Journal of Engineering Mechanics

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer hardware. However, in certain use cases, such as uncertainty quantification or high precision real-time simulation, the computational cost remains a challenge. This necessitates the adoption of reduced-order modeling methods, which can reduce the computational toll of such nonlinear analyses. In this work, we propose a reduction scheme relying on the exploitation of an autoencoder as means to infer a latent space from output-only response data. This latent space, which in essence approximates the system’s nonlinear normal modes (NNMs), serves as an invertible reduction basis for the nonlinear system. The proposed machine learning framework is then complemented via the use of long short-term memory (LSTM) networks in the reduced space. These are used for creating a nonlinear reduced-order model (ROM) of the system, able to recreate the full system’s dynamic response under a known driving input.

This work presents a cell-based smoothed finite-element method (CS-FEM) for simulating strongly coupled non-Newtonian fluid–structure interactions. The governing equations of a Carreau-Yasuda fluid and an elastic solid are discretized by the CS-FEM, which softens all gradient-related terms. The stress equilibrium along the interface is also derived from the CS-FEM notion. After discussing a two-level mesh-updating strategy, the strong coupling between the two physical media is realized via the block Gauss-Seidel iterative procedure. Numerical examples are presented to demonstrate the performance of the proposed method.

A field-enriched finite-element method for simulating crack propagation and coalescence in geomaterials is proposed in this work. In the novel numerical method, the physical position of the crack is characterized by the field variables, and the propagation evolution of the crack is controlled by the fracture criterion. The field-enriched finite-element method is first verified by a benchmark example. Then, it is used to simulate crack initiation, propagation, and coalescence in the different configuration specimens under various loads. The numerical results show that the field-enriched finite-element method has the capability to efficiently simulate crack propagation and coalescence in geomaterials.

Hydraulic fracturing technology most often involves multiple fluids with different properties to achieve desired treatments. This study examines the effects of multiple sequential fluids on the stress, strain, and deformation fields in the near-tip region of a semi-infinite fracture. It is assumed that the immiscible displacement of multiple power-law fluids is separated by stable boundaries. The fracture opening of a steadily propagating hydraulic fracture is computed by solving the elasticity and lubrication equations. The numerical solution correctly captures the well-known asymptotic behavior at the crack tip for multiple fluids. Specifically, the multiple-fluids solution asymptotically approaches the solution for the first fluid in the immediate vicinity of the tip and approaches the solution corresponding to the last fluid far from the tip. In the transition region, the behavior depends on the presence of additional fluids and the locations of their respective boundaries. Illustrative results for multiple fluids with different properties and boundary locations are included.

Corrosion of metal in soils has been intensively investigated in the past. However, a review of the published literature shows that there are challenges for researchers to accurately predict the corrosion growth of buried pipes with spatial and temporal variations. This paper intends to develop a methodology to predict the corrosion pit growth for buried pipelines by thoroughly considering the spatial and temporal variability of corrosion processes. The developed method integrates the corrosion science, conditional random field theory, stochastic process, and copula method into an interrelated simulation algorithm for generating corrosion pit growth fields. It is found in the paper that the shape parameter and rate parameter of the gamma process, as well as the correlation structure of corrosion processes, are not only time-variant but also exhibit spatial variability with time. It is also found that the developed method is much superior to other methods in terms of accuracy and effectiveness. The proposed method considers the correlation between corrosion processes in a long pipeline, which is more practical. It can be concluded that generating an accurate corrosion growth field fully requires consideration of the spatial and temporal variability of model parameters.

A probabilistic model is devised for predicting the plastic hinge lengths (PHLs) of RC columns. Seven existing parametric models are evaluated first using a comprehensive database comprising PHL measurements from 133 RC column tests. It is observed that the performances of these seven models are fair (as opposed to strong), and their predictions bear significant uncertainties. A novel technique is devised to combine them into a weighted-average supermodel wherein the weights are determined via Bayesian inference. This approach naturally produces the weights’ statistical moments, and thus, the resulting model is a probabilistic one that is amenable for performance-based seismic design and assessment analyses. Prediction comparisons indicate that the proposed supermodel has a higher performance than all prior models. The new model is easily expandable should more test data become available.

This study investigated uncoupled crosswind and alongwind responses of base-isolated tall buildings under nonstationary wind excitations. The base isolation system has hysteretic restoring force characteristics represented in the Bouc–Wen model, while the upper building is modeled as a linear elastic multiple-degrees-of-freedom shear building. The nonstationary story wind forces are modeled in terms of evolutionary power spectra. Response time-history analysis was performed to characterize the response statistics including mean, standard deviation (STD), and extreme value. This work included an analytical solution of nonstationary time-varying response statistics. The time-varying mean of alongwind base displacement is determined from the solution of the state-space equation. The time-varying STDs of both alongwind and crosswind responses were estimated from the statistical linearization with Gaussian assumption combined with evolutionary spectra analysis. The numerical examples show that the transient effect of nonstationary excitations declines when yielding becomes significant, which leads to an increase in system damping. In the case of alongwind response, the transient effect on the time-varying mean of base displacement is more significant. This study not only presents an effective analytical approach but also sheds new insights toward improved understanding of inelastic responses of base-isolated tall buildings under nonstationary winds, contributing to a safer and more economical design of base-isolated tall buildings.

A fundamental materials failure theory is used to predict the angle of repose for granular solids. This long-existing classical problem is now solved. The solution only requires two properties: (1) the uniaxial compressive strength of the aggregate and (2) the effective grain size. There are no adjustable parameters. When subjected to the specified gravity field, the angle of repose $\theta$ between the free surface and the horizontal datum is uniquely determined. The results are compatible with observations existing in nature and with specific cases involving materials products in granular forms. The general failure theory is specialized to the limiting case of a cohesionless materials form in order to consummate the solution to the problem. The significance of this work for all isotropic materials failure problems is assessed in the final section.

In geotechnical engineering, it is challenging to construct a site-specific multivariate probability distribution model for soil/rock properties because the site-specific data are usually sparse and incomplete. In contrast, there are abundant generic soil/rock data in the literature for the construction of a generic multivariate probability distribution model, but this model is typically biased and/or imprecise for a specific site. A hybridization method has been proposed to combine these two sources of soil/rock data (site-specific data and a generic database) to produce a quasi-site-specific model, but this method is essentially heuristic. In the current paper, a more rational method that exploits the geologic origin of soil/rock data is proposed. There is a tendency for data to be more similar within a single site and less similar between sites. This is called site uniqueness in geotechnical engineering practice, but no data-driven methods exist to quantify this data feature currently. The hierarchical Bayesian model (HBM) is a natural model to exploit this group information. The grouping criterion can be site localization, soil/rock types, or others. This paper only studies the group criterion based on site localization. This means that a generic database is now viewed as a collection of data groups labeled by qualitative site labels. This site label does not contain any quantitative information such as GPS location, it merely demarcates each group as distinct. The novel contribution is the development of an efficient HBM with closed-form conditional probabilities based on suitably chosen conjugate priors that can handle multivariate, uncertain and unique, sparse, incomplete, and potentially corrupted (MUSIC) data containing site labels. Numerical comparisons between the hybridization method (which cannot incorporate group information) and HBM show that even the simple qualitative knowledge that data belong to a geographically constrained site can improve the estimation of soil/rock properties. The GPS location of each site is not needed.

Mitigating losses from a storm surge requires an accurate prediction of its peak, duration, and current speed along the coastline. Because this prediction depends on varying atmospheric and oceanic conditions, the uncertainty of predicted values must also be evaluated. Sensitivity analysis can serve to assess how variations in storm parameters can impact the surge characteristics. Such analysis is usually performed by varying one of the parameters, e.g., central pressure, by a certain percentage while assuming all other parameters, e.g., radius of maximum wind and forward speed, constant. A more reliable sensitivity analysis can be obtained when performed together with stochastic analysis. Uncertainty quantification approaches that are based on polynomial approximations of the output values with respect to input parameters can be effectively implemented to provide output sensitivities to variations in input parameters. Towards that objective, we implement a nonintrusive polynomial chaos expansion to a series of idealized hurricane storm surge simulations to quantify the sensitivity of storm surge height, duration, and current speed to variations in hurricane parameters, including size, speed, and central pressure. Particular attention is paid to the spatial variation in the sensitivity of the surge height along the shoreline, which is not well investigated. Physical reasoning behind quantified sensitivities are discussed.

This research can be viewed as a development of the critical review of the Monasterio’s manuscript Nueva teórica sobre el empuje de bóvedas, proposed by the authors in previous studies; this unpublished manuscript is devoted to the collapse of nonsymmetric masonry arches, modeled as an assemblage of rigid voussoirs, infinitely resistant to compression, and characterized by nil strength to tension and finite friction. As its starting point, the current work examines the conditions identified by Monasterio for the activation of the pure sliding collapse mechanism: his approach is applied to a case study, i.e., a nonsymmetric arch of a given geometry, by showing some critical aspects related to the apparent independence of the collapse from the thickness of the arch. Thus, an alternative formulation based on an appositely developed mixed approach is proposed that allows for identifying under the hypothesis of finite friction some critical issues related to nonstandard behavior. This approach shows that the search for the various collapse mechanisms depends on the general equilibrium conditions of the arch, expressed as a function of the internal reactions—that is thrust and shear acting at the key joint—by extending Coulomb’s method of maximis and minimis to the case of nonsymmetric arches. The activation of the various collapse mechanisms—in particular those by pure sliding and mixed type—is therefore identified only after having determined the rotational equilibrium domain and its intersection with the sliding domain allowed by friction performance.

Previous studies based on the discrete-element method have pointed out that the evolution of fabric anisotropy plays a significant role in liquefaction, but current constitutive models of sand considering fabric anisotropy effects are not proficient at simulating the evolution of fabric anisotropy and its effect on liquefaction during cyclic undrained loading. This study proposes a unified elastoplastic model of sand to model the liquefaction-induced large deformation by incorporating the effects of fabric anisotropy evolution. The key point is to relate the evolution of fabric anisotropy to the octahedral plastic shear strain and to propose a new expression of the dilatancy coefficient considering fabric effects. In addition, an expression of the critical state line with relative density is presented, with a modified mapping rule based on bounding-surface theory for cyclic loading, and Bouc–Wen type elastoplasticity is introduced with a hardening exponent determined by fabric anisotropy. Moreover, an explicit adaptive Runge–Kutta–Fehlberg algorithm is adopted for numerical stability in the model implementation. The capacity of the proposed model to simulate the behavior of sand under monotonic and cyclic loading was validated against experimental data for three kinds of sand. The results demonstrated that the proposed model can predict not only liquefaction-induced large deformation but also the liquefaction resistance of sand with different relative densities.

The problem of vibrations of double-beam systems is of technological interest and has been extensively studied in the literature. However, a general solution is yet to be developed for the general boundary conditions. In this paper, a general solution of the free and forced vibrations of double-beam systems under classical, nonclassical, and mixed boundary conditions is derived. The obtained mode-shape solutions are exact and explicit. The characteristic frequency equation of a double-beam system is of order-4 and order-8 for the classical boundary conditions and the nonclassical boundary conditions, respectively. The solution of forced vibrations is developed with the classical modal expansion technique. In addition to the theory, applications of the proposed method are illustrated by numerical examples. The obtained frequencies for special problems are compared with the literature, and the agreement between the proposed method and the literature is remarkably good. This shows that the proposed shape function method may be applied reliably to determine the transverse vibration mode shapes and natural frequencies of the double-beam system under the general boundary conditions. The solutions of free and forced vibrations of the double-beam systems presented in the paper could easily be programmed into a computer for vibration analyses.

Presented in this study is a numerical analysis of the size effect in the transverse compressive strength of unidirectional (UD) composites by employing the fixed crack model. The model is calibrated and verified using available coupon level test data on transverse compression of a carbon-epoxy T700/MTM57 unidirectional composite. Then, it is used to predict the failure of geometrically scaled notched specimens of different sizes, each subjected to transverse compression. Two different notch orientations are considered. All specimens are predicted to fail in a geometrically similar fashion by an inclined shear crack starting from the notch tip. The predicted size effect in the nominal strength is fitted well by Bažant’s size effect law and is consistent with the estimated size of the fracture process zone. Thus, the results provide strong evidence for the applicability of quasi-brittle fracture mechanics in propagating transverse compressive failures in UD composites. Moreover, a strong anisotropy in the fracturing behavior, as well as the degree of quasi-brittleness, is demonstrated. Therefore, the findings emphasize the need for characterization of these effects via suitable experiments.

Many natural and human-made material systems (e.g., bone, shale, and cement-based composites) exhibit heterogeneous microstructures. Lattice models have reemerged to simulate such material systems because of their inherent simplicity while offering tremendous capabilities. However, current lattice models suffer from several deficiencies; for example, some lattice models cannot span the necessary range of Poisson’s ratio, some others are not isotropic (e.g., the standard square lattice), and others are not practical for complex domains (e.g., equilateral triangular lattice and hexagonal lattice). Thus, there is a need for a simple lattice that can handle Poisson’s ratio without any limitations, capture all the possible deformation modes of an isotropic elastic material, have minimal degrees-of-freedom, and provide positive definite stiffness and mass matrices. In this paper, we develop such a lattice model. Our approach hinges on equating the Lagrangians of the continuous (continuum) and discrete (lattice) systems, defining the strains consistently in terms of displacements in the lattice, adding a local interaction term to span the entire invariant space, and using an energy preserving time-stepping scheme. Using a Bloch wave analysis, we show that the lattice is, in fact, isotropic. Also, the lattice model does not suffer from volumetric locking, which is not the case with low-order finite elements. We verify the accuracy of the model using analytical solutions on benchmark problems. Finally, we demonstrate the application of the model on a practical example by performing propagation analysis in cement paste microstructure acquired from scanning electron microscopy (SEM).

The high-frequency force balance (HFFB) technique is commonly used in wind tunnels to investigate the wind loads and wind-induced responses of high-rise buildings. This paper presents a time-domain correction method for the signal distortion in HFFB tests, including the coupling effect among the balance components and the dynamic amplification of the balance-model system (BMS) on aerodynamic loads. The proposed method uses an adaptive blind source separation (BSS) method to decouple the measured aerodynamic loads in real-time and a fitting method considering the actual aerodynamic characteristics to conduct modal parameter identification of the decoupled modal signals. Subsequently, a digital compensation filter is constructed on the basis of the identified parameters, and the decoupled modal signals are corrected in the time domain by the filter. Finally, the corrected modal signals are transformed into physical signals by using the mode shape, and the time history of the corrected aerodynamic loads is obtained. The proposed method can update the separating matrix (i.e., the inverse of the mode shape) of the coupled signals online and accomplish the real-time decoupling. Besides, the time history of the corrected aerodynamic loads can be directly obtained using the filter-based correction method, which is convenient for further time history analysis. The proposed method is applied to both a numerical simulation example and an HFFB test and compared with other existing methods. The proposed method reduces the error maximum and the standard deviation by 81.9% and 88.9%, respectively, in the numerical simulation. The results show the effectiveness and superiority of the proposed method.

This paper focuses on modeling the hysteretic behavior of disc spring self-centering energy dissipation braces (DS-SCEDBs) from the inactive state to the design limit state, and proposes two restoring force models for structural design. A logistic function is used in the modified nonlinear mechanical model to represent the behavior of the self-centering system, and the Bouc–Wen model is employed to represent the performance of the energy dissipation system. In the modified model, the logistic function improves the numerical convergence and reduces the computational cost, but the Bouc–Wen model must be solved by numerical algorithms. The modified model does not reproduce accurately the hysteretic response at small displacements. Therefore, a flag-shaped hysteretic variable model formulated using the primitive functions of the logistic function is proposed to address the shortcomings of the modified nonlinear mechanical model. The flag-shaped hysteretic variable model can be solved directly using the brace design parameters, and the hysteretic law is consistent with the theory. The hysteretic response of the DS-SCEDBs at the displacement exceeding the desired stroke also can be simulated by the primitive function of the logistic function. The dominant parameters of the proposed models are related to the design parameters, which is convenient for use in structural design and simulation. Comparisons of the prediction and test results indicated that both models can replicate the restoring forces and hysteretic responses of the DS-SCEDBs during normal operation or when the disc springs are compressed fully. The flag-shaped hysteretic variable model has higher calculation accuracy and better programmability than the modified nonlinear mechanical model.

The response of masonry structures to explosions cannot be exclusively investigated relying only on numerical and analytical tools. Experimental tests are of paramount importance for improving current understanding and validating existing models. However, experiments involving blast scenarios are, at present, partial and limited in number compared to tests under different dynamic conditions, such as earthquakes. The reason for lies in the fact that full-scale blast experiments present many difficulties, mainly due to the nature of loading action. In constrast, experiments on a reduced scale offer greater flexibility. Nevertheless, appropriate scaling laws for the response of masonry structures under blast excitations are needed before such tests are performed. We propose here new scaling laws for the dynamic, rigid-body response, and structural failure modes (e.g., overturning) of masonry structures under blast loads. This work grows out of previous studies, where closed-form solutions for the rocking response of slender blocks due to explosions were derived and validated against numerical and experimental tests. The proposed scaling laws are validated here with detailed numerical simulations accounting for combined rocking, uplifting, and sliding mechanisms of monolithic structures. Then the application to blocky masonry structures is studied. Multidrum stone columns are considered as examples for the application of scaling laws. In particular, we show that, despite the presence of complex behaviors, such as wobbling and impacts, similarity is assured.

As an economical and effective testing method, real-time hybrid simulation (RTHS) can be understood as a dynamic system with substructure feedback, where the time delay in feedback caused by servo-hydraulics may destabilize the system. Existing research does not realize that the time delay in each component has a different effect on stability. This study categorizes RTHS into neutral or retarded delay systems to differentiate their pole distribution and explore how time delay affects the stability. The analysis results show that (1) time delay introduces infinite pairs of conjugate characteristic roots into both neutral and retarded systems but results in different patterns of root distribution; (2) the characteristic roots approach based on the rational function approximation is only suitable for stability analysis of a retarded delay system, not for a neutral delay system; and (3) the definite integral stability analysis approach can directly determine the stability of both retarded and neutral delay systems without solving the transcendental equation. The computational simulation demonstrated the difference between retarded and neutral delay systems and the effectiveness of the new approach. This study provides fresh insights for the dynamic analysis of RTHS system with time delay.

Much progress has been made in the assessment of structural damage and unknown input (UI) using incomplete and noisy measurement signals. The unscented Kalman filter (UKF) has proved to be a sophisticated approach to this task. A novel method using UKF with unknown input (UKF-UI) for recursive identification of a state-input system has been proposed by the authors. However, the purpose of this study was to propose the new UKF-UI framework and validate it with some simple structures. Although very limited research has been conducted on the UKF for health assessment of large structural systems, including two-dimensional (2D) and three-dimensional (3D) frame structures, it is based on a two-stage approach and requires full measurement of all acceleration, velocity, and displacement responses in the substructure containing the UI. Some implementations either have limitations in real-time identification or need assumptions on the time evolution of UI. One example is the random walk hypothesis, which heavily depends on the tuning of noise parameters. The application of UKF to large structural systems is still a challenging problem. This observation has prompted the authors to investigate the UKF-UI framework for identification of large structural systems. Here, it is extended to the assessment of damage and UI by the UKF-UI method for 2D and a 3D finite-element (FE) frame models. By the partially measured noise-polluted structural acceleration and displacement responses, the extent and location of damage is assessed at the element level. The unknown external excitations are simultaneously identified with no assumptions about the time evolutions of a one-stage identification process.

In the last two decades, particle morphology has emerged as an essential and critical property for proper evaluation of the constitutive behavior of granular materials. When a mass of sand is loaded in a confined compression, a complex network of force chains develops and evolves to resist the applied stresses. Force chains have been extensively studied in the literature using the discrete element method (DEM) and to a lesser extent using the finite-element method (FEM). This paper investigates the influence of three-dimensional (3D) sand morphology on the onset and evolution of force chains within sand using both 3D DEM and FEM simulations. In-situ synchrotron microcomputed tomography (SMT) technique was utilized to acquire multiple 3D scans of a specimen composed of natural silica sand that was loaded under one-dimensional (1D) confined uniaxial compression. The SMT scans were processed and used to calibrate parameters for both DEM and FEM models, where particle sizes and shapes closely matched the natural morphology and fabric of sand particles within the tested specimen. In another virtual specimen, individual sand particles were substituted with equivalent spherical particles that have the same volume and center of mass. FEM and DEM simulations were then executed on the virtual specimen using the same model parameters that were calibrated by the tested sand specimen. A comparison between the numerically simulated results of the virtual and tested specimens revealed a stiffer boundary response of reaction load versus displacement at the top loading platen of the specimen composed of particles with sand-like morphology. On the contrary, a microscale assessment showed higher particle stresses and interparticle contact forces between the spherical particles than the sand-like particles under the same boundary load on the top-loading platen. The results of the paper advocate for the importance of modeling sand using the actual sand morphology in a quest for an accurate numerical prediction of interparticle contact forces, particle stresses, and the development of force chains in sands.