considering SSI effect usually is a time-consuming process because the numerical model should involve the structure itself, a wide-range soil domain and the soil–structure interface, especially for large-scale structure. This study aims to incorporate the inelasticity-separated finite element method (IS-FEM), which is an algorithm recently developed for efficient structural nonlinear analysis, to improve the efficiency of the soil-structure interaction system. To this end, an inelasticity-separated contact element model for modeling the nonlinear behavior of soil and structure interface is developed in this study. To derive the inelasticity-separated governing equation of this model, a reference elastic stiffness is defined so that the normal and shear deformation of any point pair in the presented contact element is decomposed into reference linear and reference nonlinear parts according to this reference elastic stiffness. As a result, the problem of inconsistency between the requirement of IS-FEM for constant initial linear elastic stiffness and the existence of inflection point for the stress versus relative displacement relationship of contact behavior can be solved. Then, the Goodman element formulation for depicting the nonlinear contact behavior is introduced and an interpolation scheme to establish the reference nonlinear deformation field in an element is incorporated. By combining the proposed model with existing inelasticity-separated elements, a global analytical model of the soil–structure interaction system can be established within the framework of IS-FEM. Because the nonlinearity usually occur in some local regions of the global model and the use of the IS-FEM only require performing these operations for a small scale matrix representing local nonlinearity, the computational efficiency of nonlinear structural response analysis considering SSI effect can be improved significantly. The applicability and efficiency of the proposed method is finally verified by two numerical examples.

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.

An approach of dynamic response analysis of nonlinear structures based on least square Volterra kernel function identification

Abstract Analysis of the dynamic response of a complex nonlinear system is always a difficult problem. By using Volterra functional series to describe a nonlinear system, its response analysis can be similar to using Fourier/Laplace transform and linear transfer function method to analyse a linear system's response. In this paper, a dynamic response analysis method for nonlinear systems based on Volterra series is developed. Firstly, the recursive formula of the least square method is established to solve the Volterra kernel function vector, and the corresponding MATLAB programme is compiled. Then, the Volterra kernel vector corresponding to the nonlinear response of a structure under seismic excitation is identified, and the accuracy and applicability of using the kernel vector to predict the response of a nonlinear structure are analysed. The results show that the Volterra kernel function identified by the derived recursive formula can accurately describe the nonlinear response characteristics of a structure under an excitation. For a general nonlinear system, the first three order Volterra kernel function can relatively accurately express its nonlinear response characteristics. In addition, the obtained Volterra kernel function can be used to accurately predict the nonlinear response of a structure under the similar type of dynamic load.

Random response analysis of nonlinear structures with inerter system

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

Determination and application of path duration of seismic ground motions based on the K-NET data in Sagami Bay, Japan

Duration models are one of the important parameters in ground-motion simulations. This model varies in different study areas, and plays a critical role in nonlinear structural response analysis. Currently, available empirical models are being globally used in ground-motion simulations, with limited research focusing on path duration in specific regions. In this study, we collected 6,486 sets of three-component strong-motion records from 29 K-NET stations in the Sagami Bay, Japan, and its surrounding areas between January 2000 to October 2018. We extracted the effective duration of 386 pieces of ground-motion records by manually picking up the S-wave arrival time and calculating the significant duration. We then obtained the path duration model of the study area based on the empirical equation of dynamic corner frequency and source duration of [7]. Compared with the results of the available empirical models, the Fourier spectrum of the simulated ground motion from our effective duration model showed higher accuracy in the long-term range, with less fitting residuals. This path duration model was then applied to simulate two earthquakes of MW5.4 and MW6.2, respectively, in the region using the stochastic finite-fault method with a set of reliable source, path, and site parameters determined for the study area. The simulation results of most stations fit well with observation records in the 0–30 Hz frequency band. For the MW5.4 earthquake, the simulated ground motions at KNG005/KNG010/SZO008 stations were relatively weak in the mid to high frequency band (1–30 Hz) because the quality factor and geometric diffusion model used in the simulation were the averages of the entire Sagami Bay region, causing a bias in the results of a few stations owing to local crustal velocity anomalies and topographic effects. For the MW6.2 earthquake, the simulated ground motions were relatively weak at all SZO and TKY stations, mainly because of the close distance from these stations to the epicenter and the complex seismic-wave propagation paths. The analysis suggests that the differences between the simulation results of the two earthquakes were mainly related to complex geological conditions and seismic-wave propagation paths.

Machine learning accelerated transient analysis of stochastic nonlinear structures

This paper presents a non-intrusive surrogate modeling scheme for transient response analysis of nonlinear structures involving random parameters. The proposed scheme utilizes a two-level neural network architecture as a surrogate model. Specifically, it combines feed-forward neural networks with convolutional autoencoders to deliver a highly accurate and inexpensive emulator of the structural system under investigation. The surrogate is built upon an initial set of full model evaluations, which are performed for a small, yet sufficient number of parameter values and serve as the training data set. For each type of degree of freedom in the structural problem, a convolutional autoencoder is trained over the corresponding solution matrices in order to obtain a low-dimensional vector representation through its encoder and a reconstruction map by the decoder. Subsequently, a feed forward neural network is efficiently trained to map points from the problem’s parametric space to the latent space given by the encoder, which can be further mapped to the actual, high-dimensional, system responses by the decoder mapping. The proposed surrogate is capable of predicting the entire time history response almost instantaneously and with remarkable accuracy, despite the nonlinearities present in the system’s response. The elaborated methodology is demonstrated on the stochastic nonlinear transient analysis of single and multiple degree of freedom structural systems.

An Approach for Geometrically Nonlinear Topology Optimization Using Moving Wide-Bézier Components With Constrained Ends

Abstract Standard moving morphable component (MMC)-based topology optimization methods use free components with explicitly geometrical parameters as design units to obtain the optimal structural topology by moving, deforming, and covering such components. In this study, we intend to present a method for geometrically nonlinear explicit topology optimization using moving wide-Bézier components with constrained ends. Not only can the method efficiently avoid the convergence issues associated with nonlinear structural response analysis, but it can also alleviate the component disconnection issues associated with the standard MMC-based topology optimization methods. The numerical investigations proposed in this work indicate that the proposed method allows us to obtain results in accordance with the current literature with a more stable optimization process. In addition, the proposed method can easily achieve minimum length scale control without adding constraints.

An Equivalent Damping Numerical Prediction Method for the Ring Damper Used in Gears under Axial Vibration

In aircraft gas turbine engines, gears in the transmission system are typically cyclic in structure and inevitably encounter large dynamic loads, such as meshing excitation, resulting in high vibration loads in resonance. To prevent gear resonance failure, a ring damper is employed to reduce the resonance response. As relative motion between the gear and the ring damper occurs, vibration loads can be reduced by friction energy dissipation. Moreover, the gears in the aircraft engine are thin-walled and their axial stiffness is much smaller than radial stiffness; thus, it is easier for axial vibration to cause resonance failure. This paper proposes an equivalent damping numerical prediction method for a ring damper under axial vibration, which greatly shortens the calculation time and prevents the forced response analysis of nonlinear structures. Via this method, the influence of ring damper structural parameters on friction damping in gears under axial vibration is investigated. The results indicate that the friction coefficient and mass of the ring damper have a great influence on damping performance.

Multi-fidelity uncertainty quantification method with application to nonlinear structural response analysis

• A multi-fidelity method is proposed for statistical moment calculations of nonlinear structural responses. • The proposed formulation requires only small numbers of high fidelity solution and simple statistical techniques. • High-cost material damage analysis can be limited in local areas without biasing results of uncertainty quantification . • A computational cost reduction of 52.7% has been achieved in the numerical example. The application of uncertainty quantification (UQ) in complex structural response analysis is limited by solution efficiency. A multi-fidelity (MF) method for UQ is proposed in this paper, in which statistical moments are first evaluated using low cost low-fidelity (LF) model first, and then calibrated with a small number of high-fidelity (HF) samples. Only the error distribution of LF solutions and the covariance between the errors and the LF solutions are employed to derive a simple and straight forward MF formulation. The proposed method is demonstrated in the UQ of damage analysis of a C/SiC plate with a hole, where the HF model is a nonlinear global model considering C/SiC material damage, and the LF model is a linear global model driven nonlinear sub model. Uncertainty propagation is carried out using a sparse polynomial chaos expansion method. Evaluations of the MF method based on four factors: correctness, efficiency, precision and reliability, are carried out. The results show that the MF method can estimate the statistical moments of nonlinear strain responses unbiasedly. Computational cost is reduced by 52.7% compared to that utilizing HF model alone. MF methods can reduce computational cost significantly while maintaining accuracy and can be used for wide range of applications.

A Prediction Method for the Damping Effect of Ring Dampers Applied to Thin-Walled Gears Based on Energy Method

In turbomachinery applications, thin-walled gears are cyclic symmetric structures and often subject to dynamic meshing loading which may result in high cycle fatigue (HCF) of the thin-walled gear. To avoid HCF failure, ring dampers are designed for gears to increase damping and reduce resonance amplitude. Ring dampers are installed in the groove. They are held in contact with the groove by normal pressure generated by interference or centrifugal force. Vibration energy is attenuated (converted to heat) by frictional force on the contact interface when the relative motion between ring dampers and gears takes place. In this article, a numerical method for the prediction of friction damping in thin-walled gears with ring dampers is proposed. The nonlinear damping due to the friction is expressed as equivalent mechanical damping in the form of vibration stress dependence. This method avoids the forced response analysis of nonlinear structures, thereby significantly reducing the time required for calculation. The validity of this numerical method is examined by a comparison with literature data. The method is applied to a thin-walled gear with a ring damper and the effect of design parameters on friction damping is studied. It is shown that the rotating speed, geometric size of ring dampers and friction coefficient significantly influence the damping performance.

Explicit structural topology optimization under finite deformation via Moving Morphable Void (MMV) approach

In the present work, we intend to show how to perform structural topology optimization under finite deformation with the use of explicit geometry description. To this end, a Moving Morphable Void (MMV)-based approach is developed. Compared to existing approaches in the literature, the advantages of the proposed method consist in the fact that it can not only reduce the number of design variables substantially, but also alleviate the convergence problems associated with nonlinear structural response analysis significantly. Furthermore, smooth structural boundaries with explicit B-spline descriptions, which are always desirable for CAD/CAE softwares, can also be obtained straightforwardly via this approach. Numerical examples provided demonstrate the effectiveness of the proposed approach.

Seismic response analysis of nonlinear structures with uncertain parameters under stochastic ground motions

An orthogonal expansion of stochastic ground motion model is incorporated into the probability density evolution method (PDEM). In this regard, a new methodology for seismic response analysis of nonlinear structures with uncertain parameters under stochastic ground motions can be formulated. The fundamentals and numerical algorithms of the methodology are introduced. Then, a rotational quasi-symmetrical point strategy (RQ-SPS) is developed for selecting the representative points in the random-variate space, which is of paramount importance to the tradeoff of accuracy and efficiency for the proposed methodology. An eight storey shear frame structure under seismic excitations, which exhibits strong nonlinear mechanical behaviors, is investigated. The effectiveness of the RQ-SPS is first verified, where the results by Monte Carlo simulations are also provided for comparisons. Then, case studies are implemented, in which the randomness involved in both stochastic ground motions and structural parameters are taken into account. The computational results demonstrate that the effect of randomness in structural parameters cannot be ignored compared to that in stochastic ground motions. Some features of the PDF evolutionary process of response are also discussed.

A Prototype Seismic Loss Assessment Tool Using Integrated Earthquake Simulation

This study develops a seismic loss assessment (SLA) tool incorporated with the Integrated Earthquake Simulation (IES) program for urban risk evaluation due to a scenario earthquake. This proposed SLA-IES tool uses a cost-effectiveness performance of physics-based models in IES, such as site amplification analysis and nonlinear structural response analysis, with soil boring and GIS data. In this study, Sendai City was selected as a case study for a prototype of the SLA-IES tool. For pre-processing, the tool was used to couple available raw data, such as building shape, building attribute, and soil boring data, and then generate input data for IES. For post-processing, this tool was used to translate output data from IES in order to obtain inter-story drift of each floor of each building. From inter-story drift, the SLA-IES tool evaluates damage state of a building, such as level I (none), level II (slight), level III (moderate), level IV (extensive), and level V (complete), for a scenario earthquake. Then, direct economic loss, such as repair cost, was estimated based on damage state and construction cost. The results of the SLA-IES tool were stored as a database of all individual buildings including damage level, repair cost, structural type (wooden, steel, reinforced concrete, and steel frame and reinforced concrete structures), and building occupancy (private, ordinary, office, and landmark buildings).

Probabilistic Seismic Hazard Analysis and Synthetic Ground Motion Generation for Seismic Risk Assessment of Structures in the Northeast India

This article outlines the performance-based seismic risk assessment (PBSRA) of structures requiring probabilistic seismic hazard analysis (PSHA) to obtain hazard curves and an evaluation of the demand model by a nonlinear structural response analysis under properly selected ground motion records. Unfortunately, such site-specific information is not readily available for Northeast region of India. The present study focuses on these two aspects to supplement the PBSRA. The estimations of hazard curves are demonstrated by considering the seismicity within 300 km radius around the considered locations and specified exposure period. Due to limited availability of natural records in this region, synthetic accelerograms are generated using stochastic point source models by identifying the most contributing magnitude distance combinations from disaggregation of the PSHA results. The significant variabilities observed in the estimated hazard, synthetic accelerograms and nonlinear building responses in the various locations indicate the need of explicit site-specific analysis for PBRSA of structures in the region.

A marginal fractional moments based strategy for points selection in seismic response analysis of nonlinear structures with uncertain parameters

The present paper proposes a new strategy for selecting representative points in the probability density evolution method (PDEM) to conduct stochastic seismic response analysis of nonlinear structures with uncertain parameters. In PDEM, the strategy for selecting representative points in random-variate space is of critical importance to the efficiency and accuracy. The proposed strategy is established based on the marginal fractional moments of input random variables, which can be evaluated both analytically and numerically without difficulty before performing stochastic analysis. In this strategy, an optimization problem is actually involved. First, the initial points are generated by a low discrepancy sequence and the corresponding assigned probabilities can be computed accordingly. Then, the initial points are rearranged to minimize the index, which is adopted as the maximum relative error between the estimated marginal moments and the exact ones. The rearranged points are accepted as the representative points in PDEM when the index reaches the prescribed tolerance. Numerical example is investigated, showing that the proposed strategy can achieve the good tradeoff of efficiency and accuracy in PDEM for seismic response analysis of structures with uncertain parameters.

해양플랜트 구조물의 화재 사고 시 PFP 효과를 고려한 비선형 구조응답 해석 기법에 대한 연구

해양플랜트 구조물의 화재 사고 시 PFP 효과를 고려한 비선형 구조응답 해석 기법에 대한 연구

Stochastic Response Analysis and Reliability Evaluation of Nonlinear Structures under Earthquake

The probability density evolution method (PDEM) for random earthquake response analysis of non-linear structure is constructed by incorporating orthogonal expansion method for earthquake ground motion into the PDEM. In this method, seismic acceleration process is represented as a linear combination of deterministic functions that are modulated by 10 uncorrelated random variables. The stochastic seismic response analysis and reliability evaluation of nonlinear structures under earthquake excitations will be successfully carried out if the above methods can be combined together. In order to validate the proposed method, the author takes a nonlinear frame structure subjected to ground motion as an example to illustrate it.

Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method (PDEM) is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

Discussion of “The effect of energy concentration of earthquake ground motions on the nonlinear response of RC structures” by H. Cao, M.I. Friswell

This discussion raises a few comments and questions on the paper by Cao and Friswell [Cao H, Friswell MI. The effect of energy concentration of earthquake ground motions on the nonlinear response of RC structures. Soil Dyn Earthquake Eng 2009; 29: 292–9.]. The authors consider an interesting problem on seismic response analysis of nonlinear structures. Specifically, the study examines the implication of the energy concentration of the adopted ground acceleration record on the nonlinear response of reinforced concrete structures. The paper employs the wavelet transform to characterize the energy content of the ground acceleration in time and frequency domains.

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density function (PDF) of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a frame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.