Random Structural Responses Research Articles

Fatigue Crack Propagation Life of Metallic Materials Under Random Loading: A Coupling Analysis Method in the Frequency Domain

ABSTRACTThis paper proposes an equivalent spectrum method to predict the fatigue crack propagation (FCP) life of metallic materials subjected to random loading. To adequately account for the coupling effects between crack propagation and the random response of structures, a coupling analysis model is introduced. The stress intensity factor (SIF) can be estimated based on the power spectral density (PSD) of an equivalent displacement. Random vibration fatigue tests were conducted to evaluate the proposed model on aluminum alloy specimens. Results indicate significant variations in natural frequency with crack length. The predicted results are compared with the experimental values, demonstrating satisfactory prediction accuracy of the proposed coupling analysis model. This model enables the assessment of coupling effects between crack length and random response, facilitating more precise predictions of FCP life in metallic materials and guiding the expanded application of damage tolerance criteria in structural engineering.

Suppressing random response of structure via inertial nonlinear energy sink

Suppressing random response of structure via inertial nonlinear energy sink

Design for Random Response of Structures Subject to Rhythmic Crowd Loading

Overall, this paper provides a comprehensive approach for designing structures subject to rhythmic crowd loading. By considering the randomness of the load model and structural response, the design method provides a more realistic evaluation of the structure’s performance. The establishment of links between the deterministic individual loading and the random crowd loading simplifies the calculation process and makes it more practical for real-world applications. The use of reduction factors based on experimentally determined standard deviations ensures that the design method provides a lower bound for the expected response of the structure. The consideration of the involvement of an infinite number of people in the reduction factors adds an additional level of conservatism to the design, further ensuring the safety of the structure. The examples provided illustrate the effectiveness of the design method in evaluating the maximum displacements and accelerations of a floor structure subjected to rhythmic crowd loading. Overall, the paper provides a valuable contribution to the field of structural engineering by providing a practical and realistic approach for designing structures subject to rhythmic crowd loading.

Random finite element analysis of a clay-core-wall rockfill dam considering three-dimensional conditional random fields of soil parameters

Structural reliability and safety have been investigated using the random finite element method (RFEM) based on conditional random field (RF) by many researchers. However, the constraint RFEM has not been studied sufficiently to assess its influences on dam structural behaviours, especially in clay-core-wall rockfill dams. In this study, based on Kriging theory and in-situ measurements, a method is applied for constructing conditional RFs of dam material parameters. The results demonstrate that conditional RF has little effect on the mean values of maximum settlement, maximum deformation gradient and hydraulic fracture area ratio; relative to the unconditional simulations, the relative differences are 1%, 3%, and 7%, respectively. By establishing an effective Kriging estimation, the standard deviations of conditional maximum settlement, maximum deformation gradient and hydraulic fracture area ratio are relatively reduced by 16%, 4%, and 24%, respectively. Thus, the conditional simulation can provide more accurate security estimations for the cumulative probabilities of the structural responses. Measurement layout has a great effect on variation accuracy of random structural responses. The measurements should be taken near the locations of the structural behaviours of interest so that the conditional RFs can more accurately represent the spatial variability of soil properties and reduce simulation variation.

High dimensional model representation for flood fragility analysis of highway bridge

Climate changes and global warming have increased the frequency and severity of rains, hence the vulnerability of structures due to floods. Bridges are the most affected components of the transportation infrastructure affected by floods. Analysis in a probabilistic framework is required for reliable performance assessments of bridges. However, the detailed performance assessment of bridges requires consideration of the uncertainties in geometry, material properties, and flood loading. The random structural responses due to flood loading can be obtained by stochastic analysis; conventionally, this is carried out using Monte Carlo Simulations (MCS). Due to the high computational cost required for MCS, non-statistical methods like High Dimensional Model Representation (HDMR) can be a feasible alternative to MCS. The present study is an application of the HDMR method to develop metamodels for the flood response of the highway bridge, considering the uncertainties. The structural responses due to flood at the sampling points of the HDMR are obtained by conducting finite element analysis. The HDMR could predict the random bridge responses due to flood loading fairly well compared to other popular response surface methods (like Central Composite Design, Box Behnken Design, and Full Factorial Design) with significantly fewer simulations. HDMR provides a flood response metamodel, as a function of the sensitive random parameters, with a substantial reduction in the computational effort. The efficiency of the HDMR method can be attributed to the ability of HDMR to model the nonlinear flood responses in terms of the statistical properties of random variables. The metamodels for the pier drifts developed are further utilized to generate flood fragility curves. The HDMR metamodels are found to simplify the fragility computations.

Stochastic power spectra models for typhoon and non-typhoon winds: A data-driven algorithm

The shape of power spectra both for typhoon and non-typhoon winds directly affect the response level of the structure. The conventional deterministic spectrum models fail to reproduce the randomness of the structure response and could underestimate the real vibration amplitudes, especially for typhoon winds featured with stronger gustiness due to internal circulation and thermodynamic effects. Based on long-term observation data captured by the structural health monitoring system installed at Xihoumen suspension bridge, the parameters of wind power spectra in along-wind, cross-wind and vertical directions for typhoon and non-typhoon winds are extracted, respectively. The statistical characteristics and correlations among these parameters are examined. The data-driven stochastic power spectra models are then proposed by utilizing the moment-based theoretical solutions and Monte Carlo technique, respectively. The mean wind speed is incorporated in these models which allows the random simulations of power spectra with respect to different mean wind speeds. The proposed stochastic model is finally applied to generate a large number of wind power spectra adapted to the mean extreme wind speed return period curves in typhoon and non-typhoon mixed climates. It is suggested that the present stochastic power spectra model can be applied to estimate the random response of structures at different return periods due to typhoon and non-typhoon winds, which can be extended to conduct the performance-based design and uniform-risk-based design of structures in wind engineering.

A hybrid method for analysing stationary random vibration of structures with uncertain parameters

This paper presents a new hybrid polynomial dimensional decomposition-pseudo excitation method (PDD-PEM) for analysing stationary random vibration of structures with uncertain parameters. The power spectral density (PSD) of the structural random response is expressed as a function of uncertain parameters using the PEM and a finite hierarchical expansion is performed using the component functions of the PDD. The component functions are then represented by approximate Fourier-polynomial expansions with orthonormal polynomial bases and expressions are given for calculating the first two moments of the PSD of random structural responses, using the coefficients of the expansion. Considering that calculating the coefficients requires difficult multi-dimensional integration, a dimension-reduction integration method and a Gaussian numerical integration method are introduced to effectively reduce the computational efforts of the calculation of the coefficients. The results of five numerical examples indicate that the proposed method is nearly as accurate as but more efficient than the Monte Carlo simulation method.

Interval spectral stochastic finite element analysis of structures with aggregation of random field and bounded parameters

SummaryThis paper presents the study on non‐deterministic problems of structures with a mixture of random field and interval material properties under uncertain‐but‐bounded forces. Probabilistic framework is extended to handle the mixed uncertainties from structural parameters and loads by incorporating interval algorithms into spectral stochastic finite element method. Random interval formulations are developed based on K–L expansion and polynomial chaos accommodating the random field Young's modulus, interval Poisson's ratios and bounded applied forces. Numerical characteristics including mean value and standard deviation of the interval random structural responses are consequently obtained as intervals rather than deterministic values. The randomised low‐discrepancy sequences initialized particles and high‐order nonlinear inertia weight with multi‐dimensional parameters are employed to determine the change ranges of statistical moments of the random interval structural responses. The bounded probability density and cumulative distribution of the interval random response are then visualised. The feasibility, efficiency and usefulness of the proposed interval spectral stochastic finite element method are illustrated by three numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

Use of the random decrement technique for nondestructive detection of damage to beams

The random decrement (RD) technique is a time-domain procedure in which the random structural response under service loads is transformed into the free decay response. The RD technique is used for monitoring and determining structural performance, being able to predict damage and handle the occurrence of sudden failures during operation of the structure. The technique is considered a unique method for nondestructive testing. The RD signature can be utilized as a damage indicator. The technique is based on output measurements, whereas both input and output measurements are required for other, traditional methods commonly used in aerospace and mechanical engineering, including frequency- and time-domain methods such as the frequency response function and state equation. In civil engineering, input excitation forces such as wind, earthquake, and traffic loads are often hard to determine. The RD technique determines the changes of the structure’s dynamic parameters according to external forces without knowledge of the magnitude of the excitation forces. The method is already considered efficient for detecting damage to steel structural members, so the current study focuses on use of the RD technique to determine dynamic parameters for reinforced-concrete (RC) members and explores the possibility of determining the presence of damage and its location. The main focus of this research work is assessment of the suitability of RD for monitoring RC beams. Two laboratory investigations were performed to determine the applicability of the RD technique for RC members and compare the indication of damage using a random signature for RC and steel beams. The beams were excited randomly, then the response signals were detected and the dynamic response signature was calculated at each stage. The RC beam was subjected to damage by applying a concentrated load at its midpoint, while the steel beam was subjected to different structural damage ratios by cutting the cross section to 25, 50, and 75 % damage ratio using a mechanical saw. The natural frequencies and damping ratios were calculated for different applied loads on the RC beam and the steel beam for different damage ratios. The changes in the dynamic parameters of the structure were determined for both undamaged and damaged beams. The investigation indicates the role of the change in the random signature due to damage, which was detected for different damage ratios for steel and RC beams, also revealing the particular significance of this technique for small damage and cracks. The results indicate meaningful changes in damping values that enable detection of the level of damage for the RC beam. The RD technique provides a promising, efficient approach for determination of dynamic parameters for important structures.

Energy Density Prediction of Random Structures Using Perturbation Method

To predict energy density response of random structures using EFEM, a perturbation method was introduced into governing equations of energy density for one- and two-dimensional structures. Two equation sets governing the energy density response of random structures were obtained. Simulations were carried for a plate with random damping ratio and the energy density response was obtained. It can be seen that EFEM provides space- and frequency-averaged response. Comparing with probabilistic method, the governing equation sets provide the same mean response and a smaller response range. The perturbation method using in EFEM turns out an effective method with less uncertainty and a promising method for response prediction for random structures.

The Random Response Analysis of Structure Subjected to Non-Stationary Seismic Excitation

The evolutionary power spectrum which can reflect the non-stationary characteristics of earthquake ground motion is estimated by the Hilbert-Huang Transform (HHT), and with reference to the experiential statistical method, an evolutionary spectrum prediction model for given earthquake magnitude and distance is established based on the 121 near-source acceleration records at rock surface with large magnitude from the ground motion database of western U S. The pseudo excitation method is adopted to acquire the solution for structure random response under specific non-stationary seismic excitation. The results demonstrate that the non-stationary contents included in seismic excitation will enlarge greatly the random response of structure in comparison with uniform modulation random excitation.

The Random Response Analysis of Structure Subjected to Non-Stationary Seismic Excitation

The evolutionary power spectrum which can reflect the non-stationary characteristics of earthquake ground motion is estimated by the Hilbert-Huang Transform (HHT), and with reference to the experiential statistical method, an evolutionary spectrum prediction model for given earthquake magnitude and distance is established based on the 121 near-source acceleration records at rock surface with large magnitude from the ground motion database of western U S. The pseudo excitation method is adopted to acquire the solution for structure random response under specific non-stationary seismic excitation. The results demonstrate that the non-stationary contents included in seismic excitation will enlarge greatly the random response of structure in comparison with uniform modulation random excitation.

Random Response Analysis of Curvilinearly Stiffened Plates Using Element-Free Galerkin Method

An Element Free Galerkin (EFG) formulation is presented for studying the random response of curvilinearly-stiffened plates. The structure is subjected to stationary random stochastic loading. The random loads are assumed as stationary in time but can be nonhomogeneous in space. The spectral density of the nodal force vector is formulated using the displacement shape functions. The direct complex matrix inversion method and modal superposition method are used to obtain the random response of structure. The spectral density of displacement for un-stiffened plate under white noise and plate with straight stiffeners subjected to jet noise are compared with those available in the literature. The power spectral density of displacement of curvilinearly-stiffened plate under white noise is also verified using the commercial finite element software ANSYS. Excellent agreement is seen in all cases. The effect of stiffener stiffness and curvature and in-plane load on spectral density of deflection of curvilinearly-stiffened plate is also investigated.

PDEM-Based Seismic Response Analysis of Structures

An orthogonal expansion method for earthquake ground motion was introduced in the first part of the paper. In the method, seismic acceleration process is represented as a linear combination of deterministic functions modulated by 10 uncorrelated random variables. In the second part of the paper, the recently developed probability density evolution method (PDEM) is employed to study linear random response of structures subjected to the external excitations. In the PDEM, a completely uncoupled one-dimensional governing partial differential equation, the generalized density evolution equation, is derived first with regard to evolutionary probability density function of the stochastic response for nonlinear structures. The solution of this equation can put out the instantaneous probability density function. So it is natural to combine the PDEM and the orthogonal expansion of seismic ground motion to study the linear random earthquake response. Finally, combining an example of a linear frame structure subjected to non-stationary ground motions, this paper validate the proposed approach and expounds the application of this method.

Prediction of uncertain structural behaviour and robust design

Robust design of structures presupposes the prediction of time-dependent structural behaviour and the quantitative assessment of robustness. Thereby, the uncertainty has to be considered by means of adequate data models selected in accordance with the available information. On the basis of the generalised uncertainty model fuzzy randomness, model-based, model-free and hybrid approaches for the prediction of uncertain structural behaviour are presented in this paper. The introduced robustness measure is capable to assess the robustness under consideration of fuzzy random structural responses.

Moving force identification based on stochastic finite element model

Abstract A moving force identification technique based on a statistical system model is developed in this paper. Karhunen–Loeve expansion is employed to represent both the random forces and system parameters which are assumed to be Gaussian distributed with the bridge–vehicle system as the background of study. Road surface roughness is a main contributor to the randomness in the moving force. A statistical relationship between the random moving force and the random structural responses is established basing on which a general stochastic force identification algorithm is formulated. Numerical simulations are given to verify the proposed algorithm and to quantify the error which arises at different stages of the identification. Case studies including the effect of number of samples and the level of randomness are conducted to check on the robustness of the proposed algorithm. Results show that the assumptions made in the identification are appropriate and the proposed Stochastic Force Identification algorithm is effective.

Exact and numerical responses of a plate under a turbulent boundary layer excitation

The aim of this paper is the analysis of the predictive capabilities of the deterministic methodologies when facing the problem of a plate excited by a stochastic pressure distribution due to a turbulent boundary layer (TBL). A full analytical solution has been assembled by considering a simply supported rectangular plate wetted on one side by a TBL. This reference exact solution, developed by using a standard separable variable model, has been used as test case for comparing the approximate solutions coming from the adoption of a numerical scheme by using discrete coordinates. The numerical algorithm has been built by using a standard finite element modal approach. The approximations introduced are thoroughly discussed and analysed; they refer to the meshing condition and the transformation of the distributed stochastic load. The application of a novel numerical procedure named as Asymptotical Scaled Modal Analysis is presented too. This innovative numerical scheme allows the analysis of the structural response of a generic plane operator in the whole frequency range, which is not always amenable by exact solutions; further and equally important, it is associated to a reduction of the computational cost. The work demonstrates that some numerical advances in the prediction of the random structural responses are feasible still using standard finite element modal inputs, without increasing the computational costs.

Spectral stochastic analysis of structures with uncertain parameters

We present a probabilistic analysis of a structure with uncertain parameters subject to arbitrary stochastic excitations in a frequency domain. The problem of stochastic dynamic analysis of a linear system in a frequency domain is formulated by taking into consideration the uncertainty of structural parameters. The solution is based on the idea of a random frequency response vector for stationary input excitation and a transient random frequency response vector for nonstationary one which are used in the context of spectral analysis in order to determine the influence of structural uncertainty on the random response of structure. The numerical spectral analysis of the building structure under wind and earthquake excitation is provided to demonstrate the described algorithms in the context of computer implementation.

A complementary note on Gegenbauer polynomial approximation for random response problem of stochastic structure

Recently, Gegenbauer polynomial approximation was proposed for solving the evolutionary random response problem of a random structure with bounded random parameters under evolutionary random excitations. The bounded random parameters used there are supposed to be proportional to a random variable with λ -PDF (probability density function). For this kind of random parameter, the Gegenbauer polynomial approximation is the unique correct choice for transforming a random structure into its deterministic equivalent system, which plays a central role in solving the response problem. Actually, the Gegenbauer polynomial approximation bridges the gap between the random structural response problem and the conventional methods. Just through its deterministic equivalent system, the random response problem of a random structure can be solved by any available, analytical and numerical method developed for deterministic systems. But the simple assumption on proportionality to λ -PDF may bring some unnecessary limitation on symmetry. Since λ -PDF is symmetrical about its center axis, so are these random parameters. However, not all random parameters have this kind of symmetry. Then, what can we do to lessen the limitation, if random parameters are non-symmetric per se? Besides, the graph of λ -PDF (see Fig. 1 in the text) shows its features’ dependence on λ , that is, the smaller the λ , the more dispersive the PDF. Then, what is the influence of different values of λ on the evolutionary random responses of the stochastic system? Moreover, is there any qualitative information about the dispersion in response with respect to every individual random parameter? This note is devoted to answering the above two questions and giving a supplementary note on Gegenbauer polynomial approximation. Our study shows that the symmetric limitation can be partly lessened by putting the random parameter into a polynomial function, even a quadratic one, of a random variable with λ -PDF. On the other hand, the second-order moment of the random responses of the stochastic structure relative to that of a nominal one can be used to describe qualitatively their relative dispersion with respect to each individual random parameter.

The random structural response due to a turbulent boundary layer excitation

In this paper, the structural random response due to the turbulent boundary layer excitation is investigated. Using the mode shapes and natural frequencies of an undamped structural operator, a fully analytical model has been assembled. The auto and cross-spectral densities of kinematic quantities are so determined through exact analytical expansions. In order to reduce the computational costs associated with the needed number of modes, it has been tested an innovative methodology based on a scaling procedure. In fact, by using a reduced spatial domain and defining accordingly an augmented artificial damping, it is possible to get the same energy response with reduced computational costs. The item to be checked was the power spectral density of the displacement response for a flexural simply supported beam; the very simple structure was selected just to highlight the main characteristics of the technique. In principle, it can be applied successfully to any quantity derived from the modal operators. The criterion and the rule of scaling the domain are also presented, investigated and discussed. The obtained results are encouraging and they allow thinking successfully to the definition of procedure that could represent a bridge between modal and energy methods.