Journal of Engineering Mechanics

In the present study, an inerter is introduced between a tuned liquid sloshing damper (TLSD) and a single degree of freedom (SDOF) system. The resulting vibration control system is known as an inerter-assisted tuned liquid sloshing damper (IA-TLSD). The liquid sloshing inside TLSD was modeled using nonlinear shallow water wave theory. The governing equations of motion of the combined SDOF system and IA-TLSD are formulated. Design parameters of IA-TLSD were obtained numerically, and its behavior and working principles have been studied. The response of the combined system under harmonic base excitation was computed numerically using the Newmark-$\beta$ method. It was found that the use of a larger inerter ratio does not help much to improve the performance of IA-TLSD for given design parameters. To retain enough liquid sloshing in IA-TLSD, a lower value of inerter ratio is suggested. With an optimal design, IA-TLSD has much better control effectiveness as compared to the TLSD with the same mass ratio. Thus, IA-TLSD can be used for vibration control of structures and has the potential for wind-induced response control of tall buildings.

Modeling of concrete damage is an important branch of concrete structural analysis; however, the damage behavior of different types of concrete varies. In this study, mechanical property tests were conducted to modify the damage model for aeolian sand self-compacting concrete (ASSC). Damage behaviors and stress–strain curves of prismatic ASSC specimens were investigated using the XTDIC technique, which demonstrated the increasingly decreased peak strain and deteriorated ductility of concrete with the increase of replacement rate of aeolian sand (AS). On the basis of the experimental results, the model proposed by Mazars and colleagues was modified, where scaling factors were introduced. Numerical simulations with the modified model were performed on the ANSYS platform using the Usermat subroutine and its mesh dependency was verified. The results revealed that the modified model could better reflect the effect of AS addition on the concrete structure, and it was less sensitive to the mesh accuracy.

A novel figure of merit based on the concept of signature curve for cold formed steel (CFS) cross sections is used to improve the structural member’s overall behavior regardless of length and boundary conditions. The objective is defined as the area under the signature curve, plus a penalty function that ensures improved performance over standard sections at specified lengths. Charged system search (CSS), a meta-heuristic optimization algorithm, is used to search the design space. End-use and other geometrical constraints suggested by previous studies are considered to arrive at practical cross sections. This includes limiting the fold angles to minimize sharp corners in the optimized cross sections, which might result in residual stresses that diminish axial capacity. Such nonlinear constraints are also taken into account using penalty functions to facilitate integration with the heuristic optimization process. The proposed strategy is examined through a couple of illustrative examples and is shown to yield higher axial capacity at all points when combined with the proper penalization. The optimized cross sections are also analyzed in simple-simple and clamped-clamped boundary conditions showing improved axial capacity compared to the standard lipped-channel sections with the same coil width.

This study evaluated two fundamental assumptions about the geometry of the wood cell wall to develop a mechanistic characterization of wood behavior at the scale of wood structural components. This paper used a three-step homogenization scheme implemented through homogenization techniques and finite-element analyses to evaluate a multilayered cell wall and a simplified single-layer method. Both earlywood and latewood geometries were considered. A three-part sensitivity analysis assessed the influence of wood constituent proportions, microfibril angle, and cellulose crystallinity on cell wall stiffness. Sensitivity to constituent ratios was evaluated through a Monte Carlo simulation of 1,000 sampled points and correlation analysis. Sensitivity to microfibril angle and cellulose crystallinity was evaluated through parametric characterization. The investigation found that both methods provided an accurate assessment of wood stiffness when compared with experimentally determined values. Care should be taken when modeling higher densities of wood, and use of either method in higher order models should be determined by the resolution of input data and computational needs.

Shape sensing refers to the deformation reconstruction of structures using measured surface strain. However, there is currently a lack of research on the shape sensing of large deformations, especially for beam structures. To address this issue, this paper proposes a new method called the rotation angle approximation (RAA) for reconstructing large deformations of beam structures. This method utilizes theoretical and actual curvatures to create a least-squares error functional. By minimizing this functional, the rotation angles of the corresponding beam can be obtained, avoiding the accumulation of errors that occurs when using traditional computation methods. The deformed shapes can be predicted utilizing the boundary conditions and the rotation angles along the beam. This method can reconstruct the large deformation of a beam without requiring prior knowledge about the material properties or external loads. The accuracy and effectiveness of this method were validated through numerical simulations and experiments. The results indicate that this method can accurately predict the different deformations of a beam induced by various loading conditions.

We consider in this paper the general properties of laminates designed to be isotropic in extension and in bending and with a coupling between the in- and out-of-plane responses. In particular, we analyze the mathematical properties of the tensors describing the elastic and thermal behavior and the mechanical consequences of these properties. The polar formalism for planar tensors is used in this study. By this approach, it is easy to put in light some interesting, qualitative, mechanical, and mathematical facts concerning coupled isotropic laminates and to appreciate the fundamental differences, from the mathematical and mechanical point of view, between hybrid laminates, i.e., composed by layers of different materials, and laminates made of identical plies.

This paper introduces a novel approach to analyze the seismic stability of rock slopes using the stress characteristics method (SCM). Based on a prescribed factor of safety (FS), the slope profile (SP) is forthrightly determined without involving any optimization technique. A theoretical model is developed to execute the seismic analysis by coupling the SCM with the modified pseudo-dynamic (MPD) approach. The SCM obliterates the necessity of predefined slope geometry and slip surfaces in the analysis, whereas the MPD approach captures more credible nonuniform seismic inertia forces during earthquake excitation. The generalized Hoek–Brown criterion is employed to model the nonlinear strength characteristics of the rock mass. With different recommended values of FS, chart solutions comprising SPs are presented to readily evaluate the seismic stability of rock slopes. A comprehensive parametric analysis is conducted to interpret the behavior of obtained SPs under the influence of various input parameters. The overall slope angle of the present curvilinear SPs is found to be in close agreement with that of traditional linear SPs reported in the literature. Moreover, the legitimacy of the current methodology for designing open pit mines and assessing the safety status of existing rock slopes is showcased through different case studies along with a numerical simulation of the derived SPs.

Pipeline guided wave inspection is an efficient tool for determining the defect location. However, quantifying the defect size remains a challenging task. This paper proposes a quantification method for corrosion-like defects in pipelines based on the multifrequency identification of nondispersive torsional guided waves. First, a theoretical scattering model describing the T(0,1) wave’s interaction with a simplified corrosion-like defect is introduced. Subsequently, a multifrequency identification method is proposed, enabling the inverse quantification of defect parameters by a defined spectral defect index (SDI). To implement this approach, a pseudo pulse-echo configuration is devised, which contains two rings of piezoelectric transducers attached on the pipeline’s outer surface. Finite-element (FE) models are employed to test the performance of the proposed method for both axisymmetric and nonaxisymmetric defects, and an analysis of the robustness of the method is also conducted. The results show that this method has good accuracy even for signals with a very low signal-to-noise (SNR) ratio. Furthermore, an FE model is developed to validate the feasibility of this method for long-distance detection considering attenuation effect. Finally, experimental validation of the proposed method demonstrates close agreement between predicted and actual defect sizes, showing its potential for practical applications.

Approximation frameworks for phase-field models of brittle fracture are presented and compared in this work. Such methods aim to address the computational cost associated with conducting full-scale simulations of brittle fracture in heterogeneous materials where material parameters, such as fracture toughness, can vary spatially. They proceed by combining a dimension reduction with learning between function spaces. Two classes of approximations are considered. In the first class, deep learning models are used to perform regression in ad hoc latent spaces. PCA-Net and Fourier neural operators are specifically presented for the sake of comparison. In the second class of techniques, statistical sampling is used to approximate the forward map in latent space, using conditioning. To ensure proper measure concentration, a reduced-order Hamiltonian Monte Carlo technique (namely, probabilistic learning on manifold) is employed. The accuracy of these methods is then investigated on a proxy application where the fracture toughness is modeled as a non-Gaussian random field. It is shown that the probabilistic framework achieves comparable performance in the $L^2$ sense while enabling the end-user to bypass the art of defining and training deep learning models.

Measuring the dynamic displacements of a structure provides a comprehensive understanding of the structure, especially when subjected to different types of dynamic loading (i.e., wind, traffic, impact loads, blast loads, etc.). Despite their usefulness, direct displacement measurements are typically not collected due to the cumbersome logistical issues of sensor placement and maintenance and the impracticality of instrumenting contact-based sensors across all significant structures. In this context, this study proposes a novel dual stereovision technique to measure the dynamic displacement of structures using a portable, noncontact measurement system that involves an uncrewed aerial system (UAS) and four optical cameras. One pair of cameras tracks the three-component ($x$, $y$, and $z$) motion of a region of interest (ROI) on a structure with respect to the UAS system, and the other pair of cameras measure the six degrees of freedom motion (6-DOF) (both rotational and translational motion) of the UAS system by tracking a stationary reference. The motion of the UAS is then compensated for to recover the true dynamic displacement of the ROI. The proposed dual stereovision technique realizes simultaneous measurement of all three components of displacements of the structure and 6-DOF of UAS motion through a mathematically elegant process. The unique dual stereovision technique allows flexibility in choosing a global reference coordinate system, greatly enhancing the feasibility of applying the new technology in various field environments. This new technique has overcome the major challenge of significant UAS motions in full-scale applications. Furthermore, this technique relies on natural features and eliminates the requirement of artificial targets on the structure, permitting applications to difficult-to-access structures.

Overland flow from inundation events (IEs) such as hurricanes or tsunamis produce destructive loading conditions on nearshore structures. The magnitude of this loading and its associated impact can be substantially reduced by the existence of natural and/or anthropogenic obstacles, such as planted vegetation patches or neighboring structures. This paper examines the shielding effects offered by onshore coastal vegetation to nearshore structures, by establishing a numerical framework in combination with statistical computing methods to explore how vegetation properties, such as density and, more important, geometry relative to a row of shoreline infrastructure elements, impacts the resultant IE loads and subsequently the structural vulnerability. Computational fluid dynamics (CFD) simulations are first conducted to predict the intensity measures (IMs) of interest (momentum flux, free surface elevation, water pressure, and depth-averaged velocities, as well as base shear forces) on the shoreline structures for different excitation intensities (wave heights) and vegetation configurations. This information is used to develop a predictive model for the IMs using surrogate modeling techniques in order to expedite the succeeding risk assessment process. Gaussian process (GP) regression is specifically adopted as the surrogate modeling technique here, since it can accommodate noise in the training observations (CFD numerical errors) and quantify the associated predictive uncertainty (originating from the surrogate model) with minimal additional computational complexity. The spatial correlation between some of the examined IMs is explicitly addressed at the GP calibration stage. The developed predictive model is then used to estimate the structural vulnerability, with the surrogate model prediction errors explicitly considered when calculating the probability of exceedance for the different damage states, as warranted in such a vulnerability setting. Comparisons among different vegetation configurations, including the bare earth case, support an in-depth exploration of the impact of vegetation geometry on the shielding effects it can offer. Two case studies are examined, demonstrating applicability of the proposed framework for both system- and component-level vulnerability assessments.

The paper presents a modified differential quadrature method (DQM) to solve buckling problems of beams and rectangular plates. The proposed method addresses the problem of applying multiple boundary conditions at each boundary point by developing a novel approach that constructs basis functions satisfying multiple boundary conditions. The weighting coefficient matrices of high-order derivatives in the DQM can then be calculated directly from the basis function, and additional equations about boundary conditions can be avoided. The method is first applied to derive the basis functions of beams with various boundary conditions and to solve beam buckling problems. Then, the method is extended to the buckling of rectangular plates, where the plate deflection is assumed as the sum of multiplications of two basis functions for beams with the corresponding boundary conditions. To verify the accuracy of the proposed method, several examples are presented, and very good agreement is observed between the results obtained by the proposed method and those reported in the literature as well as those obtained by the finite element method.

Abstract

We extend the applicability of the embedded unit cell (EUC) method to three-dimensional (3D) fracture problems, which are modeled by the extended finite element method (XFEM). The EUC method is a concurrent multiscale method based on the computational homogenization theory for nonperiodic domains. Herein, we show that this method can accurately estimate fracture parameters and, in particular, stress intensity factors using the J-integral method. Additionally, the method is shown to capture crack propagation within the microscale domain, as well as cracks initiating at the microscale and propagating outwards onto the macroscale through the internal subdomain boundaries. To demonstrate the accuracy, robustness, and computational efficiency of the proposed method, several 3D numerical benchmark examples, including planar cracks with single and mixed-mode fractures, are considered. In particular, we analyze horizontal, inclined, square, and penny-shaped cracks embedded in a homogeneous material. The results are verified against full FEM models and known analytical solutions if available.

Practical Applications

The insights of this research offer practical application for engineers and scientists in designing more resilient and durable structures. By extending the EUC method to 3D fracture problems, the study addresses the ability to forecast and access fracture phenomena in materials. This method is shown to be an effective approach for exploring the interaction between local microscopic discontinuities and cross-scale crack propagation, crucial for evaluating the durability of engineering structures. The EUC approach, integrated with XFEM, provides a comprehensive methodology for analyzing different fracture scenarios, including stationary mixed-mode cracks and crack-propagation examples. Its ability to accurately transition from microscale to macroscale analysis without remeshing introduces a valuable computational advantage, making it a more cost-efficient solution in fracture analysis. This research’s application offers tangible benefits in industrial context, especially in aerospace, automotive, and construction industries, where precise evaluation of structure and material failure can lead to more cost-efficient and safer designs by reducing the maintenance costs and failure risks.

The paper proposes a spectral decomposition–based approach for implementing a multisurface coupled damage–plasticity model for concrete subjected to fire. The multisurface approach enables distinct flow rules to be used for plastic flow in compression and tension. The spectral decomposition–based procedure enables, for general multiaxial loading, the Jacobian for the return mapping algorithm to be determined analytically without the need for finite difference approximations or additional nested iterations. The proposed approach, developed in the context of a general multisurface plasticity model subject to the small strain assumption, is specialized to the case of a combined Drucker-Prager and Rankine yield surface, and can account for situations where the eigenvalues of the stress tensor are degenerate. It is verified by solving finite element models for concrete structural components subjected to high temperature under a wide variety of mechanical loads. The simulation results, obtained using a sequentially coupled approach, are found to closely match established experimental results.

A series of laboratory experiments was conducted to study the dynamics of sand–water coaxial jets in stagnant water. The effects of the velocity ratio of the annular to the core jets on the sand concentration, velocity, mixing properties, and energy distribution of sand–water coaxial jets were studied. In comparison to sand jets, the existence of carrier fluid in sand–water coaxial jets decreased the concentration fluctuations of sand particles. Proper orthogonal decomposition (POD) and spectral proper orthogonal decomposition (SPOD) techniques were utilized to study the low-rank dynamic behavior on flow entrainment and particle oscillations. It was indicated that the first two POD modes have the most coherent and energetic quantitative flow features during the entrainment process. The energy contribution of the first five POD modes was reduced by 50% in sand–water coaxial jets with relatively low velocity ratios of $Ru<0.35$. The SPOD analysis revealed that particle oscillations can be characterized by the Kelvin–Helmholtz type wave instabilities, and sand–water coaxial jets with small velocity ratios (i.e., $Ru<1.24$) had weaker vortex shedding and particle velocity fluctuations. The SPOD analysis indicated that most of the turbulence kinetic energy was concentrated in the low-frequency modes and coaxial jets with high-velocity ratios. The power spectral density (PSD) of concentration signals demonstrated that the dominant frequency of vortex shedding increased by increasing the radial distance from the jet axis. The PSD analysis of sand concentration for $Ru=0.62$ and 0.74 was consistent with the Kolmogorov scaling law at dominant frequencies ranging between 30 and 40 Hz.

This technical note presents the optimal shape of an arch carrying a central point load to two pinned supports for maximum in-plane bifurcation buckling load. The arch shapes considered are triangular, parabolic, circular, catenary, and ogival. It is assumed that the arches are elastic and inextensible and their flexural rigidity is uniform throughout the arch length. The Hencky bar-chain model was used for elastic buckling analysis. It is found that the optimal arch shape depends on the arch apex height to length ($h/L$) ratio. The optimal arch shape changes from circular to catenary to parabolic and finally to triangular from $h/L=0.1$ to 1. This shows that the funicular triangular arch shape for the central point load is not the optimal arch shape against in-plane buckling when $h/L$ is less than 0.528. For maximum buckling load, one may use either the circular, catenary, or parabolic arch with $h/L$ approximately equal to 0.3.