Journal of Engineering Mechanics

The Daikai Station subway structure in Japan completely collapsed during the Hyogoken-Nanbu earthquake that occurred on January 17, 1995. Based on the numerical results obtained by two-dimensional finite-element analysis, the structure is believed to have collapsed as a result of strong lateral vibration. However, because it deformed in an approximately symmetrical manner with respect to the shortened central columns, it might have experienced catastrophic collapse due to vertical impulse motion. To investigate the dynamic response behavior of the structure due to sudden upward loading, a three-dimensional elastoplastic transient response analysis was conducted considering an isolated upward pulselike displacement wave from the bedrock. The results of this study suggest that the central column of the structure reached axial compression failure due to the amplitude of the displacement wave increasing significantly at the lower end of the column. This method can numerically reproduce the collapsed state of the structure and the considerable settlement of the ground surface due to the occurrence of the high-intensity earthquake.

The frequency content and spatial correlation of nonstationary wind fields during extreme events typically present time-variant characteristics. Several effective schemes [e.g., using evolutionary power spectral density (EPSD) or Hilbert spectrum] have been highly developed and extensively used for analysis and the synthesis of time-dependent frequency distributions, whereas, until very recently, little attention has been paid to the accurate and efficient simulation of time-varying spatial correlations. The Hilbert transform together with the wavelet technique (Hilbert–wavelet scheme) holds great promise in accomplishing this task since a nonlinear, statistical relationship between the instantaneous phase difference and time-variant spatial correlation has recently been established. However, its engineering application is limited by the need to simultaneously solve a large number of nonlinear equations. To address this issue, the simultaneous matrix diagonalization (SMD) technique is introduced here to accelerate the Hilbert–wavelet simulation of nonstationary wind fields. Specifically, the SMD effectively obtains the target spatial correlation by the linear combination of uncorrelated wavelet subcomponents of the multivariate wind process. In addition, memory usage in the simulation of time-variant spatial correlation is greatly reduced using SMD. The SMD technique is usually implemented with iterative algorithms. To further improve the simulation efficiency, two-dimensional singular value decomposition (2dSVD) is employed to achieve a noniterative SMD. The high simulation fidelity and efficiency of the proposed Hilbert-wavelet-SMD approach are demonstrated by numerical examples. The simulation time consumption is compared with the state-of-the-art EPSD-based approach, and the proposed Hilbert-wavelet-SMD scheme shows superior efficiency.

Force applied and location it occurred are of growing interest for smart buildings, particularly in the area of human activity. The ability to localize human activity through the vibrations caused by the activity on the structure has the potential to be a low-cost, privacy-respecting solution to areas of interest such as building occupancy estimations, customer flow through retail stores, and human fall detection. This paper introduces the Force Estimation and Event Localization (FEEL) Algorithm, which estimates the force of an impact that caused a structural vibration and additionally locates the location the impact occurred. The main feature of FEEL is that it does not require time synchronization like other time-of-flight techniques. FEEL was validated using the human-induced vibration benchmark data set totaling 3,500 impact events of seven different types at five different locations, and an additional 75 force hammer impacts. FEEL displayed 96.4% location accuracy and a force magnitude estimate accuracy of $-2.0\%\pm 1.3\%$ in a 99% confidence interval in the experiments.

Multidirectional shearing of granular soils involves shearing more than one shear stress component, and thus may result in more-complex soil responses than unidirectional shearing. This study developed an advanced numerical procedure that can impose an arbitrary loading path on a granular assembly in three-dimensional space as a basis for discrete-element simulations to investigate the behavior of granular assemblies under undrained cyclic multidirectional shearing conditions. The tests included varying stress trajectories on the deviatoric stress plane, including straight-line, circular, figure-8, and teardrop shapes. The numerical results indicated that the liquefaction resistance of a sample for a given cyclic shear stress ratio (CSR) depends on the stress orbits, and that of the teardrop shape was the highest and that of the figure-8 shape was the lowest. The microstructure of the granular assembly was quantified by the contact-normal-based fabric tensor, and its evolution trend correlation with stress–strain responses was explored. The evolution of fabric and stress–strain relationships from discrete-element modeling under multidirectional shearing conditions can provide useful insights into the behavior of granular soils.

A fluid-structure model based on nonlinear Mindlin-Reissner plate theory and linearized piston theory is used to study the aeroelastic flutter of panels of arbitrary planforms at supersonic Mach numbers. A finite-element procedure is used to reduce the continuous system to a fully coupled finite-dimension flow-structure system, which is solved in the time domain using the Newmark method. Panels with hinged or clamped boundary conditions and surrounded by a rigid baffle are considered. Critical velocity and frequency at onset of flutter are determined for triangular, square, circular, semi-circular, elliptic, and hexagonal forms. Limit cycle oscillations (LCOs) amplitudes are computed for a range of aerodynamic loading for all panels. Based on the finite-element data, scaling laws in the form of simple algebraic formulas are proposed that enable prediction of modal coalescence flutter velocity, frequency, and LCO amplitudes in terms of geometric and materials properties of panels. Such scaling laws are helpful in the preliminary design and optimization of supersonic panels or developing reduced-order models of supersonic panel flutter.

Direct integration algorithms are effective methods to solve the temporally discretized differential equations of motion for structural dynamics. Numerous researchers have worked out various algorithms to achieve desirable properties of explicit expression, unconditional stability, and controllable numerical dissipation. However, studies involving the numerical dispersion of integration algorithms are limited. In this paper, a precorrected bilinear transformation from a continuous domain to a discrete domain associating with pole-matching based on the control theory is utilized to develop a new family of explicit structure-dependent integration algorithms, referred to as TL-$\phi$ algorithms. In contrast to the existing algorithms, the significant improvement of the proposed method is that it can control the amount of numerical dispersion by an additional parameter related to the critical frequency of the structure. Stability, energy dissipation, and numerical dispersion properties of the proposed algorithms for both linear and nonlinear systems are fully studied. It is shown that the proposed family of algorithms is unconditionally stable for linear systems while only conditionally stable for nonlinear systems. Though the numerical dissipation property of the TL-$\phi$ algorithms is quite similar to that of other well-developed methods, its ability to minimize the period errors when compared with other methods makes it beneficial to the accuracy of the numerical simulation of dynamic responses. Four numerical examples are used to investigate the improved performance of the new method, and the results show that the proposed algorithms can be potentially used to solve linear and nonlinear structural dynamic problems with desirable numerical dispersion performance.

The blast response of arching masonry walls is a challenging and complex structural mechanism that involves a range of physical phenomena, such as rocking, cracking, unloading and reloading effects, dynamic variation of the reactions, and time-dependent stability characteristics. The evolution of longitudinal and lateral inertial forces results in a coupled in-plane/out-of-plane dynamic response that, in turn, affects the arching mechanism and its stabilizing/destabilizing effect. This paper studies the blast response of realistically supported walls in which the elongation of the wall is restrained by the supporting structural elements. The study explores the dynamic development of the arching action in such walls and the evolution of a time-dependent thrust force. The latter affects almost any aspect of the wall response: in-plane and out-of-plane coupling, evolution of longitudinal stress waves, and global strength and stability. To address this challenge, a rigid–flexible multibody model for the nonlinear-dynamic analysis of one-way arching walls subjected to blast loads is developed. The nonlinear model takes into consideration the aforementioned physical aspects and aims at minimizing the required computational time. Based on the principle of virtual work, the model considers dynamic equilibrium conditions, cracking processes, geometrically nonlinear kinematics, dynamic contact at the interfaces, and nonlinear constitutive behavior of the mortar material. This spectrum of features is compiled into a unified specially tailored finite-element formulation. The masonry units are modeled as rigid bodies, whereas the mortar joints are modeled as inelastic nonlinear flexural members. The study is accompanied by a series of analyses and comparison with existing models and experiments that altogether validate the model and quantitatively explore the critical aspects of the physical behavior.

This article discusses the stability analysis of thermal signals of a thermodynamic consistent model including temperature-rate dependence thermoelasticity theory (Green-Lindsay) with a memory-dependent derivative (MDD). A unifying approach (an extension of Lyapunov’s original method to the stability theory developed by Zubov together with Korn’s inequality in elasticity under homogeneous boundary condition on displacement components) is employed to characterize the stability of the present thermoelastic system. In continuation, a uniqueness of the solutions of the present thermoelastic system is presented as a corollary of the stability theorem, and corresponding results in the absence of MDD are also mentioned as special cases. Finally, based on theoretical importance and understanding, with the help of an analogy between the homogeneous and nonhomogeneous boundary conditions on the displacement components, an open mathematical problem as alternate to the employed unifying approach is proposed.

This paper incorporated two important characteristics of clay, namely its rate-dependent and strain-softening behavior, into a theoretical framework based on cavity expansion. The modified Tresca model for clay proposed by Einav and Randolph was selected to describe the effects of the rate dependency and gradual softening of clay as it is sheared and remolded. First, the modified Tresca model was reduced to a strain-softening model without considering the rate effect. The exponential degradation (ED) function of the strength reduction proposed by Einav and Randolph was simplified further to a bilinear degradation (SBD) function. This step allowed an approximate closed-form solution to be obtained for the cavity expansion response, including the plastic zone radius, stress distribution, and cavity pressure-expansion relation, of the SBD model. The approximate closed-form solution for the SBD model was compared with the numerical integration solution for the ED model, and the comparison showed that the approximate closed-form solution is relatively accurate. Subsequently, the rate effects were incorporated into the SBD and ED strain-softening models, which are referred to as the rate-dependent (RD)-SBD and RD-ED models. Numerical integration solutions for cavity expansion in the RD-SBD and RD-ED models were obtained. A series of parametric analyses was conducted to investigate the effects of the cavity expansion velocity, strength reduction, and rate-dependent parameters on the cavity expansion responses. A closed-form solution for the limit expansion pressure (LEP) of the cavity expansion was obtained through a simple regression analysis based on the parametric results. The LEP solution was used to interpret the results of the cone penetration test (CPT) test, and a modified expression for the cone penetration resistance factor that incorporates the rate effect and strain softening was given. This simple modification provides a convenient way to evaluate the influence of the two factors on the CPT test results and allows the clay properties to be captured appropriately.

Flexibility is an important index in the assessment of bridge load-carrying capacity. Impact testing is an efficient and effective method to obtain the flexibility of small- and medium-span bridges. Modal parameter identification based on excitation and response data plays a key role in flexibility identification, which can obtain the modal scaling factor. As is well known, the combined deterministic-stochastic subspace identification (DSI) algorithm is one of the most popular identification methods. However, unavoidable factors often result in the appearance of spurious modes, which can affect flexibility identification. In this paper, a novel mode selection method is implemented to achieve better extraction of physical modes during the flexibility identification process. A simulated example is used to verify that the proposed method can effectively extract physical modes to obtain a flexibility matrix.